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Sample records for two-loop self-energy integrals

  1. Two loop low temperature corrections to electron self energy

    Institute of Scientific and Technical Information of China (English)

    Mahnaz Q. Haseeb; Samina S. Masood

    2011-01-01

    We recalculate the two loop corrections in the background heat bath using real time formalism. The procedure of the integrations of loop momenta with dependence on finite temperature before the momenta without it has been followed. We determine the mass a

  2. Systematics of High Temperature Perturbation Theory: The Two-Loop Electron Self-Energy in QED

    CERN Document Server

    Mottola, Emil; 10.1103/PhysRevD.81.025014

    2010-01-01

    In order to investigate the systematics of the loop expansion in high temperature gauge theories beyond the leading order hard thermal loop (HTL) approximation, we calculate the two-loop electron proper self-energy in high temperature QED. The two-loop bubble diagram contains a linear infrared divergence. Even if regulated with a non-zero photon mass M of order of the Debye mass, this infrared sensitivity implies that the two-loop self-energy contributes terms to the fermion dispersion relation that are comparable to or even larger than the next-to-leading-order (NLO) contributions at one-loop. Additional evidence for the necessity of a systematic restructuring of the loop expansion comes from the explicit gauge parameter dependence of the fermion damping rate at both one and two-loops. The leading terms in the high temperature expansion of the two-loop self-energy for all topologies arise from an explicit hard-soft factorization pattern, in which one of the loop integrals is hard, nested inside a second loop...

  3. Two loop low temperature corrections to electron self energy

    Institute of Scientific and Technical Information of China (English)

    Mahnaz Q. Haseeb; Samina S. Masood

    2011-01-01

    We xecalculate the two loop corrections in the background heat bath using real time formalism.The procedure of the integrations of loop momenta with dependence on finite temperature before the moments without it has been followed. We determine the mass and wavefunction renormalization constants in the low temperature limit of QED, for the first time with this preferred order of integrations. The correction to electron mass and spinors in this limit is important in the early universe at the time of primordial nucleosynthesis as well as in astrophysics.

  4. Two-loop fermion self-energy in reduced quantum electrodynamics and application to the ultra-relativistic limit of graphene

    CERN Document Server

    Kotikov, A V

    2013-01-01

    We compute the two-loop fermion self-energy in massless reduced quantum electrodynamics for an arbitrary gauge using the method of integration by parts. Focusing on the limit where the photon field is four-dimensional, our formula involves only recursively one-loop integrals and can therefore be evaluated exactly. From this formula, we deduce the anomalous scaling dimension of the fermion field as well as the renormalized fermion propagator up to two loops. The results are then applied to the ultra-relativistic limit of graphene and compared with similar results obtained for four-dimensional and three-dimensional quantum electrodynamics.

  5. Towards a Basis for Planar Two-Loop Integrals

    CERN Document Server

    Gluza, Janusz; Kosower, David A

    2010-01-01

    The existence of a finite basis of algebraically independent one-loop integrals has underpinned important developments in the computation of one-loop amplitudes in field theories and gauge theories in particular. We give an explicit construction reducing integrals to a finite basis for planar integrals at two loops, both to all orders in the dimensional regulator e, and also when all integrals are truncated to O(e). We show how to reorganize integration-by-parts equations to obtain elements of the first basis efficiently, and how to use Gram determinants to obtain additional linear relations reducing this all-orders basis to the second one. The techniques we present should apply to non-planar integrals, to integrals with massive propagators, and beyond two loops as well.

  6. Two-Loop Tensor Integrals in Quantum Field Theory

    CERN Document Server

    Actis, S; Passarino, G; Passera, M; Uccirati, S

    2004-01-01

    A comprehensive study is performed of general massive, tensor, two-loop Feynman diagrams with two and three external legs. Reduction to generalized scalar functions is discussed and integral representations are introduced, family-by-family of diagrams, that support the same class of algorithms (algorithms of smoothness) already employed for the numerical evaluation of ordinary scalar functions.

  7. Two-Loop Quark Self-Energy in a New Formalism; 2, Renormalization of the Quark Propagator in the Light-Cone Gauge

    CERN Document Server

    Leibbrandt, George; Leibbrandt, George; Williams, Jimmy D.

    2000-01-01

    The complete two-loop correction to the quark propagator, consisting of the spider, rainbow, gluon bubble and quark bubble diagrams, is evaluated in the noncovariant light-cone gauge (lcg). (The overlapping self-energy diagram had already been computed.) The chief technical tools include the powerful matrix integration technique, the n^*-prescription for the spurious poles of 1/qn, and the detailed analysis of the boundary singularities in five- and six-dimensional parameter space. It is shown that the total divergent contribution to the two-loop correction Sigma_2 contains both covariant and noncovariant components, and is a local function of the external momentum p, even off the mass-shell, as all nonlocal divergent terms cancel exactly. Consequently, both the quark mass and field renormalizations are local. The structure of Sigma_2 implies a quark mass counterterm of the form $\\delta m (lcg) = m\\tilde\\alpha_s C_F(3+\\tilde\\alpha_sW) + {\\rm O} (\\tilde\\alpha_s^3)$, the dimensional regulator epsilon, and on th...

  8. Two-loop quark self-energy in a new formalism; 2, Renormalization of the quark propagator in the light-cone gauge

    CERN Document Server

    Leibbrandt, G

    2000-01-01

    For pt.I see ibid., vol.440, p.537-602, 1995. The complete two-loop correction to the quark propagator, consisting of the spider, rainbow, gluon bubble and quark bubble diagrams, is evaluated in the non-covariant light-cone gauge (LCG), n.A/sup a/(x)=0, n/sup 2/=0. (The overlapping self-energy diagram had already been computed.) The chief technical tools include the powerful matrix integration technique, the n*/sub mu /-prescription for the spurious poles of (q.n)/sup -1/, and the detailed analysis of the boundary singularities in five- and six-dimensional parameter space. It is shown that the total divergent contribution to the two-loop correction Sigma /sub 2/ contains both covariant and non-covariant components, and is a local function of the external momentum p, even off the mass-shell, as all non-local divergent terms cancel exactly. Consequently, both the quark mass and field renormalizations are local. The structure of Sigma /sub 2/ implies a quark mass counterterm of the form delta m(LCG)=m alpha /sub...

  9. The two-loop sunrise integral and elliptic polylogarithms

    Energy Technology Data Exchange (ETDEWEB)

    Adams, Luise; Weinzierl, Stefan [Institut fuer Physik, Johannes Gutenberg-Universitaet Mainz (Germany); Bogner, Christian [Institut fuer Physik, Humboldt-Universitaet zu Berlin (Germany)

    2016-07-01

    In this talk, we present a solution for the two-loop sunrise integral with arbitrary masses around two and four space-time dimensions in terms of a generalised elliptic version of the multiple polylogarithms. Furthermore we investigate the elliptic polylogarithms appearing in higher orders in the dimensional regularisation ε of the two-dimensional equal mass solution. Around two space-time dimensions the solution consists of a sum of three elliptic dilogarithms where the arguments have a nice geometric interpretation as intersection points of the integration region and an elliptic curve associated to the sunrise integral. Around four space-time dimensions the sunrise integral can be expressed with the ε{sup 0}- and ε{sup 1}-solution around two dimensions, mass derivatives thereof and simpler terms. Considering higher orders of the two-dimensional equal mass solution we find certain generalisations of the elliptic polylogarithms appearing in the ε{sup 0}- and ε{sup 1}-solutions around two and four space-time dimensions. We show that these higher order-solutions can be found by iterative integration within this class of functions.

  10. On master integrals for two loop Bhabha scattering

    CERN Document Server

    Czakon, M; Riemann, Tord

    2004-01-01

    All scalar master integrals (MIs) for massive 2-loop QED Bhabha scattering are identified. The 2- and 3-point MIs have been calculated in terms of harmonic polylogarithms with the differential equation method. The calculation of 4-point MIs is underway. We sketch some alternative methods which help to solve (mainly) singularities of some MIs.

  11. On master integrals for two loop Bhabha scattering

    Energy Technology Data Exchange (ETDEWEB)

    Czakon, M.; Gluza, J. [Uniwersytet Slaski, Katowice (Poland). Inst. Fizyki; Riemann, T.

    2004-09-01

    All scalar master integrals (MIs) for massive 2-loop QED Bhabha scattering are identified. The 2- and 3-point MIs have been calculated in terms of harmonic polylogarithms with the differential equation method. The calculation of 4-point MIs is underway. We sketch some alternative methods which help to solve (mainly) singularities of some MIs. (orig.)

  12. The complete two-loop integrated jet thrust distribution in soft-collinear effective theory

    Energy Technology Data Exchange (ETDEWEB)

    von Manteuffel, Andreas; Schabinger, Robert M.; Zhu, Hua Xing

    2014-03-01

    In this work, we complete the calculation of the soft part of the two-loop integrated jet thrust distribution in e+e- annihilation. This jet mass observable is based on the thrust cone jet algorithm, which involves a veto scale for out-of-jet radiation. The previously uncomputed part of our result depends in a complicated way on the jet cone size, r, and at intermediate stages of the calculation we actually encounter a new class of multiple polylogarithms. We employ an extension of the coproduct calculus to systematically exploit functional relations and represent our results concisely. In contrast to the individual contributions, the sum of all global terms can be expressed in terms of classical polylogarithms. Our explicit two-loop calculation enables us to clarify the small r picture discussed in earlier work. In particular, we show that the resummation of the logarithms of r that appear in the previously uncomputed part of the two-loop integrated jet thrust distribution is inextricably linked to the resummation of the non-global logarithms. Furthermore, we find that the logarithms of r which cannot be absorbed into the non-global logarithms in the way advocated in earlier work have coefficients fixed by the two-loop cusp anomalous dimension. We also show that in many cases one can straightforwardly predict potentially large logarithmic contributions to the integrated jet thrust distribution at L loops by making use of analogous contributions to the simpler integrated hemisphere soft function.

  13. Master integrals for massive two-loop Bhabha scattering in QED

    CERN Document Server

    Czakon, M; Riemann, Tord

    2004-01-01

    We present a set of scalar master integrals (MIs) needed for a complete treatment of massive two-loop corrections to Bhabha scattering in QED, including integrals with arbitrary fermionic loops. The status of analytical solutions for the MIs is reviewed and examples of some methods to solve MIs analytically are worked out in more detail. Analytical results for the pole terms in epsilon of so far unknown box MIs with five internal lines are given.

  14. Master integrals for massive two-loop Bhabha scattering in QED

    Energy Technology Data Exchange (ETDEWEB)

    Czakon, M. [Wuerzburg Univ. (Germany). Inst. fuer Theoretische Physik und Astrophysik]|[Uniwersytet Slaski, Katowice (Poland). Inst. Fizyki; Gluza, J. [Uniwersytet Slaski, Katowice (Poland). Inst. Fizyki; Riemann, T.

    2004-12-01

    We present a set of scalar master integrals (MIs) needed for a complete treatment of massive two-loop corrections to Bhabha scattering in QED, including integrals with arbitrary fermionic loops. The status of analytical solutions for the MIs is reviewed and examples of some methods to solve MIs analytically are worked out in more detail. Analytical results for the pole terms in {epsilon} of so far unknown box MIs with five internal lines are given. (orig.)

  15. Integral Reduction by Unitarity Method for Two-loop Amplitudes: A Case Study

    CERN Document Server

    Feng, Bo; Huang, Rijun; Zhou, Kang

    2014-01-01

    In this paper, we generalize the unitarity method to two-loop diagrams and use it to discuss the integral bases of reduction. To test out method, we focus on the four-point double-box diagram as well as its related daughter diagrams, i.e., the double-triangle diagram and the triangle-box diagram. For later two kinds of diagrams, we have given complete analytical results in general (4-2\\eps)-dimension.

  16. Precise numerical evaluation of the two loop sunrise graph Master Integrals in the equal mass case

    CERN Document Server

    Pozzorini, Stefano

    2006-01-01

    We present a double precision routine in Fortran for the precise and fast numerical evaluation of the two Master Integrals (MIs) of the equal mass two-loop sunrise graph for arbitrary momentum transfer in d=2 and d=4 dimensions. The routine implements the accelerated power series expansions obtained by solving the corresponding differential equations for the MIs at their singular points. With a maximum of 22 terms for the worst case expansion a relative precision of better than a part in 10^{15} is achieved for arbitrary real values of the momentum transfer.

  17. Planar two-loop master integrals for massive Bhabha scattering: N_f=1 and N_f=2

    CERN Document Server

    Actis, S; Gluza, J; Riemann, Tord; Actis, Stefano; Czakon, Michal; Gluza, Janusz; Riemann, Tord

    2006-01-01

    Recent developments in the computation of two-loop master integrals for massive Bhabha scattering are briefly reviewed. We apply a method based on expansions of exact Mellin-Barnes representations and evaluate all planar four-point master integrals in the approximation of small electron mass at fixed scattering angle for the one-flavor case. The same technique is employed to derive and evaluate also all two-loop masters generated by additional fermion flavors. The approximation is sufficient for the determination of QED two-loop corrections for Bhabha scattering in the kinematics planned to be used for the luminosity determination at the ILC.

  18. Numerical integration of massive two-loop Mellin-Barnes integrals in Minkowskian regions

    Energy Technology Data Exchange (ETDEWEB)

    Dubovyk, Ievgen [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany); Hamburg Univ. (Germany). 2. Inst. fuer Theoretische Physik; Gluza, Janusz [Uniwersytet Slaski, Katowice (Poland). Inst. Fizyki; Riemann, Tord [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany); Uniwersytet Slaski, Katowice (Poland). Inst. Fizyki; Usovitsch, Johann [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany)

    2016-07-15

    Mellin-Barnes (MB) techniques applied to integrals emerging in particle physics perturbative calculations are summarized. New versions of AMBRE packages which construct planar and nonplanar MB representations are shortly discussed. The numerical package MBnumerics.m is presented for the first time which is able to calculate with a high precision multidimensional MB integrals in Minkowskian regions. Examples are given for massive vertex integrals which include threshold effects and several scale parameters.

  19. 30 years, some 700 integrals, and 1 dessert, or: Electroweak two-loop corrections to the Zbb vertex

    CERN Document Server

    Dubovyk, I; Gluza, J; Riemann, T; Usovitsch, J

    2016-01-01

    The one-loop corrections to the weak mixing angle $\\sin^2\\theta_{eff}^b$ derived from the $Z{\\bar b}b$ vertex, are known since 1985. It took another 30 years to calculate the complete electroweak two-loop corrections to $\\sin^2\\theta_{eff}^b$. The main obstacle was the calculation of the O(700) bosonic two-loop vertex integrals with up to three mass scales, at $s=M_Z^2$. We did not perform the usual integral reduction and master evaluation, but chose a completely numerical approach, using two different calculational chains. One method relies on publicly available sector decomposition implementations. Further, we derived Mellin-Barnes (MB) representations, exploring the publicly available MB suite. We had to supplement the MB suite by two new packages: AMBRE~3, a Mathematica program, for the efficient treatment of non-planar integrals and MBnumerics for advanced numerics in the Minkowskian space-time. Our preliminary result for LL2016, the "dessert", for the electroweak bosonic two-loop contributions to $\\sin^...

  20. Two-loop planar master integrals for Higgs$\\to 3$ partons with full heavy-quark mass dependence

    CERN Document Server

    Bonciani, Roberto; Frellesvig, Hjalte; Henn, Johannes M; Moriello, Francesco; Smirnov, Vladimir A

    2016-01-01

    We present the analytic computation of all the planar master integrals which contribute to the two-loop scattering amplitudes for Higgs$\\to 3$ partons, with full heavy-quark mass dependence. These are relevant for the NNLO corrections to fully inclusive Higgs production and to the NLO corrections to Higgs production in association with a jet, in the full theory. The computation is performed using the differential equations method. Whenever possible, a basis of master integrals that are pure functions of uniform weight is used. The result is expressed in terms of one-fold integrals of polylogarithms and elementary functions up to transcendental weight four. Two integral sectors are expressed in terms of elliptic functions. We show that by introducing a one-dimensional parametrization of the integrals the relevant second order differential equation can be readily solved, and the solution can be expressed to all orders of the dimensional regularization parameter in terms of iterated integrals over elliptic kerne...

  1. Two-loop amplitudes and master integrals for the production of a Higgs boson via a massive quark and a scalar-quark loop

    CERN Document Server

    Anastasiou, C; Bucherer, S; Daleo, A; Kunszt, Zoltán; Anastasiou, Charalampos; Beerli, Stefan; Bucherer, Stefan; Daleo, Alejandro; Kunszt, Zoltan

    2007-01-01

    We compute all two-loop master integrals which are required for the evaluation of next-to-leading order QCD corrections in Higgs boson production via gluon fusion. Many two-loop amplitudes for 2 -> 1 processes in the Standard Model and beyond can be expressed in terms of these integrals using automated reduction techniques. These integrals also form a subset of the master integrals for more complicated 2 -> 2 amplitudes with massive propagators in the loops. As a first application, we evaluate the two-loop amplitude for Higgs boson production in gluon fusion via a massive quark. Our result is the first independent check of the calculation of Spira, Djouadi, Graudenz and Zerwas. We also present for the first time the two-loop amplitude for gg -> h via a massive squark.

  2. Two-loop master integrals for the mixed EW-QCD virtual corrections to Drell-Yan scattering

    Science.gov (United States)

    Bonciani, Roberto; Di Vita, Stefano; Mastrolia, Pierpaolo; Schubert, Ulrich

    2016-09-01

    We present the calculation of the master integrals needed for the two-loop QCD × EW corrections to q+overline{q}to {l}-+{l}+ and q+overline{q}^'to {l}-+overline{ν} , for massless external particles. We treat the W and Z bosons as degenerate in mass. We identify three types of diagrams, according to the presence of massive internal lines: the no-mass type, the one-mass type, and the two-mass type, where all massive propagators, when occurring, contain the same mass value. We find a basis of 49 master integrals and evaluate them with the method of the differential equations. The Magnus exponential is employed to choose a set of master integrals that obeys a canonical system of differential equations. Boundary conditions are found either by matching the solutions onto simpler integrals in special kinematic configurations, or by requiring the regularity of the solution at pseudothresholds. The canonical master integrals are finally given as Taylor series around d = 4 space-time dimensions, up to order four, with coefficients given in terms of iterated integrals, respectively up to weight four.

  3. Two-loop master integrals for the mixed EW-QCD virtual corrections to Drell-Yan scattering

    Energy Technology Data Exchange (ETDEWEB)

    Bonciani, Roberto [' ' La Sapienza' ' Univ., Rome (Italy). Dipt. di Fisica; INFN Sezione Roma (Italy); Di Vita, Stefano [Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany); Mastrolia, Pierpaolo [Max-Planck-Institut fuer Physik, Muenchen (Germany); Padova Univ. (Italy). Dipt. di Fisica e Astronomia; INFN Sezione di Padova (Italy); Schubert, Ulrich [Max-Planck-Institut fuer Physik, Muenchen (Germany)

    2016-04-15

    We present the calculation of the master integrals needed for the two-loop QCD x EW corrections to q+ anti q → l{sup -}+l{sup +} and q+ anti q{sup '} → l{sup -}+ anti ν, for massless external particles. We treat W and Z bosons as degenerate in mass. We identify three types of diagrams, according to the presence of massive internal lines: the no-mass type, the one-mass type, and the two-mass type, where all massive propagators, when occurring, contain the same mass value. We find a basis of 49 master integrals and evaluate them with the method of the differential equations. The Magnus exponential is employed to choose a set of master integrals that obeys a canonical system of differential equations. Boundary conditions are found either by matching the solutions onto simpler integrals in special kinematic configurations, or by requiring the regularity of the solution at pseudo-thresholds. The canonical master integrals are finally given as Taylor series around d=4 space-time dimensions, up to order four, with coefficients given in terms of iterated integrals, respectively up to weight four.

  4. Numerical integration for ab initio many-electron self energy calculations within the GW approximation

    CERN Document Server

    Liu, Fang; Vigil-Fowler, Derek; Lischner, Johannes; Kemper, Alexander F; Sharifzadeh, Sahar; da Jornada, Felipe Homrich; Deslippe, Jack; Yang, Chao; Neaton, Jeffrey B; Louie, Steven G

    2014-01-01

    We present a numerical integration scheme for evaluating the convolution of a Green's function with a screened Coulomb potential on the real axis in the GW approximation of the self energy. Our scheme takes the zero broadening limit in Green's function first, replaces the numerator of the integrand with a piecewise polynomial approximation, and performs principal value integration on subintervals analytically. We give the error bound of our numerical integration scheme and show by numerical examples that it is more reliable and accurate than the standard quadrature rules such as the composite trapezoidal rule. We also discuss the benefit of using different self energy expressions to perform the numerical convolution at different frequencies.

  5. The two-loop sunrise integral around four space-time dimensions and generalisations of the Clausen and Glaisher functions towards the elliptic case

    Science.gov (United States)

    Adams, Luise; Bogner, Christian; Weinzierl, Stefan

    2015-07-01

    We present the result for the finite part of the two-loop sunrise integral with unequal masses in four space-time dimensions in terms of the O ( ɛ0) -part and the O ( ɛ1) -part of the sunrise integral around two space-time dimensions. The latter two integrals are given in terms of elliptic generalisations of Clausen and Glaisher functions. Interesting aspects of the result for the O ( ɛ1 ) -part of the sunrise integral around two space-time dimensions are the occurrence of depth two elliptic objects and the weights of the individual terms.

  6. The two-loop sunrise integral around four space-time dimensions and generalisations of the Clausen and Glaisher functions towards the elliptic case

    CERN Document Server

    Adams, Luise; Weinzierl, Stefan

    2015-01-01

    We present the result for the finite part of the two-loop sunrise integral with unequal masses in four space-time dimensions in terms of the ${\\mathcal O}(\\varepsilon^0)$-part and the ${\\mathcal O}(\\varepsilon^1)$-part of the sunrise integral around two space-time dimensions. The latter two integrals are given in terms of elliptic generalisations of Clausen and Glaisher functions. Interesting aspects of the result for the ${\\mathcal O}(\\varepsilon^1)$-part of the sunrise integral around two space-time dimensions are the occurrence of depth two elliptic objects and the weights of the individual terms.

  7. Numerical integration for ab initio many-electron self energy calculations within the GW approximation

    Energy Technology Data Exchange (ETDEWEB)

    Liu, Fang, E-mail: fliu@lsec.cc.ac.cn [School of Statistics and Mathematics, Central University of Finance and Economics, Beijing 100081 (China); Lin, Lin, E-mail: linlin@math.berkeley.edu [Department of Mathematics, University of California, Berkeley, CA 94720 (United States); Computational Research Division, Lawrence Berkeley National Laboratory, Berkeley, CA 94720 (United States); Vigil-Fowler, Derek, E-mail: vigil@berkeley.edu [Department of Physics, University of California, Berkeley, CA 94720 (United States); Materials Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, CA 94720 (United States); Lischner, Johannes, E-mail: jlischner597@gmail.com [Department of Physics, University of California, Berkeley, CA 94720 (United States); Materials Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, CA 94720 (United States); Kemper, Alexander F., E-mail: afkemper@lbl.gov [Computational Research Division, Lawrence Berkeley National Laboratory, Berkeley, CA 94720 (United States); Sharifzadeh, Sahar, E-mail: ssharifz@bu.edu [Department of Electrical and Computer Engineering and Division of Materials Science and Engineering, Boston University, Boston, MA 02215 (United States); Jornada, Felipe H. da, E-mail: jornada@berkeley.edu [Department of Physics, University of California, Berkeley, CA 94720 (United States); Materials Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, CA 94720 (United States); Deslippe, Jack, E-mail: jdeslippe@lbl.gov [NERSC, Lawrence Berkeley National Laboratory, Berkeley, CA 94720 (United States); Yang, Chao, E-mail: cyang@lbl.gov [Computational Research Division, Lawrence Berkeley National Laboratory, Berkeley, CA 94720 (United States); and others

    2015-04-01

    We present a numerical integration scheme for evaluating the convolution of a Green's function with a screened Coulomb potential on the real axis in the GW approximation of the self energy. Our scheme takes the zero broadening limit in Green's function first, replaces the numerator of the integrand with a piecewise polynomial approximation, and performs principal value integration on subintervals analytically. We give the error bound of our numerical integration scheme and show by numerical examples that it is more reliable and accurate than the standard quadrature rules such as the composite trapezoidal rule. We also discuss the benefit of using different self energy expressions to perform the numerical convolution at different frequencies.

  8. Differential equations and dispersion relations for Feynman amplitudes. The two-loop massive sunrise and the kite integral

    CERN Document Server

    Remiddi, Ettore

    2016-01-01

    It is shown that the study of the imaginary part and of the corresponding dispersion relations of Feynman graph amplitudes within the differential equations method can provide a powerful tool for the solution of the equations, especially in the massive case. The main features of the approach are illustrated by discussing the simple cases of the 1-loop self-mass and of a particular vertex amplitude, and then used for the evaluation of the two-loop massive sunrise and the QED kite graph (the problem studied by Sabry in 1962), up to first order in the (d-4) expansion.

  9. Differential equations and dispersion relations for Feynman amplitudes. The two-loop massive sunrise and the kite integral

    Science.gov (United States)

    Remiddi, Ettore; Tancredi, Lorenzo

    2016-06-01

    It is shown that the study of the imaginary part and of the corresponding dispersion relations of Feynman graph amplitudes within the differential equations method can provide a powerful tool for the solution of the equations, especially in the massive case. The main features of the approach are illustrated by discussing the simple cases of the 1-loop self-mass and of a particular vertex amplitude, and then used for the evaluation of the two-loop massive sunrise and the QED kite graph (the problem studied by Sabry in 1962), up to first order in the (d - 4) expansion.

  10. Two-loop two-point functions with masses asymptotic expansions and Taylor series, in any dimension

    CERN Document Server

    Broadhurst, D J; Tarasov, O V

    1993-01-01

    In all mass cases needed for quark and gluon self-energies, the two-loop master diagram is expanded at large and small $q^2$, in $d$ dimensions, using identities derived from integration by parts. Expansions are given, in terms of hypergeometric series, for all gluon diagrams and for all but one of the quark diagrams; expansions of the latter are obtained from differential equations. Pad\\'{e} approximants to truncations of the expansions are shown to be of great utility. As an application, we obtain the two-loop photon self-energy, for all $d$, and achieve highly accelerated convergence of its expansions in powers of $q^2/m^2$ or $m^2/q^2$, for $d=4$.

  11. Supersymmetric Wilson loops at two loops

    CERN Document Server

    Bassetto, Antonio; Pucci, Fabrizio; Seminara, Domenico

    2008-01-01

    We study the quantum properties of certain BPS Wilson loops in ${\\cal N}=4$ supersymmetric Yang-Mills theory. They belong to a general family, introduced recently, in which the addition of particular scalar couplings endows generic loops on $S^3$ with a fraction of supersymmetry. When restricted to $S^2$, their quantum average has been further conjectured to be exactly computed by the matrix model governing the zero-instanton sector of YM$_2$ on the sphere. We perform a complete two-loop analysis on a class of cusped Wilson loops lying on a two-dimensional sphere, finding perfect agreement with the conjecture. The perturbative computation reproduces the matrix-model expectation through a highly non-trivial interplay between ladder diagrams and self-energies/vertex contributions, suggesting the existence of a localization procedure.

  12. Complex-mass renormalization in hadronic EFT: applicability at two-loop order

    CERN Document Server

    Djukanovic, D; Gegelia, J; Krebs, H; Meißner, U -G

    2015-01-01

    We discuss the application of the complex-mass scheme to multi-loop diagrams in hadronic effective field theory by considering as an example a two-loop self-energy diagram. We show that the renormalized two-loop diagram satisfies the power counting.

  13. Complex-mass renormalization in hadronic EFT: Applicability at two-loop order

    Energy Technology Data Exchange (ETDEWEB)

    Djukanovic, D. [University of Mainz, Helmholtz Institute Mainz, Mainz (Germany); Epelbaum, E.; Krebs, H. [Ruhr-Universitaet Bochum, Institut fuer Theoretische Physik II, Bochum (Germany); Gegelia, J. [Forschungszentrum Juelich, Institute for Advanced Simulation, Institut fuer Kernphysik and Juelich Center for Hadron Physics, Juelich (Germany); Tbilisi State University, Tbilisi (Georgia); Meissner, U.G. [Universitaet Bonn, Helmholtz Institut fuer Strahlen- und Kernphysik and Bethe Center for Theoretical Physics, Bonn (Germany); Forschungszentrum Juelich, Institute for Advanced Simulation, Institut fuer Kernphysik and Juelich Center for Hadron Physics, Juelich (Germany)

    2015-08-15

    We discuss the application of the complex-mass scheme to multi-loop diagrams in hadronic effective field theory by considering as an example a two-loop self-energy diagram. We show that the renormalized two-loop diagram satisfies the power counting. (orig.)

  14. Two-Loop Maximal Unitarity with External Masses

    CERN Document Server

    Johansson, Henrik; Larsen, Kasper J

    2013-01-01

    We extend the maximal unitarity method at two loops to double-box basis integrals with up to three external massive legs. We use consistency equations based on the requirement that integrals of total derivatives vanish. We obtain unique formulae for the coefficients of the master double-box integrals. These formulae can be used either analytically or numerically.

  15. An Overview of Maximal Unitarity at Two Loops

    CERN Document Server

    Johansson, Henrik; Larsen, Kasper J.

    2012-01-01

    We discuss the extension of the maximal-unitarity method to two loops, focusing on the example of the planar double box. Maximal cuts are reinterpreted as contour integrals, with the choice of contour fixed by the requirement that integrals of total derivatives vanish on it. The resulting formulae, like their one-loop counterparts, can be applied either analytically or numerically.

  16. Maximal Unitarity at Two Loops

    CERN Document Server

    Kosower, David A

    2012-01-01

    We show how to compute the coefficients of the double box basis integrals in a massless four-point amplitude in terms of tree amplitudes. We show how to choose suitable multidimensional contours for performing the required cuts, and derive consistency equations from the requirement that integrals of total derivatives vanish. Our formulae for the coefficients can be used either analytically or numerically.

  17. Contributions to the nonlinear integrated Sachs-Wolfe effect: Birkinshaw-Gull effect and gravitational self-energy density

    CERN Document Server

    Merkel, Philipp

    2012-01-01

    In this paper, we recompute contributions to the spectrum of the nonlinear integrated Sachs-Wolfe (iSW)/Rees-Sciama effect in a dark energy cosmology. Focusing on the moderate nonlinear regime, all dynamical fields involved are derived from the density contrast in Eulerian perturbation theory. Shape and amplitude of the resulting angular power spectrum are similar to that derived in previous work. With our purely analytical approach we identify two distinct contributions to the signal of the nonlinear iSW-effect: the change of the gravitational self-energy density of the large scale structure with (conformal) time and gravitational lenses moving with the large scale matter stream. In the latter we recover the Birkinshaw-Gull effect. As the nonlinear iSW-effect itself is inherently hard to detect, observational discrimination between its individual contributions is almost excluded. Our analysis, however, yields valuable insights into the theory of the nonlinear iSW-effect as a post-Newtonian relativistic effec...

  18. Off-shell two loop QCD vertices

    CERN Document Server

    Gracey, J A

    2014-01-01

    We calculate the triple gluon, ghost-gluon and quark-gluon vertex functions at two loops in the MSbar scheme in the chiral limit for an arbitrary linear covariant gauge when the external legs are all off-shell.

  19. Two-loop top-Yukawa-coupling corrections to the charged Higgs-boson mass in the MSSM

    Energy Technology Data Exchange (ETDEWEB)

    Hollik, Wolfgang [Max-Planck-Institut fuer Physik (Werner-Heisenberg-Institut), Muenchen (Germany); Passehr, Sebastian [Deutsches Elektronen-Synchrotron DESY, Hamburg (Germany)

    2015-07-15

    The top-Yukawa-coupling enhanced two-loop corrections to the charged Higgs-boson mass in the real MSSM are presented. The contributing two-loop self-energies are calculated in the Feynman-diagrammatic approach in the gaugeless limit with vanishing external momentum and bottom mass, within a renormalization scheme comprising on-shell and DR conditions. Numerical results illustrate the effect of the O(α{sub t}{sup 2}) contributions and the importance of the two-loop corrections to the mass of the charged Higgs bosons. (orig.)

  20. Two Loop Effective Kähler Potential

    CERN Document Server

    Nyawelo, T S; Nyawelo, Tino S.; Nibbelink, Stefan Groot

    2007-01-01

    In this talk we study the renormalization of the effective Kaehler potential at one and two loops for general four dimensional (non--renormalizable) N=1 supersymmetric theories described by arbitrary Kaehler potential, superpotential and gauge kinetic function. We consider the Wess-Zumino model as an example.

  1. Numerical Computation of Two-loop Box Diagrams with Masses

    CERN Document Server

    Yuasa, F; Hamaguchi, N; Ishikawa, T; Kato, K; Kurihara, Y; Fujimoto, J; Shimizu, Y

    2011-01-01

    A new approach is presented to evaluate multi-loop integrals, which appear in the calculation of cross-sections in high-energy physics. It relies on a fully numerical method and is applicable to a wide class of integrals with various mass configurations. As an example, the computation of two-loop planar and non-planar box diagrams is shown. The results are confirmed by comparisons with other techniques, including the reduction method, and by a consistency check using the dispersion relation.

  2. Two loop scalar bilinears for inflationary SQED

    Energy Technology Data Exchange (ETDEWEB)

    Prokopec, T [Institute for Theoretical Physics and Spinoza Institute, Utrecht University Leuvenlaan 4, Postbus 80.195, 3508 TD Utrecht (Netherlands); Tsamis, N C [Department of Physics, University of Crete GR-710 03 Heraklion, Hellas (Greece); Woodard, R P [Department of Physics, University of Florida Gainesville, FL 32611 (United States)

    2007-01-07

    We evaluate the one- and two-loop contributions to the expectation values of two coincident and gauge invariant scalar bilinears in the theory of massless, minimally coupled scalar quantum electrodynamics on a locally de Sitter background. One of these bilinears is the product of two covariantly differentiated scalars, the other is the product of two undifferentiated scalars. The computations are done using dimensional regularization and the Schwinger-Keldysh formalism. Our results are in perfect agreement with the stochastic predictions at this order.

  3. Two-Loop Fermionic Corrections to Massive Bhabha Scattering

    CERN Document Server

    Actis, S; Gluza, J; Riemann, T

    2007-01-01

    We evaluate the two-loop corrections to Bhabha scattering from fermion loops in the context of pure Quantum Electrodynamics. The differential cross section is expressed by a small number of Master Integrals with exact dependence on the fermion masses me, mf and the Mandelstam invariants s,t,u. We determine the limit of fixed scattering angle and high energy, assuming the hierarchy of scales me^2 << mf^2 << s,t,u. The numerical result is combined with the available non-fermionic contributions. As a by-product, we provide an independent check of the known electron-loop contributions.

  4. A note on two-loop superloop

    Science.gov (United States)

    Belitsky, A. V.

    2012-11-01

    We explore the duality between supersymmetric Wilson loop on null polygonal contours in maximally supersymmetric Yang-Mills theory and next-to-maximal helicity violating (NMHV) scattering amplitudes. Earlier analyses demonstrated that the use of a dimensional regulator for ultraviolet divergences, induced due to presence of the cusps on the loop, yields anomalies that break both conformal symmetry and supersymmetry. At one-loop order, these are present only in Grassmann components localized in the vicinity of a single cusp and result in a universal function for any number of sites of the polygon that can be subtracted away in a systematic manner leaving a well-defined supersymmetric remainder dual to corresponding components of the superamplitude. The question remains though whether components which were free from the aforementioned supersymmetric anomaly at leading order of perturbation theory remain so once computed at higher orders. Presently we verify this fact by calculating a particular component of the null polygonal super Wilson loop at two loops restricting the contour kinematics to a two-dimensional subspace. This allows one to perform all computations in a concise analytical form and trace the pattern of cancellations between individual Feynman graphs in a transparent fashion. As a consequence of our consideration we obtain a dual conformally invariant result for the remainder function in agreement with one-loop NMHV amplitudes.

  5. Two-Loop Renormalization in the Standard Model

    CERN Document Server

    Actis, S

    2006-01-01

    In part I general aspects of the renormalization of a spontaneously broken gauge theory have been introduced. Here, in part II, two-loop renormalization is introduced and discussed within the context of the minimal Standard Model. Therefore, this paper deals with the transition between bare parameters and fields to renormalized ones. The full list of one- and two-loop counterterms is shown and it is proven that, by a suitable extension of the formalism already introduced at the one-loop level, two-point functions suffice in renormalizing the model. The problem of overlapping ultraviolet divergencies is analyzed and it is shown that all counterterms are local and of polynomial nature. The original program of 't Hooft and Veltman is at work. Finite parts are written in a way that allows for a fast and reliable numerical integration with all collinear logarithms extracted analytically. Finite renormalization, the transition between renormalized parameters and physical (pseudo-)observables, will be discussed in p...

  6. Two-loop RG functions of the massive φ4 field theory in general dimensions

    Directory of Open Access Journals (Sweden)

    M.A. Shpot

    2010-01-01

    Full Text Available Two-loop Feynman integrals of the massive φ4d field theory are explicitly obtained for generic space dimensions d. Corresponding renormalization-group functions are expressed in a compact form in terms of Gauss hypergeometric functions. A number of interesting and useful relations are given for these integrals as well as for several special mathematical functions and constants.

  7. On-shell two-loop three-gluon vertex

    CERN Document Server

    Davydychev, A I

    1999-01-01

    The two-loop three-gluon vertex is calculated in an arbitrary covariant gauge, in the limit when two of the gluons are on the mass shell. The corresponding two-loop results for the ghost-gluon vertex are also obtained. It is shown that the results are consistent with the Ward-Slavnov-Taylor identities.

  8. Two-loop renormalization of the effective field theory of a static quark

    CERN Document Server

    Broadhurst, D J

    1991-01-01

    We give a recurrence relation for two-loop integrals encountered in the effective field theory of an infinitely heavy quark, Q, interacting with gluons and Nl massless quarks, q, from which we obtain exact two-loop results, in any dimension and covariant gauge, for the propagator of Q and the vertex function of the heavy-light current J = Q Gamma q, at zero q momentum. The anomalous dimension of the Q field agrees with the recent result of Broadhurst, Gray and Schilcher. The anomalous dimension of the current is gamma_J = d log Z_J / d log mu = - alpha_s/pi (1 + (127 + 56 zeta(2) - 10 Nl)/72) alpha_s/pi + O(alpha_s^2)) which gives the new two-loop correction to the result of Voloshin and Shifman.

  9. Two-loop Bethe-logarithm correction in hydrogenlike atoms.

    Science.gov (United States)

    Pachucki, Krzysztof; Jentschura, Ulrich D

    2003-09-12

    We calculate the two-loop Bethe logarithm correction to atomic energy levels in hydrogenlike systems. The two-loop Bethe logarithm is a low-energy quantum electrodynamic (QED) effect involving multiple summations over virtual excited atomic states. Although much smaller in absolute magnitude than the well-known one-loop Bethe logarithm, the two-loop analog is quite significant when compared to the current experimental accuracy of the 1S-2S transition: It contributes -8.19 and -0.84 kHz for the 1S and the 2S state, respectively. The two-loop Bethe logarithm has been the largest unknown correction to the hydrogen Lamb shift to date. Together with the ongoing measurement of the proton charge radius at the Paul Scherrer Institute, its calculation will bring theoretical and experimental accuracy for the Lamb shift in atomic hydrogen to the level of 10(-7).

  10. Off-shell two-loop QCD vertices

    Science.gov (United States)

    Gracey, J. A.

    2014-07-01

    We calculate the triple gluon, ghost-gluon and quark-gluon vertex functions at two loops in the MS¯ scheme in the chiral limit for an arbitrary linear covariant gauge when the external legs are all off shell.

  11. The two-loop helicity amplitudes for $q \\bar q' \\to V_1 V_2 \\to 4~\\mathrm{leptons}$

    CERN Document Server

    Gehrmann, Thomas; Tancredi, Lorenzo

    2015-01-01

    We compute the two-loop massless QCD corrections to the helicity amplitudes for the production of two massive vector bosons in quark-antiquark annihilation, allowing for an arbitrary virtuality of the vector bosons: $q \\bar q' \\to V_1V_2$. Combining with the leptonic decay currents, we obtain the full two-loop QCD description of the corresponding electroweak four-lepton production processes. The calculation is performed by projecting the two-loop diagrams onto an appropriate basis of Lorentz structures. All two-loop Feynman integrals are reduced to a basis of master integrals, which are then computed using the differential equations method and optimised for numerical performance. We provide a public C++ code which allows for fast and precise numerical evaluations of the amplitudes.

  12. QCD two-loop corrections for hadronic single top-quark production in the t-channel

    CERN Document Server

    Assadsolimani, M; Tausk, B; Uwer, P

    2014-01-01

    In this article we discuss the calculation of single top-quark production in the t-channel at two-loop order in QCD. In particular we present the decomposition of the amplitude according to its spin and colour structure and present complete results for the two-loop amplitudes in terms of master integrals. For the vertex corrections compact analytic expressions are given. The box contributions are implemented in a publicly available C program.

  13. N >= 4 Supergravity Amplitudes from Gauge Theory at Two Loops

    Energy Technology Data Exchange (ETDEWEB)

    Boucher-Veronneau, C.; Dixon, L.J.; /SLAC

    2012-02-15

    We present the full two-loop four-graviton amplitudes in N = 4, 5, 6 supergravity. These results were obtained using the double-copy structure of gravity, which follows from the recently conjectured color-kinematics duality in gauge theory. The two-loop four-gluon scattering amplitudes in N = 0, 1, 2 supersymmetric gauge theory are a second essential ingredient. The gravity amplitudes have the expected infrared behavior: the two-loop divergences are given in terms of the squares of the corresponding one-loop amplitudes. The finite remainders are presented in a compact form. The finite remainder for N = 8 supergravity is also presented, in a form that utilizes a pure function with a very simple symbol.

  14. Two-Loop Renormalization in the Standard Model

    CERN Document Server

    Actis, S; Passarino, G; Passera, M

    2006-01-01

    In this paper the building blocks for the two-loop renormalization of the Standard Model are introduced with a comprehensive discussion of the special vertices induced in the Lagrangian by a particular diagonalization of the neutral sector and by two alternative treatments of the Higgs tadpoles. Dyson resummed propagators for the gauge bosons are derived, and two-loop Ward-Slavnov-Taylor identities are discussed. In part II, the complete set of counterterms needed for the two-loop renormalization will be derived. In part III, a renormalization scheme will be introduced, connecting the renormalized quantities to an input parameter set of (pseudo-)experimental data, critically discussing renormalization of a gauge theory with unstable particles.

  15. Two-Loop Threshold Singularities, Unstable Particles and Complex Masses

    CERN Document Server

    Actis, S; Sturm, C; Uccirati, S

    2008-01-01

    The effect of threshold singularities induced by unstable particles on two-loop observables is investigated and it is shown how to cure them working in the complex-mass scheme. The impact on radiative corrections around thresholds is thoroughly analyzed and shown to be relevant for two selected LHC and ILC applications: Higgs production via gluon fusion and decay into two photons at two loops in the Standard Model. Concerning Higgs production, it is essential to understand possible sources of large corrections in addition to the well-known QCD effects. It is shown that NLO electroweak corrections can incongruently reach a 10 % level around the WW vector-boson threshold without a complete implementation of the complex-mass scheme in the two-loop calculation.

  16. Two-Loop Gluon to Gluon-Gluon Splitting Amplitudes in QCD

    Energy Technology Data Exchange (ETDEWEB)

    Bern, Z.

    2004-04-30

    Splitting amplitudes are universal functions governing the collinear behavior of scattering amplitudes for massless particles. We compute the two-loop g {yields} gg splitting amplitudes in QCD, N = 1, and N = 4 super-Yang-Mills theories, which describe the limits of two-loop n-point amplitudes where two gluon momenta become parallel. They also represent an ingredient in a direct x-space computation of DGLAP evolution kernels at next-to-next-to-leading order. To obtain the splitting amplitudes, we use the unitarity sewing method. In contrast to the usual light-cone gauge treatment, our calculation does not rely on the principal-value or Mandelstam-Leibbrandt prescriptions, even though the loop integrals contain some of the denominators typically encountered in light-cone gauge. We reduce the integrals to a set of 13 master integrals using integration-by-parts and Lorentz invariance identities. The master integrals are computed with the aid of differential equations in the splitting momentum fraction z. The {epsilon}-poles of the splitting amplitudes are consistent with a formula due to Catani for the infrared singularities of two-loop scattering amplitudes. This consistency essentially provides an inductive proof of Catani's formula, as well as an ansatz for previously-unknown 1/{epsilon} pole terms having non-trivial color structure. Finite terms in the splitting amplitudes determine the collinear behavior of finite remainders in this formula.

  17. Matching the $D^{6}R^{4}$ interaction at two-loops

    CERN Document Server

    D'Hoker, Eric; Pioline, Boris; Russo, Rodolfo

    2015-01-01

    The coefficient of the $D^6 {\\cal R}^4$ interaction in the low energy expansion of the two-loop four-graviton amplitude in type II superstring theory is known to be proportional to the integral of the Zhang-Kawazumi (ZK) invariant over the moduli space of genus-two Riemann surfaces. We demonstrate that the ZK invariant is an eigenfunction with eigenvalue 5 of the Laplace-Beltrami operator in the interior of moduli space. Exploiting this result, we evaluate the integral of the ZK invariant explicitly, finding agreement with the value of the two-loop $D^6 {\\cal R}^4$ interaction predicted on the basis of S-duality and supersymmetry. A review of the current understanding of the $D^{2p} {\\cal R}^4$ interactions in type II superstring theory compactified on a torus $T^d$ with $p \\leq 3$ and $d \\leq 4$ is included.

  18. Two-Loop Gluon Regge Trajectory from Lipatov's Effective Action

    CERN Document Server

    Chachamis, Grigorios; Madrigal, José Daniel; Vera, Agustín Sabio

    2012-01-01

    Lipatov's high-energy effective action is a useful tool for computations in the Regge limit beyond leading order. Recently, a regularisation/subtraction prescription has been proposed that allows to apply this formalism to calculate next-to-leading order corrections in a consistent way. We illustrate this procedure with the computation of the gluon Regge trajectory at two loops.

  19. Local integrands for two-loop QCD amplitudes

    CERN Document Server

    Badger, Simon; Peraro, Tiziano

    2016-01-01

    In this talk we review the recent computation of the five- and six-gluon two-loop amplitudes in Yang-Mills theory using local integrands which make the infrared pole structure manifest. We make some remarks on the connection with BCJ relations and the all-multiplicity structure.

  20. Two-loop beta functions for supersymmetric gauge theories

    Energy Technology Data Exchange (ETDEWEB)

    Jack, I. (Imperial Coll. of Science and Technology, London (UK). Blackett Lab.)

    1984-11-15

    The two-loop ..beta.. functions in the dimensional regularisation framework for a general gauge theory coupled to scalar and spinor fields are presented and by means of a finite transformation of the couplings are converted into a form which vanishes for special cases corresponding to supersymmetric gauge theories.

  1. Two-loop and n-loop eikonal vertex corrections

    OpenAIRE

    Kidonakis, Nikolaos

    2003-01-01

    I present calculations of two-loop vertex corrections with massive and massless partons in the eikonal approximation. I show that the $n$-loop result for the UV poles can be given in terms of the one-loop calculation.

  2. Two-Loop Iteration of Five-Point N=4 Super-Yang-Mills Amplitudes

    CERN Document Server

    Bern, Z; Kosower, D A; Roiban, R; Smirnov, V A

    2006-01-01

    We confirm by explicit computation the conjectured all-orders iteration of planar maximally supersymmetric N=4 Yang-Mills theory in the nontrivial case of five-point two-loop amplitudes. We compute the required unitarity cuts of the integrand and evaluate the resulting integrals numerically using a Mellin--Barnes representation and the automated package of ref.~[1]. This confirmation of the iteration relation provides further evidence suggesting that N=4 gauge theory is solvable.

  3. Bosonic self-energy functional theory

    Science.gov (United States)

    Hügel, Dario; Werner, Philipp; Pollet, Lode; Strand, Hugo U. R.

    2016-11-01

    We derive the self-energy functional theory for bosonic lattice systems with broken U(1) symmetry by parametrizing the bosonic Baym-Kadanoff effective action in terms of one- and two-point self-energies. The formalism goes beyond other approximate methods such as the pseudoparticle variational cluster approximation, the cluster composite boson mapping, and the Bogoliubov+U theory. It simplifies to bosonic dynamical-mean-field theory when constraining to local fields, whereas when neglecting kinetic contributions of noncondensed bosons, it reduces to the static mean-field approximation. To benchmark the theory, we study the Bose-Hubbard model on the two- and three-dimensional cubic lattice, comparing with exact results from path integral quantum Monte Carlo. We also study the frustrated square lattice with next-nearest-neighbor hopping, which is beyond the reach of Monte Carlo simulations. A reference system comprising a single bosonic state, corresponding to three variational parameters, is sufficient to quantitatively describe phase boundaries and thermodynamical observables, while qualitatively capturing the spectral functions, as well as the enhancement of kinetic fluctuations in the frustrated case. On the basis of these findings, we propose self-energy functional theory as the omnibus framework for treating bosonic lattice models, in particular, in cases where path integral quantum Monte Carlo methods suffer from severe sign problems (e.g., in the presence of nontrivial gauge fields or frustration). Self-energy functional theory enables the construction of diagrammatically sound approximations that are quantitatively precise and controlled in the number of optimization parameters but nevertheless remain computable by modest means.

  4. The two-loop electroweak bosonic corrections to sin2 ⁡ θeffb

    Science.gov (United States)

    Dubovyk, Ievgen; Freitas, Ayres; Gluza, Janusz; Riemann, Tord; Usovitsch, Johann

    2016-11-01

    The prediction of the effective electroweak mixing angle sin2 ⁡θeffb in the Standard Model at two-loop accuracy has now been completed by the first calculation of the bosonic two-loop corrections to the Z b bar b vertex. Numerical predictions are presented in the form of a fitting formula as function of MZ ,MW ,MH ,mt and Δα, αs. For central input values, we obtain a relative correction of Δκb (α2 , bos) = - 0.9855 ×10-4, amounting to about a quarter of the fermionic corrections, and corresponding to sin2 ⁡ θeffb = 0.232704. The integration of the corresponding two-loop vertex Feynman integrals with up to three dimensionless parameters in Minkowskian kinematics has been performed with two approaches: (i) Sector decomposition, implemented in the packages FIESTA 3 and SecDec 3, and (ii) Mellin-Barnes representations, implemented in AMBRE 3/MB and the new package MBnumerics.

  5. Two-loop corrections to Higgs boson production

    Energy Technology Data Exchange (ETDEWEB)

    Ravindran, V. [Harish-Chandra Research Institute, Chhatnag Road, Jhusi, Allahabad 211019 (India); Smith, J. [C.N. Yang Institute for Theoretical Physics, State University of New York, Stony Brook, NY 11794-3840 (United States); Neerven, W.L. van [Instituut-Lorentz, University of Leiden, PO Box 9506, 2300 RA Leiden (Netherlands)]. E-mail: neerven@lorentz.leidenuniv.nl

    2005-01-03

    In this paper we present the complete two-loop vertex corrections to scalar and pseudo-scalar Higgs boson production for general colour factors for the gauge group SU(N) in the limit where the top quark mass gets infinite. We derive a general formula for the vertex correction which holds for conserved and non-conserved operators. For the conserved operator we take the electromagnetic vertex correction as an example whereas for the non-conserved operators we take the two vertex corrections above. Our observations for the structure of the pole terms 1/-bar 4, 1/-bar 3 and 1/-bar 2 in two loop order are the same as made earlier in the literature for electromagnetism. However, we also elucidate the origin of the second order single pole term which is equal to the second order singular part of the anomalous dimension plus a universal function which is the same for the quark and the gluon.

  6. Two-Loop SL(2) Form Factors and Maximal Transcendentality

    CERN Document Server

    Loebbert, Florian; Wilhelm, Matthias; Yang, Gang

    2016-01-01

    Form factors of composite operators in the SL(2) sector of N=4 SYM theory are studied up to two loops via the on-shell unitarity method. The non-compactness of this subsector implies the novel feature and technical challenge of an unlimited number of loop momenta in the integrand's numerator. At one loop, we derive the full minimal form factor to all orders in the dimensional regularisation parameter. At two loops, we construct the complete integrand for composite operators with an arbitrary number of covariant derivatives, and we obtain the remainder functions as well as the dilatation operator for composite operators with up to three covariant derivatives. The remainder functions reveal curious patterns suggesting a hidden maximal uniform transcendentality for the full form factor. Finally, we speculate about an extension of these patterns to QCD.

  7. Two-Loop Renormalization in the Standard Model

    CERN Document Server

    Actis, S

    2006-01-01

    In part I and II of this series of papers all elements have been introduced to extend, to two loops, the set of renormalization procedures which are needed in describing the properties of a spontaneously broken gauge theory. In this paper, the final step is undertaken and finite renormalization is discussed. Two-loop renormalization equations are introduced and their solutions discussed within the context of the minimal standard model of fundamental interactions. These equations relate renormalized Lagrangian parameters (couplings and masses) to some input parameter set containing physical (pseudo-)observables. Complex poles for unstable gauge and Higgs bosons are used and a consistent setup is constructed for extending the predictivity of the theory from the Lep1 Z-boson scale (or the Lep2 WW scale) to regions of interest for LHC and ILC physics.

  8. A two-loop excitation control system for synchronous generators

    Energy Technology Data Exchange (ETDEWEB)

    Alvarez-Ramirez, Jose; Cervantes, Ilse; Escarela-Perez, Rafael; Espinosa-Perez, Gerardo [Seccion de Estudios de Posgrado e Investigacion ESIME-C, Av. Santa Ana 1000 Col. San Francisco Culhuacan, Mexico D.F. 04430 (Mexico)

    2005-10-01

    An excitation controller for a single generator based on modern multi-loop design methodology is presented in this paper. The proposed controller consists of two-loops: a stabilizing (damping injection) loop and a voltage regulating loop. The task of the stabilizing loop is to add damping in the face of voltage oscillations. The voltage regulating loop is basically a PI compensator whose objective is to obtain terminal voltage regulation about the prescribed reference. The main contribution of this paper is to give some insights into the systematic derivation of multi-loop controllers of power generators. Certain connections between the two-loop excitation controller and standard PSS-AVR schemes are discussed. In this way, some insight into the stability of the standard PSS scheme is obtained from the analysis of the proposed controller. The proposed controller is evaluated via numerical simulations on a full finite-element model. (author)

  9. Analytic two-loop form factors in N=4 SYM

    CERN Document Server

    Brandhuber, Andreas; Yang, Gang

    2012-01-01

    We derive a compact expression for the three-point MHV form factors of half-BPS operators in N=4super Yang-Mills at two loops. The main tools of our calculation are generalised unitarity applied at the form factor level, and the compact expressions for supersymmetric tree-level form factors and amplitudes entering the cuts. We confirm that infrared divergences exponentiate as expected, and that collinear factorisation is entirely captured by an ABDK/BDS ansatz. Next, we construct the two-loop remainder function obtained by subtracting this ansatz from the full two-loop form factor and compute it numerically. Using symbology, combined with various physical constraints and symmetries, we find a unique solution for its symbol. With this input we construct a remarkably compact analytic expression for the remainder function, which contains only classical polylogarithms, and compare it to our numerical results. Furthermore, we make the surprising observation that our remainder is equal to the maximally transcendent...

  10. Optimized Perturbation Theory at Finite Temperature Two-Loop Analysis

    CERN Document Server

    Chiku, S

    2000-01-01

    We study the optimized perturbation theory (OPT) at finite temperature, which is a self-consistent resummation method. Firstly, we generalize the idea of the OPT to optimize the coupling constant in lambda phi^4 theory, and give a proof of the renormalizability of this generalized OPT. Secondly, the principle of minimal sensitivity and the criterion of the fastest apparent convergence, which are conditions to determine the optimal parameter values, are examined in lambda phi^4 theory. Both conditions exhibit a second-order transition at finite temperature with critical exponent beta = 0.5 in the two-loop approximation.

  11. Two-loop Dirac neutrino mass and WIMP dark matter

    CERN Document Server

    Bonilla, Cesar; Peinado, Eduardo; Valle, Jose W F

    2016-01-01

    We propose a "scotogenic" mechanism relating small neutrino mass and cosmological dark matter. Neutrinos are Dirac fermions with masses arising only in two--loop order through the sector responsible for dark matter. Two triality symmetries ensure both dark matter stability and strict lepton number conservation at higher orders. A global spontaneously broken U(1) symmetry leads to a physical $Diracon$ that induces invisible Higgs decays which add up to the Higgs to dark matter mode. This enhances sensitivities to spin-independent WIMP dark matter search below $m_h/2$.

  12. Two-loop electroweak threshold corrections in the Standard Model

    Directory of Open Access Journals (Sweden)

    Bernd A. Kniehl

    2015-07-01

    Full Text Available We study the relationships between the basic parameters of the on-shell renormalization scheme and their counterparts in the MS¯ scheme at full order O(α2 in the Standard Model. These enter as threshold corrections the renormalization group analyses underlying, e.g., the investigation of the vacuum stability. To ensure the gauge invariance of the parameters, in particular of the MS¯ masses, we work in Rξ gauge and systematically include tadpole contributions. We also consider the gaugeless-limit approximation and compare it with the full two-loop electroweak calculation.

  13. Coherent neutrino radiation in supernovae at two loops

    OpenAIRE

    Sedrakian, A.; Dieperink, A. E. L.

    2000-01-01

    We develop a neutrino transport theory, in terms of the real-time non-equilibrium Green's functions, which is applicable to physical conditions arbitrary far from thermal equilibrium. We compute the coherent neutrino radiation in cores of supernovae by evaluating the two-particle-two-hole (2p-2h) polarization function with dressed propagators. The propagator dressing is carried out in the particle-particle channel to all orders in the interaction. We show that at two loops there are two disti...

  14. Eikonal gluon bremsstrahlung at finite Nc beyond two loops

    Science.gov (United States)

    Delenda, Yazid; Khelifa-Kerfa, Kamel

    2016-03-01

    We present a general formalism for computing the matrix-element squared for the emission of soft energy-ordered gluons beyond two loops in QCD perturbation theory at finite Nc. Our formalism is valid in the eikonal approximation. A Mathematica program has been developed for the automated calculation of all real/virtual eikonal squared amplitudes needed at a given loop order. For the purpose of illustration, we show the explicit forms of the eikonal squared amplitudes up to the fifth-loop order. In the large-Nc limit, our results coincide with those previously reported in literature.

  15. Perturbative Yukawa theory at finite density: the role of masses and renormalization group flow at two loops

    CERN Document Server

    Palhares, Letícia F

    2008-01-01

    Yukawa theory at vanishing temperature provides (one of the ingredients for) an effective description of the thermodynamics of a variety of cold and dense fermionic systems. We study the role of masses and the renormalization group flow in the calculation of the equation of state up to two loops within the MSbar scheme. Two-loop integrals are computed analytically for arbitrary fermion and scalar masses, and expressed in terms of well-known special functions. The dependence of the renormalization group flow on the number of fermion flavors is also discussed.

  16. Two-Loop Scattering Amplitudes from the Riemann Sphere

    CERN Document Server

    Geyer, Yvonne; Monteiro, Ricardo; Tourkine, Piotr

    2016-01-01

    The scattering equations give striking formulae for massless scattering amplitudes at tree level and, as shown recently, at one loop. The progress at loop level was based on ambitwistor string theory, which naturally yields the scattering equations. We proposed that, for ambitwistor strings, the standard loop expansion in terms of the genus of the worldsheet is equivalent to an expansion in terms of nodes of a Riemann sphere, with the nodes carrying the loop momenta. In this paper, we show how to obtain two-loop scattering equations with the correct factorization properties. We adapt genus-two integrands from the ambitwistor string to the nodal Riemann sphere and show that these yield correct answers, by matching standard results for the four-point two-loop amplitudes of maximal supergravity and super-Yang-Mills theory. In the Yang-Mills case, this requires the loop analogue of the Parke-Taylor factor carrying the colour dependence, which includes non-planar contributions.

  17. Two-loop scattering amplitudes from the Riemann sphere

    Science.gov (United States)

    Geyer, Yvonne; Mason, Lionel; Monteiro, Ricardo; Tourkine, Piotr

    2016-12-01

    The scattering equations give striking formulas for massless scattering amplitudes at tree level and, as shown recently, at one loop. The progress at loop level was based on ambitwistor-string theory, which naturally yields the scattering equations. We proposed that, for ambitwistor strings, the standard loop expansion in terms of the genus of the world sheet is equivalent to an expansion in terms of nodes of a Riemann sphere, with the nodes carrying the loop momenta. In this paper, we show how to obtain two-loop scattering equations with the correct factorization properties. We adapt genus-two integrands from the ambitwistor string to the nodal Riemann sphere and show that these yield correct answers, by matching standard results for the four-point two-loop amplitudes of maximal supergravity and super-Yang-Mills theory. In the Yang-Mills case, this requires the loop analogue of the Parke-Taylor factor carrying the color dependence, which includes nonplanar contributions.

  18. Local integrands for two-loop all-plus Yang-Mills amplitudes

    CERN Document Server

    Badger, Simon; Peraro, Tiziano

    2016-01-01

    We express the planar five- and six-gluon two-loop Yang-Mills amplitudes with all positive helicities in compact analytic form using D-dimensional local integrands that are free of spurious singularities. The integrand is fixed from on-shell tree amplitudes in six dimensions using D-dimensional generalised unitarity cuts. The resulting expressions are shown to have manifest infrared behaviour at the integrand level. We also find simple representations of the rational terms obtained after integration in 4-2epsilon dimensions.

  19. Gravitational Two-Loop Counterterm Is Asymptotically Safe

    Science.gov (United States)

    Gies, Holger; Knorr, Benjamin; Lippoldt, Stefan; Saueressig, Frank

    2016-05-01

    Weinberg's asymptotic safety scenario provides an elegant mechanism to construct a quantum theory of gravity within the framework of quantum field theory based on a non-Gaussian fixed point of the renormalization group flow. In this work we report novel evidence for the validity of this scenario, using functional renormalization group techniques to determine the renormalization group flow of the Einstein-Hilbert action supplemented by the two-loop counterterm found by Goroff and Sagnotti. The resulting system of beta functions comprises three scale-dependent coupling constants and exhibits a non-Gaussian fixed point which constitutes the natural extension of the one found at the level of the Einstein-Hilbert action. The fixed point exhibits two ultraviolet attractive and one repulsive direction supporting a low-dimensional UV-critical hypersurface. Our result vanquishes the long-standing criticism that asymptotic safety will not survive once a "proper perturbative counterterm" is included in the projection space.

  20. The Gravitational Two-Loop Counterterm is Asymptotically Safe

    CERN Document Server

    Gies, Holger; Lippoldt, Stefan; Saueressig, Frank

    2016-01-01

    Weinberg's asymptotic safety scenario provides an elegant mechanism to construct a quantum theory of gravity within the framework of quantum field theory based on a non-Gau{\\ss}ian fixed point of the renormalization group flow. In this work we report novel evidence for the validity of this scenario, using functional renormalization group techniques to determine the renormalization group flow of the Einstein-Hilbert action supplemented by the two-loop counterterm found by Goroff and Sagnotti. The resulting system of beta functions comprises three scale-dependent coupling constants and exhibits a non-Gau{\\ss}ian fixed point which constitutes the natural extension of the one found at the level of the Einstein-Hilbert action. The fixed point exhibits two ultraviolet attractive and one repulsive direction supporting a low-dimensional UV-critical hypersurface. Our result vanquishes the longstanding criticism that asymptotic safety will not survive once a "proper perturbative counterterm" is included in the projecti...

  1. Overcoming Obstacles to Colour-Kinematics Duality at Two Loops

    CERN Document Server

    Mogull, Gustav

    2015-01-01

    The discovery of colour-kinematics duality has allowed great progress in our understanding of the UV structure of gravity. However, it has proven difficult to find numerators which satisfy colour-kinematics duality in certain cases. We discuss obstacles to building a set of such numerators in the context of the five-gluon amplitude with all helicities positive at two loops. We are able to overcome the obstacles by adding more loop momentum to our numerator to accommodate tension between the values of certain cuts and the symmetries of certain diagrams. At the same time, we maintain control over the size of our ansatz by identifying a highly constraining but desirable symmetry property of our master numerator. The resulting numerators have twelve powers of loop momenta rather than the seven one would expect from the Feynman rules.

  2. Rapidity renormalized TMD soft and beam functions at two loops

    Energy Technology Data Exchange (ETDEWEB)

    Luebbert, Thomas [Hamburg Univ. (Germany). 2. Inst. fuer Theoretische Physik; Oredsson, Joel [DESY, Hamburg (Germany). Theory Group; Lund Univ. (Sweden). Dept. of Astronomy and Theoretical Physics; Stahlhofen, Maximilian [DESY, Hamburg (Germany). Theory Group; Mainz Univ. (Germany). PRISMA Cluster of Excellence

    2016-03-15

    We compute the transverse momentum dependent (TMD) soft function for the production of a color-neutral final state at the LHC within the rapidity renormalization group (RRG) framework to next-to-next-to-leading order (NNLO). We use this result to extract the universal renormalized TMD beam functions (aka TMDPDFs) in the same scheme and at the same order from known results in another scheme. We derive recurrence relations for the logarithmic structure of the soft and beam functions, which we use to cross check our calculation. We also explicitly confirm the non-Abelian exponentiation of the TMD soft function in the RRG framework at two loops. Our results provide the ingredients for resummed predictions of p {sub perpendicular} {sub to} -differential cross sections at NNLL' in the RRG formalism. The RRG provides a systematic framework to resum large (rapidity) logarithms through (R)RG evolution and assess the associated perturbative uncertainties.

  3. Two-loop-induced neutrino masses: A model-independent perspective

    CERN Document Server

    Sierra, D Aristizabal

    2015-01-01

    We discuss Majorana neutrino mass generation mechanisms at the two-loop order. After briefly reviewing the systematic classification of one-loop realizations, we then focus on a general two-loop classification scheme which provides a model-independent catalog for neutrino mass models at the two-loop order

  4. Study of Two-Loop Neutrino Mass Generation Models

    CERN Document Server

    Geng, Chao-Qiang

    2015-01-01

    We study the models with the Majorana neutrino masses generated radiatively by two-loop diagrams due to the Yukawa $\\rho \\bar \\ell_R^c \\ell_R$ and effective $\\rho^{\\pm\\pm} W^\\mp W^\\mp$ couplings along with a scalar triplet $\\Delta$, where $\\rho$ is a doubly charged singlet scalar, $\\ell_R$ the charged lepton and $W$ the charged gauge boson. A generic feature in these types of models is that the neutrino mass spectrum has to be a normal hierarchy. Furthermore, by using the neutrino oscillation data and comparing with the global fitting result in the literature, we find a unique neutrino mass matrix and predict the Dirac and two Majorana CP phases to be $1.40\\pi$, $1.11\\pi$ and $1.47\\pi$, respectively. We also discuss the model parameters constrained by the lepton flavor violating processes and electroweak oblique parameters. In addition, we show that the rate of the neutrinoless double beta decay $(0\

  5. Hard matching for boosted tops at two loops

    Energy Technology Data Exchange (ETDEWEB)

    Hoang, Andre H. [Vienna Univ. (Austria). Faculty of Physics; Vienna Univ. (Austria). Erwin Schroeder International Institute for Mathematical Physics; Pathak, Aditya; Stewart, Iain W. [Massachusetts Institute of Technology, Cambridge, MA (United States). Center for Theoretical Physics; Pietrulewicz, Piotr [DESY Hamburg (Germany). Theory Group

    2015-08-15

    Cross sections for top quarks provide very interesting physics opportunities, being both sensitive to new physics and also perturbatively tractable due to the large top quark mass. Rigorous factorization theorems for top cross sections can be derived in several kinematic scenarios, including the boosted regime in the peak region that we consider here. In the context of the corresponding factorization theorem for e{sup +}e{sup -} collisions we extract the last missing ingredient that is needed to evaluate the cross section differential in the jet-mass at two-loop order, namely the matching coefficient at the scale μ ≅ m{sub t}. Our extraction also yields the final ingredients needed to carry out logarithmic resummation at next-to-next-to-leading logarithmic order (or N3LL if we ignore the missing 4-loop cusp anomalous dimension). This coefficient exhibits an amplitude level rapidity logarithm starting at O(α{sup 2}{sub s}) due to virtual top quark loops, which we treat using rapidity renormalization group (RG) evolution. Interestingly, this rapidity RG evolution appears in the matching coefficient between two effective theories around the heavy quark mass scale μ≅m{sub t}.

  6. Coherent neutrino radiation in supernovae at two loops

    Science.gov (United States)

    Sedrakian, A.; Dieperink, A. E. L.

    2000-10-01

    We develop a neutrino transport theory, in terms of the real-time nonequilibrium Green's functions, which is applicable to physical conditions arbitrary far from thermal equilibrium. We compute the coherent neutrino radiation in cores of supernovae by evaluating the two-particle-two-hole (2p-2h) polarization function with dressed propagators. The propagator dressing is carried out in the particle-particle channel to all orders in the interaction. We show that at two loops there are two distinct sources of coherence effects in the bremsstrahlung. One is the generically off-shell intermediate state propagation, which leads to the Landau-Pomeranchuk-Migdal type suppression of radiation. We extend previous perturbative results, obtained in the leading order in quasiparticle width, by deriving the exact nonperturbative expression. A new contribution due to off-shell final or initial baryon states is treated in the leading order in the quasiparticle width. The latter contribution corresponds to processes of higher order than second order in the virial expansion in the number of quasiparticles. At the 2p-2h level, the time component of the polarization tensor for the vector transitions vanishes identically in the soft neutrino approximation. Vector current thereby is conserved. The contraction of the neutral axial vector current with the tensor interaction among the baryons leads to a nonvanishing contribution to the bremsstrahlung rate. These rates are evaluated numerically for finite temperature pure neutron matter at and above the nuclear saturation density.

  7. Two-loop electroweak corrections to Higgs-gluon couplings to higher orders in the dimensional regularization parameter

    CERN Document Server

    Bonetti, Marco; Tancredi, Lorenzo

    2016-01-01

    We compute the two-loop electroweak correction to the production of the Higgs boson in gluon fusion to higher orders in the dimensional-regularization parameter $\\epsilon = (d-4)/2$. We employ the method of differential equations to compute the relevant integrals and express them in terms of Goncharov polylogarithms. Our result provides one of the necessary inputs for the computation of mixed three-loop QCD-electroweak corrections to $gg \\to H$.

  8. Two-loop renormalization of vector, axial-vector and tensor fermion bilinears on the lattice

    CERN Document Server

    Skouroupathis, A

    2008-01-01

    We compute the two-loop renormalization functions, in the RI' scheme, of local bilinear quark operators $\\bar{\\psi}\\Gamma\\psi$, where $\\Gamma$ corresponds to the Vector, Axial-Vector and Tensor Dirac operators, in the lattice formulation of QCD. We consider both the flavor nonsinglet and singlet operators. We use the clover action for fermions and the Wilson action for gluons. Our results are given as a polynomial in $c_{SW}$, in terms of both the renormalized and bare coupling constant, in the renormalized Feynman gauge. Finally, we present our results in the MSbar scheme, for easier comparison with calculations in the continuum. The corresponding results, for fermions in an arbitrary representation, together with some special features of superficially divergent integrals, are included in the Appendices.

  9. The two-loop electroweak bosonic corrections to $\\sin^2\\theta_{\\rm eff}^{\\rm b}$

    CERN Document Server

    Dubovyk, Ievgen; Gluza, Janusz; Riemann, Tord; Usovitsch, Johann

    2016-01-01

    The prediction of the effective electroweak mixing angle $\\sin^2\\theta_{\\rm eff}^{\\rm b}$ in the Standard Model at two-loop accuracy has now been completed by the first calculation of the bosonic two-loop corrections to the $Z{\\bar b}b$ vertex. Numerical predictions are presented in the form of a fitting formula as function of $M_Z, M_W, M_H, m_t$ and $\\Delta{\\alpha}$, ${\\alpha_{\\rm s}}$. For central input values, we obtain a relative correction of $\\Delta\\kappa_{\\rm b}^{(\\alpha^2,\\rm bos)} = -0.9855 \\times 10^{-4}$, amounting to about a quarter of the fermionic corrections, and corresponding to $\\sin^2\\theta_{\\rm eff}^{\\rm b} = 0.232704$. The integration of the corresponding two-loop vertex Feynman integrals with up to three dimensionless parameters in Minkowskian kinematics has been performed with two approaches: (i) Sector decomposition, implemented in the packages FIESTA 3 and SecDec 3, and (ii) Mellin-Barnes representations, implemented in AMBRE 3/MB and the new package MBnumerics.

  10. $K_{l4}$ at two-loops and CHPT predictions for $\\pi\\pi$-scattering

    CERN Document Server

    Amorós, G; Talavera, P; Amoros, Gabriel; Bijnens, Johan; Talavera, Pere

    2000-01-01

    We present the results from our two-loop calculations of masses, decay-constants, vacuum-expectation-values and the $K_{\\ell4}$ form-factors in three-flavour Chiral Perturbation Theory (CHPT). We use this to fit the $L_i^r$ to two-loops and discuss the ensuing predictions for $\\pi\\pi$-threshold parameters.

  11. Turbulent magnetic Prandtl number in kinematic magnetohydrodynamic turbulence: two-loop approximation.

    Science.gov (United States)

    Jurčišinová, E; Jurčišin, M; Remecký, R

    2011-10-01

    The turbulent magnetic Prandtl number in the framework of the kinematic magnetohydrodynamic (MHD) turbulence, where the magnetic field behaves as a passive vector field advected by the stochastic Navier-Stokes equation, is calculated by the field theoretic renormalization group technique in the two-loop approximation. It is shown that the two-loop corrections to the turbulent magnetic Prandtl number in the kinematic MHD turbulence are less than 2% of its leading order value (the one-loop value) and, at the same time, the two-loop turbulent magnetic Prandtl number is the same as the two-loop turbulent Prandtl number obtained in the corresponding model of a passively advected scalar field. The dependence of the turbulent magnetic Prandtl number on the spatial dimension d is investigated and the source of the smallness of the two-loop corrections for spatial dimension d=3 is identified and analyzed.

  12. Analytic Result for the Two-loop Six-point NMHV Amplitude in N = 4 Super Yang-Mills Theory

    Energy Technology Data Exchange (ETDEWEB)

    Dixon, Lance J.; /SLAC; Drummond, James M.; /CERN /Annecy, LAPTH; Henn, Johannes M.; /Humboldt U., Berlin /Princeton, Inst. Advanced Study

    2012-02-15

    We provide a simple analytic formula for the two-loop six-point ratio function of planar N = 4 super Yang-Mills theory. This result extends the analytic knowledge of multi-loop six-point amplitudes beyond those with maximal helicity violation. We make a natural ansatz for the symbols of the relevant functions appearing in the two-loop amplitude, and impose various consistency conditions, including symmetry, the absence of spurious poles, the correct collinear behavior, and agreement with the operator product expansion for light-like (super) Wilson loops. This information reduces the ansatz to a small number of relatively simple functions. In order to fix these parameters uniquely, we utilize an explicit representation of the amplitude in terms of loop integrals that can be evaluated analytically in various kinematic limits. The final compact analytic result is expressed in terms of classical polylogarithms, whose arguments are rational functions of the dual conformal cross-ratios, plus precisely two functions that are not of this type. One of the functions, the loop integral {Omega}{sup (2)}, also plays a key role in a new representation of the remainder function R{sub 6}{sup (2)} in the maximally helicity violating sector. Another interesting feature at two loops is the appearance of a new (parity odd) x (parity odd) sector of the amplitude, which is absent at one loop, and which is uniquely determined in a natural way in terms of the more familiar (parity even) x (parity even) part. The second non-polylogarithmic function, the loop integral {tilde {Omega}}{sup (2)}, characterizes this sector. Both {Omega}{sup (2)} and {tilde {Omega}}{sup (2)} can be expressed as one-dimensional integrals over classical polylogarithms with rational arguments.

  13. Analytic Result for the Two-loop Six-point NMHV Amplitude in N = 4 Super Yang-Mills Theory

    Energy Technology Data Exchange (ETDEWEB)

    Dixon, Lance J.; /SLAC; Drummond, James M.; /CERN /Annecy, LAPTH; Henn, Johannes M.; /Humboldt U., Berlin /Princeton, Inst. Advanced Study

    2012-02-15

    We provide a simple analytic formula for the two-loop six-point ratio function of planar N = 4 super Yang-Mills theory. This result extends the analytic knowledge of multi-loop six-point amplitudes beyond those with maximal helicity violation. We make a natural ansatz for the symbols of the relevant functions appearing in the two-loop amplitude, and impose various consistency conditions, including symmetry, the absence of spurious poles, the correct collinear behavior, and agreement with the operator product expansion for light-like (super) Wilson loops. This information reduces the ansatz to a small number of relatively simple functions. In order to fix these parameters uniquely, we utilize an explicit representation of the amplitude in terms of loop integrals that can be evaluated analytically in various kinematic limits. The final compact analytic result is expressed in terms of classical polylogarithms, whose arguments are rational functions of the dual conformal cross-ratios, plus precisely two functions that are not of this type. One of the functions, the loop integral {Omega}{sup (2)}, also plays a key role in a new representation of the remainder function R{sub 6}{sup (2)} in the maximally helicity violating sector. Another interesting feature at two loops is the appearance of a new (parity odd) x (parity odd) sector of the amplitude, which is absent at one loop, and which is uniquely determined in a natural way in terms of the more familiar (parity even) x (parity even) part. The second non-polylogarithmic function, the loop integral {tilde {Omega}}{sup (2)}, characterizes this sector. Both {Omega}{sup (2)} and {tilde {Omega}}{sup (2)} can be expressed as one-dimensional integrals over classical polylogarithms with rational arguments.

  14. The Two-Loop Six-Gluon MHV Amplitude in Maximally Supersymmetric Yang-Mills Theory

    CERN Document Server

    Bern, Z; Kosower, D A; Roiban, R; Spradlin, M; Vergu, C; Volovich, A

    2008-01-01

    We give a representation of the parity-even part of the planar two-loop six-gluon MHV amplitude of N=4 super-Yang-Mills theory, in terms of loop-momentum integrals with simple dual conformal properties. We evaluate the integrals numerically in order to test directly the ABDK/BDS all-loop ansatz for planar MHV amplitudes. We find that the ansatz requires an additive remainder function, in accord with previous indications from strong-coupling and Regge limits. The planar six-gluon amplitude can also be compared with the hexagonal Wilson loop computed by Drummond, Henn, Korchemsky and Sokatchev in arXiv:0803.1466 [hep-th]. After accounting for differing singularities and other constants independent of the kinematics, we find that the Wilson loop and MHV-amplitude remainders are identical, to within our numerical precision. This result provides non-trivial confirmation of a proposed n-point equivalence between Wilson loops and planar MHV amplitudes, and suggests that an additional mechanism besides dual conformal...

  15. Two-loop Prediction for Scaling Exponents in $(2 + \\epsilon)$-dimensional Quantum Gravity

    CERN Document Server

    Aida, T; Aida, Toshiaki; Kitazawa, Yoshihisa

    1996-01-01

    We perform the two loop level renormalization of quantum gravity in $2+\\epsilon$ dimensions. We work in the background gauge whose manifest covariance enables us to use the short distance expansion of the Green's functions. We explicitly show that the theory is renormalizable to the two loop level in our formalism. We further make a physical prediction for the scaling relation between the gravitational coupling constant and the cosmological constant which is expected to hold at the short distance fixed point of the renormalization group. It is found that the two loop level calculation is necessary to determine the scaling exponent to the leading order in $\\epsilon$.

  16. Two loop computation of a running coupling in lattice Yang-Mills theory

    CERN Document Server

    Narayanan, R A; Narayanan, Rajamani; Wolff, Ulli

    1995-01-01

    We compute the two loop coefficient in the relation between the lattice bare coupling and the running coupling defined through the Schroedinger functional for the case of pure SU(2) gauge theory. This result is needed as one computational component to relate the latter to the MSbar-coupling, and it allows us to implement O(a) improvement of the Schroedinger functional to two-loop order. In addition, the two-loop beta-function is verified in a perturbative computation on the lattice, and the behavior of an improved bare coupling is investigated beyond one loop.

  17. Two-loop anomalous dimensions of heavy baryon currents in heavy quark effective theory

    CERN Document Server

    Groote, S; Yakovlev, O I

    1996-01-01

    We present results on the two-loop anomalous dimensions of the heavy baryon HQET currents J=(q^TC\\Gamma\\tau q)\\Gamma'Q with arbitrary Dirac matrices \\Gamma and \\Gamma'. From our general result we obtain the two-loop anomalous dimensions for currents with quantum numbers of the ground state heavy baryons \\Lambda_Q, \\Sigma_Q and \\Sigma_Q^*. As a by-product of our calculation and as an additional check we rederive the known two-loop anomalous dimensions of mesonic scalar, pseudoscalar, vector, axial vector and tensor currents (J=\\bar q\\Gamma q) in massless QCD as well as in HQET.

  18. Algorithmic calculation of two-loop Feynman diagrams

    CERN Document Server

    Fleischer, J; Fleischer, J; Tarasov, O V

    1995-01-01

    In a recent paper \\cite{ft} a new powerful method to calculate Feynman diagrams was proposed. It consists in setting up a Taylor series expansion in the external momenta squared. The Taylor coefficients are obtained from the original diagram by differentiation and putting the external momenta equal to zero. It was demonstrated that by a certain conformal mapping and subsequent resummation by means of Pad\\'{e} approximants it is possible to obtain high precision numerical values of the Feynman integrals in the whole cut plane. The real problem in this approach is the calculation of the Taylor coefficients for the arbitrary mass case. Since their analytic evaluation by means of CA packages uses enormous CPU and yields very lengthy expressions, we develop an algorithm with the aim to set up a FORTRAN package for their numerical evaluation. This development is guided by the possibilities offered by the formulae manipulating language FORM \\cite{FORM}.

  19. The two-loop helicity amplitudes for $gg \\to V_1 V_2 \\to 4~\\mathrm{leptons}$

    CERN Document Server

    von Manteuffel, Andreas

    2015-01-01

    We compute the two-loop massless QCD corrections to the helicity amplitudes for the production of two electroweak gauge bosons in the gluon fusion channel, $gg \\to V_1 V_2$, keeping the virtuality of the vector bosons $V_1$ and $V_2$ arbitrary and taking their decays into leptons into account. The amplitudes are expressed in terms of master integrals, whose representation has been optimised for fast and reliable numerical evaluation. We provide analytical results and a public C++ code for their numerical evaluation on HepForge at http://vvamp.hepforge.org .

  20. A Two-loop Test of Buscher's T-duality, 1

    CERN Document Server

    Horváth, Z; Palla, L; Horvath, Zalan; Karp, Robert L.; Palla, Laszlo

    2000-01-01

    We study the two loop quantum equivalence of sigma models related by Buscher's T-duality transformation. The computation of the two loop perturbative free energy density is performed in the case of a certain deformation of the SU(2) principal sigma model, and its T-dual, using dimensional regularization and the geometric sigma model perturbation theory. We obtain agreement between the free energy density expressions of the two models.

  1. Two-Loop Beam and Soft Functions for Rapidity-Dependent Jet Vetoes

    CERN Document Server

    Gangal, Shireen; Stahlhofen, Maximilian; Tackmann, Frank J

    2016-01-01

    Jet vetoes play an important role in many analyses at the LHC. Traditionally, jet vetoes have been imposed using a restriction on the transverse momentum $p_{Tj}$ of jets. Alternatively, one can also consider jet observables for which $p_{Tj}$ is weighted by a smooth function of the jet rapidity $y_j$ that vanishes as $|y_j| \\to \\infty$. Such observables are useful as they provide a natural way to impose a tight veto on central jets but a looser one at forward rapidities. We consider two such rapidity-dependent jet veto observables, $\\mathcal{T}_{Bj}$ and $\\mathcal{T}_{Cj}$, and compute the required beam and dijet soft functions for the jet-vetoed color-singlet production cross section at two loops. At this order, clustering effects from the jet algorithm become important. The dominant contributions are computed fully analytically while corrections that are subleading in the limit of small jet radii are expressed in terms of finite numerical integrals. Our results enable the full NNLL' resummation and are an ...

  2. Graviton self-energy from worldlines

    CERN Document Server

    Bastianelli, Fiorenzo

    2015-01-01

    Worldline approaches, when available, often simplify and make more efficient the calculation of various observables in quantum field theories. In this contribution we first review the calculation of the graviton self-energy due to a loop of virtual particles of spin 0, 1/2 and 1, all of which have a well-known worldline description. For the case of the graviton itself, an elegant worldline description is still missing, though one can still describe it by constructing a worldline representation of the differential operators that arise in the quadratic approximation of the Einstein-Hilbert action. We have recently analyzed the latter approach, and we use it here to calculate the one-loop graviton self energy due to the graviton itself in this formalism.

  3. Two-loop electroweak threshold corrections to the bottom and top Yukawa couplings

    CERN Document Server

    Kniehl, Bernd A

    2014-01-01

    We study the relationship between the MS-bar Yukawa coupling and the pole mass for the bottom and top quarks at the two-loop electroweak order O(alpha^2) in the gaugeless limit of the standard model. We also consider the MS-bar to pole mass relationships at this order, which include tadpole contributions to ensure the gauge independence of the MS-bar masses. In order to avoid the presence of tadpoles, we propose a redefinition of the running heavy-quark mass in terms of the MS-bar Yukawa coupling. We also present Delta r in the MS-bar scheme at O(alpha^2) in the gaugeless limit. As an aside, we also present the exact two-loop expression for the heavy-quark mass counterterm at two loops.

  4. FDR, an easier way to NNLO calculations: a two-loop case study

    CERN Document Server

    Donati, Alice Maria

    2013-01-01

    In this paper we advertise the important simplifications produced by FDR in NNLO computations. We show that - due to its four-dimensionality - FDR does not require an order-by-order renormalization and that, unlike the one-loop case, FDR and dimensional regularization (DR) generate intermediate two-loop results which are no longer linked by a simple subtraction of the ultraviolet (UV) poles in epsilon. As an illustrative example, we re-derive the known two-loop result for H -> gamma gamma mediated by an infinitely heavy top loop in the presence of gluonic corrections. The calculation establishes FDR as a simpler and fully consistent approach to the UV problem at the two-loop level, that, in turn, is an essential ingredient toward purely numerical NNLO calculations.

  5. Two-loop renormalization of scalar and pseudoscalar fermion bilinears on the lattice

    Science.gov (United States)

    Skouroupathis, A.; Panagopoulos, H.

    2007-11-01

    We compute the two-loop renormalization functions, in the RI' scheme, of local bilinear quark operators ψ¯Γψ, where Γ denotes the scalar and pseudoscalar Dirac matrices, in the lattice formulation of QCD. We consider both the flavor nonsinglet and singlet operators; the latter, in the scalar case, leads directly to the two-loop fermion mass renormalization, Zm. As a prerequisite for the above, we also compute the quark field renormalization, Zψ, up to two loops. We use the clover action for fermions and the Wilson action for gluons. Our results are given as a polynomial in cSW, in terms of both the renormalized and bare coupling constants, in the renormalized Feynman gauge. We also confirm the one-loop renormalization functions, for generic gauge. Finally, we present our results in the MS¯ scheme, for easier comparison with calculations in the continuum. The corresponding results, for fermions in an arbitrary representation, are included in the Appendix.

  6. Two-loop renormalization of scalar and pseudoscalar fermion bilinears on the lattice

    CERN Document Server

    Skouroupathis, A

    2007-01-01

    We compute the two-loop renormalization functions, in the RI $^\\prime$ scheme, of local bilinear quark operators $\\bar{\\psi}\\Gamma\\psi$, where $\\Gamma$ denotes the Scalar and Pseudoscalar Dirac matrices, in the lattice formulation of QCD. We consider both the flavor non-singlet and singlet operators; the latter, in the scalar case, leads directly to the two-loop fermion mass renormalization, $Z_m$. As a prerequisite for the above, we also compute the quark field renormalization, $Z_{\\psi}$, up to two loops. We use the clover action for fermions and the Wilson action for gluons. Our results are given as a polynomial in $c_{SW}$, in terms of both the renormalized and bare coupling constant, in the renormalized Feynman gauge. We also confirm the 1-loop renormalization functions, for generic gauge. Finally, we present our results in the $\\bar{MS}$ scheme, for easier comparison with calculations in the continuum.

  7. Two-loop renormalization in the standard model, part I. Prolegomena

    Energy Technology Data Exchange (ETDEWEB)

    Actis, S. [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany); Ferroglia, A. [Albert-Ludwigs-Univ., Freiburg (Germany). Fakultat fur Phys.]|[Zuerich Univ. (Switzerland). Inst. fuer Theoretische Physik; Passera, M. [Padua Univ. (Italy). Dipt. di Fisica]|[INFN, Sezione di Padova (Italy); Passarino, G. [Torino Univ. (Italy). Dipt. di Fisica Teorica]|[INFN, Sezione di Torino (Italy)

    2006-12-15

    In this paper the building blocks for the two-loop renormalization of the Standard Model are introduced with a comprehensive discussion of the special vertices induced in the Lagrangian by a particular diagonalization of the neutral sector and by two alternative treatments of the Higgs tadpoles. Dyson resummed propagators for the gauge bosons are derived, and two-loop Ward-Slavnov-Taylor identities are discussed. In part II, the complete set of counterterms needed for the two-loop renormalization will be derived. In part III, a renormalization scheme will be introduced, connecting the renormalized quantities to an input parameter set of (pseudo-)experimental data, critically discussing renormalization of a gauge theory with unstable particles. (orig.)

  8. Neural-network-based two-loop control of robotic manipulators including actuator dynamics in task space

    Institute of Scientific and Technical Information of China (English)

    Liangyong WANG; Tianyou CHAI; Zheng FANG

    2009-01-01

    A neural-network-based motion controller in task space is presented in this paper. The proposed controller is addressed as a two-loop cascade control scheme. The outer loop is given by kinematic control in the task space. It provides a joint velocity reference signal to the inner one. The inner loop implements a velocity servo loop at the robot joint level. A radial basis function network (RBFN) is integrated with proportional-integral (PI) control to construct a velocity tracking control scheme for the inner loop. Finally, a prototype technology based control system is designed for a robotic manipulator. The proposed control scheme is applied to the robotic manipulator. Experimental results confirm the validity of the proposed control scheme by comparing it with other control strategies.

  9. Two-loop QCD Correction to Massive Spin-2 Resonance $ \\to q ~ \\bar{q} ~ g $

    CERN Document Server

    Ahmed, Taushif; Mathews, Prakash; Rana, Narayan; Ravindran, V

    2016-01-01

    Two-loop QCD correction to massive spin-2 Graviton decaying to $q ~ + ~ \\bar{q}~ + ~g$ is presented considering a generic universal spin-2 coupling to the SM through the conserved energy-momentum tensor. Such a massive spin-2 particle can arise in extra-dimensional models. The ultraviolet and infrared structure of the QCD amplitudes are studied. In dimensional regularisation, the infrared pole structure is in agreement with Catani's proposal, confirming the universal factorization property of QCD amplitudes, even with the spin-2 tensorial coupling. This computation now completes the full two-loop QCD corrections for the production of a spin-2 in association with a jet.

  10. The Vector and Scalar Form Factors of the Pion to Two Loops

    CERN Document Server

    Bijnens, J; Talavera, P

    1998-01-01

    We calculate the vector and scalar form factors of the pion to two loops in Chiral Perturbation Theory. We estimate the unknown O(p^6) constants using resonance exchange. We make a careful comparison to the available data and determine two O(p^4) constants rather precisely, and two O(p^6) constants less precisely. We also use Chiral Perturbation Theory to two loops to extract in a model--independent manner the charge radius of the pion from the available data, and obtain \\rpiV=0.437\\pm 0.016 fm^2.

  11. Two loop effective Kähler potential of (non-)renormalizable supersymmetric models

    CERN Document Server

    Nibbelink, S G; Nibbelink, Stefan Groot; Nyawelo, Tino S.

    2006-01-01

    We perform a supergraph computation of the effective Kaehler potential at one and two loops for general four dimensional N=1 supersymmetric theories described by arbitrary Kaehler potential, superpotential and gauge kinetic function. We only insist on gauge invariance of the Kaehler potential and the superpotential as we heavily rely on its consequences in the quantum theory. However, we do not require gauge invariance for the gauge kinetic functions, so that our results can also be applied to anomalous theories that involve the Green-Schwarz mechanism. We illustrate our two loop results by considering a few simple models: the (non-)renormalizable Wess-Zumino model and Super Quantum Electrodynamics.

  12. The Inverse Amplitude Method in $\\pi\\pi$ Scattering in Chiral Perturbation Theory to Two Loops

    CERN Document Server

    Nieves, J; Ruiz-Arriola, E

    2002-01-01

    The inverse amplitude method is used to unitarize the two loop $\\pi\\pi$ scattering amplitudes of SU(2) Chiral Perturbation Theory in the $I=0,J=0$, $I=1,J=1$ and $I=2,J=0$ channels. An error analysis in terms of the low energy one-loop parameters $\\bar l_{1,2,3,4,}$ and existing experimental data is undertaken. A comparison to standard resonance saturation values for the two loop coefficients $\\bar b_{1,2,3,4,5,6} $ is also carried out. Crossing violations are quantified and the convergence of the expansion is discussed.

  13. RegPT: Direct and fast calculation of regularized cosmological power spectrum at two-loop order

    CERN Document Server

    Taruya, Atsushi; Nishimichi, Takahiro; Codis, Sandrine

    2012-01-01

    We present a specific prescription for the calculation of cosmological power spectra, exploited here at two-loop order in perturbation theory (PT), based on the multi-point propagator expansion. In this approach power spectra are constructed from the regularized expressions of the propagators that reproduce both the resummed behavior in the high-k limit and the standard PT results at low-k. With the help of N-body simulations, we show that such a construction gives robust and accurate predictions for both the density power spectrum and the correlation function at percent-level in the weakly non-linear regime. We then present an algorithm that allows accelerated evaluations of all the required diagrams by reducing the computational tasks to one-dimensional integrals. This is achieved by means of pre-computed kernel sets defined for appropriately chosen fiducial models. The computational time for two-loop results is then reduced from a few minutes, with the direct method, to a few seconds with the fast one. The...

  14. Two-loop controller for maximizing performance of a grid-connected photovoltaic - fuel cell hybrid power plant

    Science.gov (United States)

    Ro, Kyoungsoo

    The study started with the requirement that a photovoltaic (PV) power source should be integrated with other supplementary power sources whether it operates in a stand-alone or grid-connected mode. First, fuel cells for a backup of varying PV power were compared in detail with batteries and were found to have more operational benefits. Next, maximizing performance of a grid-connected PV-fuel cell hybrid system by use of a two-loop controller was discussed. One loop is a neural network controller for maximum power point tracking, which extracts maximum available solar power from PV arrays under varying conditions of insolation, temperature, and system load. A real/reactive power controller (RRPC) is the other loop. The RRPC meets the system's requirement for real and reactive powers by controlling incoming fuel to fuel cell stacks as well as switching control signals to a power conditioning subsystem. The RRPC is able to achieve more versatile control of real/reactive powers than the conventional power sources since the hybrid power plant does not contain any rotating mass. Results of time-domain simulations prove not only effectiveness of the proposed computer models of the two-loop controller, but also their applicability for use in transient stability analysis of the hybrid power plant. Finally, environmental evaluation of the proposed hybrid plant was made in terms of plant's land requirement and lifetime COsb2 emissions, and then compared with that of the conventional fossil-fuel power generating forms.

  15. Renormalization of two-loop diagrams in scalar lattice field theory

    CERN Document Server

    Borasoy, B

    2006-01-01

    We present a method to calculate to very high precision the coefficients of the divergences occuring in two-loop diagrams for a massive scalar field on the lattice. The approach is based on coordinate space techniques and extensive use of the precisely known Green's function.

  16. Exact Combinatorics of Bern-Kosower-type Amplitudes for Two-Loop $\\Phi^{3}$ Theory

    CERN Document Server

    Sato, H T; Sato, Haru-Tada; Schmidt, Michael G.

    1998-01-01

    Counting the contribution rate of a world-line formula to Feynman diagrams in Bern-Kosower-like amplitudes derived from a bosonic string theory for $N$-point two-loop Feynman amplitudes. In this connection we also present a method to derive simple and compact world-line forms for the effective action.

  17. Two-loop scale-invariant scalar potential and quantum effective operators

    Energy Technology Data Exchange (ETDEWEB)

    Ghilencea, D.M. [National Institute of Physics and Nuclear Engineering (IFIN-HH), Theoretical Physics Department, Bucharest (Romania); CERN, Theory Division, Geneva 23 (Switzerland); Lalak, Z.; Olszewski, P. [University of Warsaw, Faculty of Physics, Institute of Theoretical Physics, Warsaw (Poland)

    2016-12-15

    Spontaneous breaking of quantum scale invariance may provide a solution to the hierarchy and cosmological constant problems. In a scale-invariant regularization, we compute the two-loop potential of a Higgs-like scalar φ in theories in which scale symmetry is broken only spontaneously by the dilaton (σ). Its VEV left angle σ right angle generates the DR subtraction scale (μ ∝ left angle σ right angle), which avoids the explicit scale symmetry breaking by traditional regularizations (where μ = fixed scale). The two-loop potential contains effective operators of non-polynomial nature as well as new corrections, beyond those obtained with explicit breaking (μ = fixed scale). These operators have the form φ{sup 6}/σ{sup 2}, φ{sup 8}/σ{sup 4}, etc., which generate an infinite series of higher dimensional polynomial operators upon expansion about left angle σ right angle >> left angle φ right angle, where such hierarchy is arranged by one initial, classical tuning. These operators emerge at the quantum level from evanescent interactions (∝ ε) between σ and φ that vanish in d = 4 but are required by classical scale invariance in d = 4 - 2ε. The Callan-Symanzik equation of the two-loop potential is respected and the two-loop beta functions of the couplings differ from those of the same theory regularized with μ = fixed scale. Therefore the running of the couplings enables one to distinguish between spontaneous and explicit scale symmetry breaking. (orig.)

  18. The two-loop six-point amplitude in ABJM theory

    CERN Document Server

    Huang, Yu-tin

    2012-01-01

    In this paper we present the first analytic computation of the six-point two-loop amplitude of ABJM theory. We show that the two-loop amplitude consist of corrections proportional to two distinct local Yangian invariants which can be identified as the tree- and the one-loop amplitude respectively. The two-loop correction proportional to the tree-amplitude is identical to the one-loop BDS result of N=4 SYM plus an additional remainder function, while the correction proportional to the one-loop amplitude is finite. Both the remainder and the finite correction are dual conformal invariant, which implies that the two-loop dual conformal anomaly equation for ABJM is again identical to that of one-loop N=4 SYM, as was first observed at four-point. We discuss the theory on the Higgs branch, showing that its amplitudes are infrared finite, but equal, in the small mass limit, to those obtained in dimensional regularization.

  19. Two-loop Bhabha scattering at high energy beyond leading power approximation

    Directory of Open Access Journals (Sweden)

    Alexander A. Penin

    2016-09-01

    Full Text Available We evaluate the two-loop O(me2/s contribution to the wide-angle high-energy electron–positron scattering in the double-logarithmic approximation. The origin and the general structure of the power-suppressed double logarithmic corrections are discussed in detail.

  20. Atomic orbital self-energy and electronegativity

    CERN Document Server

    Ribeiro, Mauro

    2016-01-01

    In this work, atomic calculations were performed within the local-density and generalized-gradient approximations of exchange and correlation density functionals within density-functional theory to provide accurate periodic trends of first ionization energies and electron affinities of the atomic series from hydrogen to xenon. Electronegativities were determined directly from Mulliken's formula and were shown to be equivalently calculated rather by using Slater-Janak's transition state or by calculating the electrostatic self-energies of the orbitals involved in the transition to ions. Finally, comparisons were made with other theoretical and experimental results, including Mulliken-Jaff\\'e's electronegativity scale.

  1. PyR@TE 2: A Python tool for computing RGEs at two-loop

    Science.gov (United States)

    Lyonnet, F.; Schienbein, I.

    2017-04-01

    Renormalization group equations are an essential tool for the description of theories across different energy scales. Even though their expressions at two-loop for an arbitrary gauge field theory have been known for more than thirty years, deriving the full set of equations for a given model by hand is very challenging and prone to errors. To tackle this issue, we have introduced in Lyonnet et al. (2014) a Python tool called PyR@TE; Python Renormalization group equations @ Two-loop for Everyone. With PyR@TE, it is easy to implement a given Lagrangian and derive the complete set of two-loop RGEs for all the parameters of the theory. In this paper, we present the new version of this code, PyR@TE 2, which brings many new features and in particular it incorporates kinetic mixing when several U(1) gauge groups are involved. In addition, the group theory part has been greatly improved as we introduced a new Python module dubbed PyLie that deals with all the group theoretical aspects required for the calculation of the RGEs as well as providing very useful model building capabilities. This allows the use of any irreducible representation of the SU(n) , SO(2 n) and SO(2n + 1) groups. Furthermore, it is now possible to implement terms in the Lagrangian involving fields which can be contracted into gauge singlets in more than one way. As a byproduct, results for a popular model (SM + complex triplet) for which, to our knowledge, the complete set of two-loop RGEs has not been calculated before are presented in this paper. Finally, the two-loop RGEs for the anomalous dimension of the scalar and fermion fields have been implemented as well. It is now possible to export the coupled system of beta functions into a numerical C++ function, leading to a consequent speed up in solving them.

  2. Two loop electroweak corrections from heavy fermions to b→s+γ

    Institute of Scientific and Technical Information of China (English)

    YANG Xiu-Yi; FENG Tai-Fu

    2010-01-01

    Applying an effective Lagrangian method and an on-shell scheme, we analyze the electroweak corrections to the rare decay b→, s+γ from some special two loop diagrams in which a closed heavy fermion loop is attached to the virtual charged gauge bosons or Higgs. At the decoupling limit where the virtual fermions in the inner loop are much heavier than the electroweak scale, we verify the final results satisfying the decoupling theorem explicitly when the interactions among Higgs and heavy fermions do not contain the nondecoupling couplings. Adopting the universal assumptions on the relevant couplings and mass spectrum of new physics, we find that the relative corrections from those two loop diagrams to the SM theoretical prediction on the branching ratio of B → Xsγ can reach 5% as the energy scale of new physics ANp=200 GeV.

  3. BPS Wilson loops and Bremsstrahlung function in ABJ(M): a two loop analysis

    Energy Technology Data Exchange (ETDEWEB)

    Bianchi, Marco S. [Institut für Physik, Humboldt-Universität zu Berlin,Newtonstraße 15, 12489 Berlin (Germany); Griguolo, Luca [Dipartimento di Fisica e Scienze della Terra, Università di Parmaand INFN Gruppo Collegato di Parma,Viale G.P. Usberti 7/A, 43100 Parma (Italy); Leoni, Matias [Physics Department, FCEyN-UBA & IFIBA-CONICETCiudad Universitaria, Pabellón I, 1428, Buenos Aires (Argentina); Penati, Silvia [Dipartimento di Fisica, Università di Milano-Bicoccaand INFN, Sezione di Milano-Bicocca,Piazza della Scienza 3, I-20126 Milano (Italy); Seminara, Domenico [Dipartimento di Fisica, Università di Firenzeand INFN Sezione di Firenze,via G. Sansone 1, 50019 Sesto Fiorentino (Italy)

    2014-06-19

    We study a family of circular BPS Wilson loops in N=6 super Chern-Simons-matter theories, generalizing the usual 1/2-BPS circle. The scalar and fermionic couplings depend on two deformation parameters and these operators can be considered as the ABJ(M) counterpart of the DGRT latitudes defined in N=4 SYM. We perform a complete two-loop analysis of their vacuum expectation value, discuss the appearance of framing-like phases and propose a general relation with cohomologically equivalent bosonic operators. We make an all-loop proposal for computing the Bremsstrahlung function associated to the 1/2-BPS cusp in terms of these generalized Wilson loops. When applied to our two-loop result it reproduces the known expression. Finally, we comment on the generalization of this proposal to the bosonic 1/6-BPS case.

  4. The muon magnetic moment in the 2HDM: complete two-loop result

    Science.gov (United States)

    Cherchiglia, Adriano; Kneschke, Patrick; Stöckinger, Dominik; Stöckinger-Kim, Hyejung

    2017-01-01

    We study the 2HDM contribution to the muon anomalous magnetic moment a μ and present the complete two-loop result, particularly for the bosonic contribution. We focus on the Aligned 2HDM, which has general Yukawa couplings and contains the type I, II, X, Y models as special cases. The result is expressed with physical parameters: three Higgs boson masses, Yukawa couplings, two mixing angles, and one quartic potential parameter. We show that the result can be split into several parts, each of which has a simple parameter dependence, and we document their general behavior. Taking into account constraints on parameters, we find that the full 2HDM contribution to a μ can accommodate the current experimental value, and the complete two-loop bosonic contribution can amount to (2⋯4) × 10-10, more than the future experimental uncertainty.

  5. Hard Photon production from unsaturated quark gluon plasma at two loop level

    CERN Document Server

    Dutta, D; Mohanty, A K; Kumar, K; Choudhury, R K

    2002-01-01

    The hard photon productions from bremsstrahlung and annihilation with scattering that arise at two loop level are estimated from a chemically non-equilibrated quark gluon plasma using the frame work of thermal field theory. Although, the rate of photon production is suppressed due to unsaturated phase space, the above suppression is relatively smaller than expected due to an additional collinear enhancement (arise due to decrease in thermal quark mass) as compared to it's equilibrium counterpart. Interestingly, unlike the one loop case, the reduction in the two loop processes are found to be independent of gluon chemical poential, but strongly depends on quark fugacity. It is also found that, since the phase space suppression is highest for annihilation with scattering, the photon production is entirely dominated by bremsstrahlung mechanism at all energies. This is to be contrasted with the case of the equilibrated plasma where annihilation with scattering dominates the photon production particularly at highe...

  6. Hard photon production from unsaturated quark-gluon plasma at two-loop level

    Energy Technology Data Exchange (ETDEWEB)

    Dutta, D. E-mail: ddutta@apsara.barc.ernet.in; Sastry, S.V.S.; Mohanty, A.K.; Kumar, K

    2002-11-18

    The hard photon production from bremsstrahlung and annihilation with scattering that arise at two-loop level are estimated for a chemically non-equilibrated quark-gluon plasma in the framework of Hard Thermal Loop (HTL) resummed effective field theory. The rate of photon production is found to be suppressed due to unsaturated phase space compared to equilibrated plasma. For an unsaturated plasma, unlike the effective one-loop case, the reduction in the effective two-loop processes is found to be independent of gluon fugacity, due to an additional collinear enhancement arising from the decrease in thermal quark mass but strongly depends on quark and antiquark fugacities. It is also found that the photon production is dominated by bremsstrahlung mechanism, since the phase space suppression is higher for annihilation with scattering, in contrast to the equilibrated plasma where annihilation with scattering dominates the photon production.

  7. Local Integrand Representations of All Two-Loop Amplitudes in Planar SYM

    CERN Document Server

    Bourjaily, Jacob L

    2015-01-01

    We use generalized unitarity at the integrand-level to directly construct local, manifestly dual-conformally invariant formulae for all two-loop scattering amplitudes in planar, maximally supersymmetric Yang-Mills theory (SYM). This representation separates contributions into manifestly finite and manifestly divergent terms---in a way that renders all infrared-safe observables (including ratio functions) calculable without any need for regulation. These results perfectly match the all-loop BCFW recursion relations, to which we provide a closed-form solution valid through two-loop-order. Finally, we describe and document a Mathematica package which implements these results, available as part of this work's source files on the arXiv.

  8. Two-loop renormalization in the standard model, part III. Renormalization equations and their solutions

    Energy Technology Data Exchange (ETDEWEB)

    Actis, S. [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany); Passarino, G. [Torino Univ. (Italy). Dipt. di Fisica Teorica; INFN, Sezione di Torino (Italy)

    2006-12-15

    In part I and II of this series of papers all elements have been introduced to extend, to two loops, the set of renormalization procedures which are needed in describing the properties of a spontaneously broken gauge theory. In this paper, the final step is undertaken and finite renormalization is discussed. Two-loop renormalization equations are introduced and their solutions discussed within the context of the minimal standard model of fundamental interactions. These equations relate renormalized Lagrangian parameters (couplings and masses) to some input parameter set containing physical (pseudo-)observables. Complex poles for unstable gauge and Higgs bosons are used and a consistent setup is constructed for extending the predictivity of the theory from the Lep1 Z-boson scale (or the Lep2 WW scale) to regions of interest for LHC and ILC physics. (orig.)

  9. On the impact of kinetic mixing in beta functions at two-loop

    CERN Document Server

    Lyonnet, Florian

    2016-01-01

    Kinetic mixing is a fundamental property of models with a gauge symmetry involving several $\\mathrm{U}(1)$ group factors. In this paper, we perform a numerical study of the impact of kinetic mixing on beta functions at two-loop. To do so, we use the recently published PyR@TE 2 software to derive the complete set of RGEs of the SM B-L model at two-loop including kinetic mixing. We show that it is important to properly account for kinetic mixing as the evolution of the parameters with the energy scale can change drastically. In some cases, these modifications can even lead to a different conclusion regarding the stability of the scalar potential.

  10. The muon magnetic moment in the ${\\rm{2HDM}}$: complete two-loop result

    CERN Document Server

    Cherchiglia, Adriano; Stöckinger, Dominik; Stöckinger-Kim, Hyejung

    2016-01-01

    We study the ${\\rm{2HDM}}$ contribution to the muon anomalous magnetic moment $a_\\mu$ and present the complete two-loop result, particularly for the bosonic contribution. We focus on the Aligned ${\\rm{2HDM}}$, which has general Yukawa coupling constants and is more general than the type I, II, X, Y models. The result is expressed with physical parameters: three Higgs boson masses, Yukawa couplings, two mixing angles, and one quartic potential parameter. We show that the result can be split into several parts, each of which has a simple parameter dependence, and we document the general behavior. Taking into account constraints on parameters, we find that the full ${\\rm{2HDM}}$ contribution to $a_\\mu$ can accommodate the current experimental value, and the complete two-loop bosonic result contribution can amount to $(2\\cdots 4)\\times 10^{-10}$, more than the future experimental uncertainty.

  11. Higgs boson couplings to bottom quarks: two-loop supersymmetry-QCD corrections.

    Science.gov (United States)

    Noth, David; Spira, Michael

    2008-10-31

    We present two-loop supersymmetry (SUSY) QCD corrections to the effective bottom Yukawa couplings within the minimal supersymmetric extension of the standard model (MSSM). The effective Yukawa couplings include the resummation of the nondecoupling corrections Deltam_{b} for large values of tanbeta. We have derived the two-loop SUSY-QCD corrections to the leading SUSY-QCD and top-quark-induced SUSY-electroweak contributions to Deltam_{b}. The scale dependence of the resummed Yukawa couplings is reduced from O(10%) to the percent level. These results reduce the theoretical uncertainties of the MSSM Higgs branching ratios to the accuracy which can be achieved at a future linear e;{+}e;{-} collider.

  12. Two Loop Radiative Seesaw and X-ray line Dark Matter with Global U(1) Symmetry

    CERN Document Server

    Okada, Hiroshi

    2015-01-01

    We study a two loop induced radiative neutrino model with global $U(1)$ symmetry at 0.1 GeV scale, in which we consider a keV scale of dark matter candidate recently reported by XMN-Newton X-ray observatory using data of various galaxy clusters and Andromeda galaxy. We also discuss the vacuum stability of singly charged bosons, lepton flavor violation processes, and a role of Goldstone boson.

  13. Two-loop gg → Hg amplitude mediated by a nearly massless quark

    Science.gov (United States)

    Melnikov, Kirill; Tancredi, Lorenzo; Wever, Christopher

    2016-11-01

    We analytically compute the two-loop scattering amplitude gg → Hg assuming that the mass of the quark, that mediates the ggH interaction, is vanishingly small. Our computation provides an important ingredient required to improve the theoretical description of the top-bottom interference effect in Higgs boson production in gluon fusion, and to elucidate its impact on the Higgs boson transverse momentum distribution.

  14. New results for a two-loop massless propagator-type Feynman diagram

    CERN Document Server

    Kotikov, A V

    2016-01-01

    We consider the two-loop massless propagator-type Feynman diagram with an arbitrary (non-integer) index on the central line. We analytically prove the equality of the two well-known results existing in the literature which express this diagram in terms of ${}_3F_2$-hypergeometric functions of argument $-1$ and $1$, respectively. We also derive new representations for this diagram which may be of importance in practical calculations.

  15. Two-loop current-current operator contribution to the non-leptonic QCD penguin amplitude

    CERN Document Server

    Bell, Guido; Huber, Tobias; Li, Xin-Qiang

    2015-01-01

    The computation of direct CP asymmetries in charmless B decays at next-to-next-to-leading order (NNLO) in QCD is of interest to ascertain the short-distance contribution. Here we compute the two-loop penguin contractions of the current-current operators Q_{1,2} and provide a first estimate of NNLO CP asymmetries in penguin-dominated b -> s transitions.

  16. Brief description of the flavor-changing neutral scalar interactions at two-loop level

    CERN Document Server

    Gaitán, R

    2016-01-01

    In this letter we show a general description about flavor-changing neutral currents (FCNC) mediated by scalars. The analysis is extended at two-loop level for the Two-Higgs Doublet Model type-III because others models have strong constraints on its parameters, even at high orders of the perturbation. For this letter we focus on the standard model, calculating the amplitude for the $h \\to \\gamma \\gamma$ process and discussing the results briefly.

  17. Brief description of the flavor-changing neutral scalar interactions at two-loop level

    Science.gov (United States)

    Gaitán, R.; Orduz-Ducuara, J. A.

    2016-10-01

    In this letter we show a general description about flavor-changing neutral currents (FCNC) mediated by scalars. The analysis is extended at two-loop level for the Two-Higgs Doublet Model type-III because others models have strong constraints on its parameters, even at high orders of the perturbation. For this letter we focus on the standard model, calculating the amplitude for the h→γγ process and discussing the results briefly.

  18. Modeling and Simulation of Release of Radiation in Flow Blockage Accident for Two Loops PWR

    OpenAIRE

    Khurram Mehboob; Cao Xinrong; Majid Ali

    2012-01-01

    In this study modeling and simulation of release of radiation form two loops PWR has been carried out for flow blockage accident. For this purpose, a MATLAB based program “Source Term Evaluator for Flow Blockage Accident” (STEFBA) has been developed, which uses the core inventory as its primary input. The TMI-2 reactor is considered as the reference plant for this study. For 1100 reactor operation days, the core inventory has been evaluated under the core design constrains at average reactor ...

  19. Two-loop anomalous dimensions for currents of baryons with two heavy quarks in NRQCD

    CERN Document Server

    Kiselev, V V

    1998-01-01

    We present analytical results on the two-loop anomalous dimensions of currents for baryons, containing two heavy quarks $J = [Q^{iT}C\\Gamma\\tau Q^j]\\Gamma' q^k\\epsilon_{ijk}$ with arbitrary Dirac matrices $\\Gamma$ and velocity of heavy quarks and the inverse heavy quark mass. It is shown, that in this approximation the anomalous dimensions do not depend on the Dirac structure of the current under consideration.

  20. Two-loop $gg \\to Hg$ amplitude mediated by a nearly massless quark

    CERN Document Server

    Melnikov, Kirill; Wever, Christopher

    2016-01-01

    We analytically compute the two-loop scattering amplitude $gg \\to Hg$ assuming that the mass of the quark, that mediates the ggH interaction, is vanishingly small. Our computation provides an important ingredient required to improve the theoretical description of the top-bottom interference effect in Higgs boson production in gluon fusion, and to elucidate its impact on the Higgs boson transverse momentum distribution.

  1. Two-loop Feynman Diagrams in Yang-Mills Theory from Bosonic String Amplitudes

    CERN Document Server

    Körs, B; Kors, Boris; Schmidt, Michael G.

    2000-01-01

    We present intermediate results of an ongoing investigation which attempts a generalization of the well known one-loop Bern Kosower rules of Yang-Mills theory to higher loop orders. We set up a general procedure to extract the field theoretical limit of bosonic open string diagrams, based on the sewing construction of higher loop world sheets. It is tested with one- and two-loop scalar field theory, as well as one-loop and two-loop vacuum Yang-Mills diagrams, reproducing earlier results. It is then applied to two-loop two-point Yang-Mills diagrams in order to extract universal renormalization coefficients that can be compared to field theory. While developing numerous technical tools to compute the relevant contributions, we hit upon important conceptual questions: Do string diagrams reproduce Yang-Mills Feynman diagrams in a certain preferred gauge? Do they employ a certain preferred renormalization scheme? Are four gluon vertices related to three gluon vertices? Unfortunately, our investigations remained in...

  2. Turbulent magnetic Prandtl number in helical kinematic magnetohydrodynamic turbulence: two-loop renormalization group result.

    Science.gov (United States)

    Jurčišinová, E; Jurčišin, M; Remecký, R; Zalom, P

    2013-04-01

    Using the field theoretic renormalization group technique, the influence of helicity (spatial parity violation) on the turbulent magnetic Prandtl number in the kinematic magnetohydrodynamic turbulence is investigated in the two-loop approximation. It is shown that the presence of helicity decreases the value of the turbulent magnetic Prandtl number and, at the same time, the two-loop helical contribution to the turbulent magnetic Prandtl number is at most 4.2% (in the case with the maximal helicity) of its nonhelical value. These results demonstrate, on one hand, the potential importance of the presence of asymmetries in processes in turbulent environments and, on the other hand, the rather strong stability of the properties of diffusion processes of the magnetic field in the conductive turbulent environment with the spatial parity violation in comparison to the corresponding systems without the spatial parity violation. In addition, obtained results are compared to the corresponding results found for the two-loop turbulent Prandtl number in the model of passively advected scalar field. It is shown that the turbulent Prandtl number and the turbulent magnetic Prandtl number, which are the same in fully symmetric isotropic turbulent systems, are essentially different when one considers the spatial parity violation. It means that the properties of the diffusion processes in the turbulent systems with a given symmetry breaking can considerably depend on the internal tensor structure of advected quantities.

  3. Two loop unification of non-SUSY SO(10) GUT with TeV scalars

    Science.gov (United States)

    Brennan, T. Daniel

    2017-03-01

    In this paper we examine gauge coupling unification of the non-SUSY SO(10) grand unified theory proposed by Babu and Mohapatra [Phys. Lett. B 715, 328 (2012), 10.1016/j.physletb.2012.08.006] at the two loop level. This theory breaks down to the standard model in a single step and has the distinguishing feature of TeV nonstandard model scalars. This leads to a plethora of interesting new physics at the TeV scale and the discovery of new particles at the LHC. This model gives rise to testable proton decay, neutron-antineutron oscillations, provides a mechanism for baryogenesis, and contains potential dark matter candidates. In this paper, we compute the two loop beta function and show that this model unifies to two loop order around 1 015 GeV . We then compute the proton lifetime, taking into account threshold effects and show that these effects place it above the Super-Kamiokande limit [K. Abe et al. (Super-Kamiokande Collaboration), Phys. Rev. D 95, 012004 (2017)., 10.1103/PhysRevD.95.012004].

  4. PyR@TE 2: A Python tool for computing RGEs at two-loop

    CERN Document Server

    Lyonnet, Florian

    2016-01-01

    Renormalization group equations are an essential tool for the description of theories accross different energy scales. Even though their expressions at two-loop for an arbitrary gauge field theory have been known for more than thirty years, deriving the full set of equations for a given model by hand is very challenging and prone to errors. To tackle this issue, we have introduced in [1] a Python tool called PyR@TE; Python Renormalization group equations @ Two-loop for Everyone. With PyR@TE, it is easy to implement a given Lagrangian and derive the complete set of two-loop RGEs for all the parameters of the theory. In this paper, we present the new version of this code, PyR@TE 2, which brings many new features and in particular it incorporates kinetic mixing when several $\\mathrm{U}(1)$ gauge groups are involved. In addition, the group theory part has been greatly improved as we introduced a new Python module dubbed PyLie that deals with all the group theoretical aspects required for the calculation of the RG...

  5. Regularization independent analysis of the origin of two loop contributions to N=1 Super Yang-Mills beta function

    Energy Technology Data Exchange (ETDEWEB)

    Fargnoli, H.G.; Sampaio, Marcos; Nemes, M.C. [Federal University of Minas Gerais, ICEx, Physics Department, P.O. Box 702, Belo Horizonte, MG (Brazil); Hiller, B. [Coimbra University, Faculty of Science and Technology, Physics Department, Center of Computational Physics, Coimbra (Portugal); Baeta Scarpelli, A.P. [Setor Tecnico-Cientifico, Departamento de Policia Federal, Lapa, Sao Paulo (Brazil)

    2011-05-15

    We present both an ultraviolet and an infrared regularization independent analysis in a symmetry preserving framework for the N=1 Super Yang-Mills beta function to two loop order. We show explicitly that off-shell infrared divergences as well as the overall two loop ultraviolet divergence cancel out, whilst the beta function receives contributions of infrared modes. (orig.)

  6. A reappraisal of two-loop contributions to the fermion electric dipole moments in R-parity violating supersymmetric models

    CERN Document Server

    Yamanaka, Nodoka; Kubota, Takahiro

    2012-01-01

    We reexamine the R-parity violating contribution to the fermion electric and chromo-electric dipole moments (EDM and cEDM) in the two-loop diagrams. It is found that the leading Barr-Zee type two-loop contribution is smaller than the result found in previous works, and that EDM experimental data provide looser limits on RPV couplings.

  7. Broken phase effective potential in the two-loop Phi-derivable approximation and nature of the phase transition in a scalar theory

    CERN Document Server

    Markó, Gergely; Szép, Zsolt

    2012-01-01

    We study the phase transition of a real scalar phi^4 theory in the two-loop Phi-derivable approximation using the imaginary time formalism, extending our previous (analytical) discussion of the Hartree approximation. We combine Fast Fourier Transform algorithms and accelerated Matsubara sums in order to achieve a high accuracy. Our results confirm and complete earlier ones obtained in the real time formalism [1] but which were less accurate due to the integration in Minkowski space and the discretization of the spectral density function. We also provide a complete and explicit discussion of the renormalization of the two-loop Phi-derivable approximation at finite temperature, both in the symmetric and in the broken phase, which was already used in the real-time approach, but never published. Our main result is that the two-loop Phi-derivable approximation suffices to cure the problem of the Hartree approximation regarding the order of the transition: the transition is of the second order type, as expected on ...

  8. Two-loop Induced Majorana Neutrino Mass in a Radiatively Induced Quark and Lepton Mass Model

    CERN Document Server

    Nomura, Takaaki

    2016-01-01

    A two-loop induced radiative neutrino model is proposed as an extension of our previous work in which the first and second generation standard model fermion masses are generated at one-loop level in both quark and lepton sectors. Then we discuss current neutrino oscillation data, lepton flavor violations, muon anomalous magnetic moment, and a bosonic dark matter candidate, for both the normal and inverted neutrino mass hierarchy. Our numerical analysis shows that less hierarchical Yukawa coupling constants can fit the experimental data with TeV scale dark matter.

  9. Two-loop virtual top-quark effect on Higgs-boson decay to bottom quarks.

    Science.gov (United States)

    Butenschön, Mathias; Fugel, Frank; Kniehl, Bernd A

    2007-02-16

    In most of the mass range encompassed by the limits from the direct search and the electroweak precision tests, the Higgs boson of the standard model preferably decays to bottom quarks. We present, in analytic form, the dominant two-loop electroweak correction, of O(GF2mt4), to the partial width of this decay. It amplifies the familiar enhancement due to the O(GFmt2) one-loop correction by about +16% and thus more than compensates the screening by about -8% through strong-interaction effects of order O(alphasGFmt2).

  10. Leading Chiral Logarithms of $K_{S} \\to \\gamma \\gamma$ at two Loops

    CERN Document Server

    Ghorbani, Karim

    2014-01-01

    We obtain the leading divergences at two loops for the decay $K_{S} \\to \\gamma \\gamma$ using only one-loop diagrams. We then find the double chiral logarithmic corrections to the decay branching ratio. It turns out that these effects are numerically small and therefore make a very small enhancement on the branching ratio. We also derive an expression for the corrections of type $\\log \\mu~\\times$ LEC. We find out that these single logarithmic effects can be sizable but comes with opposite sign with respect to the double chiral logarithms. Some numerical results are presented.

  11. On the two-loop corrections to the Higgs mass in trilinear R-parity violation

    Directory of Open Access Journals (Sweden)

    Herbi K. Dreiner

    2015-03-01

    Full Text Available We study the impact of large trilinear R-parity violating couplings on the lightest CP-even Higgs boson mass in supersymmetric models. We use the publicly available computer codes SARAH and SPheno to compute the leading two-loop corrections. We use the effective potential approach. For not too heavy third generation squarks (m˜≲1 TeV and couplings close to the unitarity bound we find positive corrections up to a few GeV in the Higgs mass.

  12. The two-loop QCD correction to massive spin-2 resonance → q anti qg

    Energy Technology Data Exchange (ETDEWEB)

    Ahmed, Taushif; Rana, Narayan [The Institute of Mathematical Sciences, Chennai (India); Training School Complex, Homi Bhaba National Institute, Mumbai (India); Das, Goutam; Mathews, Prakash [Saha Institute of Nuclear Physics, Theory Division, Kolkata (India); Training School Complex, Homi Bhaba National Institute, Mumbai (India); Ravindran, V. [The Institute of Mathematical Sciences, Chennai (India)

    2016-12-15

    The two-loop QCD correction to massive spin-2 graviton decaying to q + anti q + g is presented considering a generic universal spin-2 coupling to the SM through the conserved energy-momentum tensor. Such a massive spin-2 particle can arise in extra-dimensional models. The ultraviolet and infrared structure of the QCD amplitudes are studied. In dimensional regularization, the infrared pole structure is in agreement with Catani's proposal, confirming the universal factorization property of QCD amplitudes, even with the spin-2 tensorial coupling. (orig.)

  13. Two-loop NF=1 QED Bhabha scattering differential cross section

    Science.gov (United States)

    Bonciani, R.; Ferroglia, A.; Mastrolia, P.; Remiddi, E.; van der Bij, J. J.

    2004-11-01

    We calculate the two-loop virtual, UV renormalized corrections at order α(N=1) in QED to the Bhabha scattering differential cross section, for arbitrary values of the squared c.m. energy s and momentum transfer t, and on-shell electrons and positrons of finite mass m. The calculation is carried out within the dimensional regularization scheme; the remaining IR divergences appear as polar singularities in (D-4). The result is presented in terms of 1- and 2-dimensional harmonic polylogarithms, of maximum weight 3.

  14. Two-loop NF=1 QED Bhabha scattering differential cross section

    Energy Technology Data Exchange (ETDEWEB)

    Bonciani, R. [Fakultaet fuer Mathematik und Physik, Albert-Ludwigs-Universitaet Freiburg, D-79104 Freiburg (Germany)]. E-mail: roberto.bonciani@physik.uni-freiburg.de; Ferroglia, A. [Fakultaet fuer Mathematik und Physik, Albert-Ludwigs-Universitaet Freiburg, D-79104 Freiburg (Germany)]. E-mail: andrea.ferroglia@physik.uni-freiburg.de; Mastrolia, P. [Department of Physics and Astronomy, UCLA, Los Angeles, CA 90095-1547 (United States)]. E-mail: mastrolia@physics.ucla.edu; Remiddi, E. [Physics Department, Theory Division, CERN, CH-1211 Geneva 23 (Switzerland); Dipartimento di Fisica dell' Universita di Bologna, and INFN, Sezione di Bologna, I-40126 Bologna (Italy)]. E-mail: ettore.remiddi@bo.infn.it; Bij, J.J. van der [Fakultaet fuer Mathematik und Physik, Albert-Ludwigs-Universitaet Freiburg, D-79104 Freiburg (Germany)]. E-mail: jochum@physik.uni-freiburg.de

    2004-11-22

    We calculate the two-loop virtual, UV renormalized corrections at order {alpha}4(NF=1) in QED to the Bhabha scattering differential cross section, for arbitrary values of the squared c.m. energy s and momentum transfer t, and on-shell electrons and positrons of finite mass m. The calculation is carried out within the dimensional regularization scheme; the remaining IR divergences appear as polar singularities in (D-4). The result is presented in terms of 1- and 2-dimensional harmonic polylogarithms, of maximum weight 3.

  15. Reformulating the TBA equations for the quark anti-quark potential and their two loop expansion

    Energy Technology Data Exchange (ETDEWEB)

    Bajnok, Zoltán; Balog, János [MTA Lendület Holographic QFT Group, Wigner Research Centre,H-1525 Budapest 114, P.O.B. 49 (Hungary); Correa, Diego H. [Instituto de Física La Plata, CONICET, Universidad Nacional de La Plata, C.C. 67, 1900 La Plata (Argentina); Hegedűs, Árpád [MTA Lendület Holographic QFT Group, Wigner Research Centre,H-1525 Budapest 114, P.O.B. 49 (Hungary); Massolo, Fidel I. Schaposnik [Instituto de Física La Plata, CONICET, Universidad Nacional de La Plata, C.C. 67, 1900 La Plata (Argentina); Tóth, Gábor Zsolt [MTA Lendület Holographic QFT Group, Wigner Research Centre,H-1525 Budapest 114, P.O.B. 49 (Hungary)

    2014-03-11

    The boundary thermodynamic Bethe Ansatz (BTBA) equations introduced in http://dx.doi.org/10.1007/JHEP08(2012)134http://dx.doi.org/10.1007/JHEP10(2013)135 to describe the cusp anomalous dimension contain imaginary chemical potentials and singular boundary fugacities, which make its systematic expansion problematic. We propose an alternative formulation based on real chemical potentials and additional source terms. We expand our equations to double wrapping order and find complete agreement with the direct two-loop gauge theory computation of the cusp anomalous dimension.

  16. Electroweak two-loop corrections to the effective weak mixing angle

    Energy Technology Data Exchange (ETDEWEB)

    Awramik, M. [Hamburg Univ. (Germany). 2. Inst. fuer Theoretische Physik]|[Institute of Nuclear Physics, Cracow (Poland); Czakon, M. [Wuerzburg Univ. (Germany). Inst. fuer Theoretische Physik und Astrophysik]|[Silesia Univ., Katowice (Poland). Dept. of Field Theory and Particle Physics; Freitas, A. [Zuerich Univ. (Switzerland). Inst. fuer Theoretische Physik

    2006-08-15

    Recently exact results for the complete electroweak two-loop contributions to the effective weak mixing angle were published. This paper illustrates the techniques used for this computation, in particular the methods for evaluating the loop diagrams and the proper definition of Z-pole observables at next-to-next -to-leading order. Numerical results are presented in terms of simple parametrization formulae and compared in detail with a previous result of an expansion up to next-to-leading order in the top-quark mass. Finally, an estimate of the remaining theoretical uncertainties from unknown higher-order corrections is given. (Orig.)

  17. R-parity violating two-loop level rainbowlike contribution to the fermion electric dipole moment

    CERN Document Server

    Yamanaka, Nodoka

    2012-01-01

    We analyze the two-loop level R-parity violating supersymmetric contribution to the electric and chromoelectric dipole moments of the fermion with neutrino and gaugino in the intermediate state. It is found that this contribution can be sufficiently enhanced with large tan {\\beta} and that it can have comparable size with the currently known R-parity violating Barr-Zee type process in the TeV scale supersymmetry breaking. We also give new limits on the R-parity violating couplings from the experimental data of the electric dipole moments of the neutron and the electron.

  18. Two-loop level rainbow-like supersymmetric contribution to the fermion EDM

    CERN Document Server

    Yamanaka, Nodoka

    2012-01-01

    We calculate the two-loop level electric and chromo-electric dipole moments of the fermion involving fermion-sfermion inner loop, gaugino, and higgsino in the minimal supersymmetric standard model, and analyze the chromo-electric dipole moment with the top-stop inner loop. It is found that this contribution is comparable with, and even dominates in some situation over the Barr-Zee type diagram generated from the CP-violation of the top squark sector in TeV scale supersymmetry breaking.

  19. Eikonal gluon bremsstrahlung at finite N_c beyond two loops

    CERN Document Server

    Delenda, Yazid

    2015-01-01

    We present a general formalism for computing the matrix-element squared for the emission of soft energy-ordered gluons beyond two loops in QCD perturbation theory at finite $N_c$. Our formalism is valid in the eikonal approximation. A Mathematica program has been developed for the automated calculation of all real/virtual eikonal squared amplitudes needed at a given loop order. For the purpose of illustration we show the explicit forms of the eikonal squared amplitudes up to the fifth-loop order. In the large-$N_c$ limit our results coincide with those previously reported in literature.

  20. Two-loop formfactors in theories with mass gap and Z-boson production

    Energy Technology Data Exchange (ETDEWEB)

    Kotikov, A. [Joint Inst. of Nuclear Research, Moscow (Russian Federation). Bogoliubov Lab. of Theoretical Physics]|[Hamburg Univ. (Germany). 2. Inst. fuer Theoretische Physik; Kuehn, J.H. [Karlsruhe Univ. (T.H.) (Germany). Inst. fuer Theoretische Teilchenphysik; Veretin, O. [Hamburg Univ. (Germany). 2. Inst. fuer Theoretische Physik]|[Petrozavodsk Univ., Karelia (Russian Federation)

    2007-03-15

    The non-factorizable two-loop corrections to the formfactor both for a U(1) x U(1) and a SU(2) x U(1) gauge theory with massive and massless gauge bosons respectively is evaluated at arbitrary momentum transfer q{sup 2}. The asymptotic behaviour for q{sup 2}{yields}{infinity} is compared to a recent calculation of Sudakov logarithms. The result is an important ingredient for the calculation of radiative corrections to Z-boson production at hadron and lepton colliders. (orig.)

  1. Two-loop QED operator matrix elements with massive external fermion lines

    Energy Technology Data Exchange (ETDEWEB)

    Bluemlein, Johannes [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany); Freitas, Abilio de [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany); Universidad Simon Bolivar, Caracas (Venezuela). Dept. de Fisica; Neerven, Wilhelmus van [Leiden Univ. (Netherlands). Institut-Lorentz

    2011-07-15

    The two-loop massive operator matrix elements for the fermionic local twist-2 operators with external massive fermion lines in Quantum Electrodynamics (QED) are calculated up to the constant terms in the dimensional parameter {epsilon}=D-4. We investigate the hypothesis of F. A. Berends et al. (1988) that the 2-loop QED initial state corrections to e{sup +}e{sup -} annihilation into a virtual neutral gauge boson, except power corrections of O((m{sup 2}{sub f}/s){sup k}), k {>=} 1, can be represented in terms of these matrix elements and the massless 2-loop Wilson coefficients of the Drell-Yan process. (orig.)

  2. Nucleon self-energy in the relativistic Brueckner theory

    Energy Technology Data Exchange (ETDEWEB)

    Waindzoch, T.; Fuchs, C.; Faessler, A. [Inst. fuer Theoretische Physik, Univ. Tuebingen (Germany)

    1998-06-01

    The self-energy of the nucleon in nuclear matter is calculated in the relativistic Brueckner theory. We solve the Thompson equation for the two nucleon scattering in the medium using different Bonn potentials. The self-energy has a rather strong momentum dependence while the equation of state compares well with previous calculations. (orig.)

  3. Analytic calculation of two-loop QCD corrections to b → sl+l- in the high q2 region

    Science.gov (United States)

    Greub, C.; Pilipp, V.; Schüpbach, C.

    2008-12-01

    We present our results for the NNLL virtual corrections to the matrix elements of the operators O1 and O2 for the inclusive process b → sl+l- in the kinematical region q2 > 4mc2, where q2 is the invariant mass squared of the lepton-pair. This is the first analytic two-loop calculation of these matrix elements in the high q2 region. We give the matrix elements as an expansion in mc/mb and keep the full analytic dependence on q2. Making extensive use of differential equation techniques, we fully automatize the expanding of the Feynman integrals in mc/mb. In coincidence with an earlier work where the master integrals were obtained numerically [1], we find that in the high q2 region the αs corrections to the matrix elements langlesl+l-|O1,2|brangle calculated in the present paper lead to a decrease of the perturbative part of the q2-spectrum by 10%-15% relative to the NNLL result in which these contributions are put to zero and reduce the renormalization scale uncertainty to ~ 2%.

  4. Two-loop snail diagrams: relating neutrino masses to dark matter

    CERN Document Server

    Farzan, Yasaman

    2014-01-01

    Various mechanisms have been developed to explain the origin of Majorana neutrino masses. One of them is radiative mass generation. Two-loop mass generation is of particular interest because the masses and couplings of new particles propagating in the loop can be in the range testable by other experiments and observations. In order for the radiative mass suppression to be reliable, it should be guaranteed that lower loop contributions are suppressed. Based on loop topology and the form of electroweak presentation of the particles propagating in the loop, one can determine whether a lower---and therefore dominant---loop contribution is possible. We present a model based on these general considerations which leads to neutrino masses via a two-loop diagram which we dub as "snail-diagram". The model has two natural candidates for dark matter one of them being a neutral Dirac fermion which can satisfy the conditions of the thermal freeze-out scenario by annihilation to lepton pairs. We comment on the possibility o...

  5. Large mass expansion in two-loop QCD corrections of para-charmonium decay

    CERN Document Server

    Hasegawa, K; Pak, Alexey

    2006-01-01

    We calculate the light-by-light scattering type two-loop QCD corrections due to the light quark loops in the para-charmonium decays $eta_{c} rightarrow gamma gamma$ and $eta_{c} rightarrow g g$. We replace the mass of the internal charm quarks by an artificial large mass and obtain the result as a series in the large mass. The obtained series can be transformed into the good convergent ones by a change of the expansion parameter. The results are supported by two other methods to improve the convergence. We also observe that the color singlet state of $eta_{c}$ eliminates the potential divergences in the two-loop QCD corrections. The obtained corrections to the modes $eta_{c} rightarrow gamma gamma$ and $eta_{c} rightarrow g g$ account for -1.25% and -0.73% of the tree level values, respectively. Comparing the ratio of the decay rates with the experimental value, we find the constrains on the unknown contribution to these decays.

  6. Deconfinement transition in SU(2) Yang-Mills theory: a two-loop study

    CERN Document Server

    Reinosa, U; Tissier, M; Wschebor, N

    2014-01-01

    In a recent work we have proposed a perturbative approach for the study of the phase transition of pure Yang-Mills theories at finite temperature. This is based on a simple massive extension of background field methods in the Landau-DeWitt gauge, where the gluon mass term is related to the existence of Gribov ambiguities. We have shown that a one-loop calculation of the background field effective potential describes well the phase structure of the SU(2) and SU(3) theories. Here, we present the calculation of the next-to-leading order contribution in perturbation theory for the SU(2) case. In particular, we compute the background field effective potential at two-loop order and the corresponding Polyakov loop, a gauge invariant order parameter of the transition, at one-loop order. We show that the two-loop correction brings the critical temperature closer to its actual value as compared to the previous one-loop result. We also compute the thermodynamic pressure as a function of the temperature and show that two...

  7. Two-loop corrections to the ρ parameter in Two-Higgs-Doublet models

    Energy Technology Data Exchange (ETDEWEB)

    Hessenberger, Stephan; Hollik, Wolfgang [Max-Planck-Institut fuer Physik (Werner-Heisenberg-Institut), Muenchen (Germany)

    2017-03-15

    Models with two scalar doublets are among the simplest extensions of the Standard Model which fulfill the relation ρ = 1 at lowest order for the ρ parameter as favored by experimental data for electroweak observables allowing only small deviations from unity. Such small deviations Δρ originate exclusively from quantum effects with special sensitivity to mass splittings between different isospin components of fermions and scalars. In this paper the dominant two-loop electroweak corrections to Δρ are calculated in the CP-conserving THDM, resulting from the top-Yukawa coupling and the self-couplings of the Higgs bosons in the gauge-less limit. The on-shell renormalization scheme is applied. With the assumption that one of the CP-even neutral scalars represents the scalar boson observed by the LHC experiments, with standard properties, the two-loop non-standard contributions in Δρ can be separated from the standard ones. These contributions are of particular interest since they increase with mass splittings between non-standard Higgs bosons and can be additionally enhanced by tanβ and λ{sub 5}, an additional free coefficient of the Higgs potential, and can thus modify the one-loop result substantially. Numerical results are given for the dependence on the various non-standard parameters, and the influence on the calculation of electroweak precision observables is discussed. (orig.)

  8. Infrared divergences and harmonic anomalies in the two-loop superstring effective action

    CERN Document Server

    Pioline, Boris

    2015-01-01

    We analyze the pertubative contributions to the $D^4 R^4$ and $D^6 R^4$ couplings in the low-energy effective action of type II string theory compactified on a torus $T^d$, with particular emphasis on two-loop corrections. In general, it is necessary to introduce an infrared cut-off $\\Lambda$ to separate local interactions from non-local effects due to the exchange of massless states. We identify the degenerations of the genus-two Riemann surface which are responsible for power-like dependence on $\\Lambda$, and give an explicit prescription for extracting the $\\Lambda$-independent effective couplings. These renormalized couplings are then shown to be eigenmodes of the Laplace operator with respect to the torus moduli, up to computable anomalous source terms arising in the presence of logarithmic divergences, in precise agreement with predictions from U-duality. Our results for the two-loop $D^6 R^4$ contribution also probe essential properties of the Kawazumi-Zhang invariant

  9. Two-loop corrections to the $\\rho$ parameter in Two-Higgs-Doublet Models

    CERN Document Server

    Hessenberger, Stephan

    2016-01-01

    Models with two scalar doublets are among the simplest extensions of the Standard Model which fulfill the relation $\\rho = 1$ at lowest order for the $\\rho$ parameter as favored by experimental data for electroweak observables allowing only small deviations from unity. Such small deviations $\\Delta\\rho$ originate exclusively from quantum effects with special sensitivity to mass splittings between different isospin components of fermions and scalars. In this paper the dominant two-loop electroweak corrections to $\\Delta\\rho$ are calculated in the $CP$-conserving THDM, resulting from the top-Yukawa coupling and the self-couplings of the Higgs bosons in the gauge-less limit. The on-shell renormalization scheme is applied. With the assumption that one of the $CP$-even neutral scalars represents the scalar boson observed by the LHC experiments, with standard properties, the two-loop non-standard contributions in $\\Delta\\rho$ can be separated from the standard ones. These contributions are of particular interest si...

  10. Two-loop snail diagrams: relating neutrino masses to dark matter

    Energy Technology Data Exchange (ETDEWEB)

    Farzan, Yasaman [Physics school, Institute for Research in Fundamental Sciences (IPM),P.O. Box 19395-5531, Tehran (Iran, Islamic Republic of)

    2015-05-06

    Various mechanisms have been developed to explain the origin of neutrino masses. One of them is radiative mass generation. Two-loop mass generation is of particular interest because the masses and couplings of new particles propagating in the loop can be in the range testable by other experiments and observations. In order for the radiative mass suppression to be reliable, it should be guaranteed that lower loop contributions are suppressed. Based on loop topology and the form of electroweak presentation of the particles propagating in the loop, one can determine whether a lower — and therefore dominant — loop contribution is possible. We present a model based on these general considerations which leads to neutrino masses via a two-loop diagram which we dub as “snail-diagram”. The model has two natural candidates for dark matter one of them being a neutral Dirac fermion which can satisfy the conditions of the thermal freeze-out scenario by annihilation to lepton pairs. We comment on the possibility of explaining the GeV gamma ray excess observed by Fermi-LAT from the region close to the Galaxy Center. We also discuss possible signals at the LHC and at experiments searching for lepton flavor violating rare decays.

  11. Two-loop scale-invariant scalar potential and quantum effective operators

    CERN Document Server

    Ghilencea, D.M.

    2016-01-01

    Spontaneous breaking of quantum scale invariance may provide a solution to the hierarchy and cosmological constant problems. In a scale-invariant regularization, we compute the two-loop potential of a higgs-like scalar $\\phi$ in theories in which scale symmetry is broken only spontaneously by the dilaton ($\\sigma$). Its vev $\\langle\\sigma\\rangle$ generates the DR subtraction scale ($\\mu\\sim\\langle\\sigma\\rangle$), which avoids the explicit scale symmetry breaking by traditional regularizations (where $\\mu$=fixed scale). The two-loop potential contains effective operators of non-polynomial nature as well as new corrections, beyond those obtained with explicit breaking ($\\mu$=fixed scale). These operators have the form: $\\phi^6/\\sigma^2$, $\\phi^8/\\sigma^4$, etc, which generate an infinite series of higher dimensional polynomial operators upon expansion about $\\langle\\sigma\\rangle\\gg \\langle\\phi\\rangle$, where such hierarchy is arranged by {\\it one} initial, classical tuning. These operators emerge at the quantum...

  12. Testable two-loop radiative neutrino mass model based on an LLQd^cQd^c effective operator

    CERN Document Server

    Angel, Paul W; Rodd, Nicholas L; Schmidt, Michael A; Volkas, Raymond R

    2013-01-01

    A new two-loop radiative Majorana neutrino mass model is constructed from the gauge- invariant effective operator L^i L^j Q^k d^c Q^l d^c \\epsilon_{ik} \\epsilon_{jl} that violates lepton number conservation by two units. The ultraviolet completion features two scalar leptoquark flavors and a color-octet Majorana fermion. We show that there exists a region of parameter space where the neutrino oscillation data can be fitted while simultaneously meeting flavor-violation and collider bounds. The model is testable through lepton flavor-violating processes such as {\\mu} -> e{\\gamma}, {\\mu} -> eee, and {\\mu}N -> eN conversion, as well as collider searches for the scalar leptoquarks and color-octet fermion. We computed and compiled a list of necessary Passarino-Veltman integrals up to boxes in the approximation of vanishing external momenta and made them available as a Mathematica package, denoted as ANT.

  13. Two-Loop QCD Corrections to Higgs $\\rightarrow b + \\bar{b} + g$ Amplitude

    CERN Document Server

    Ahmed, Taushif; Mathews, Prakash; Rana, Narayan; Ravindran, V

    2014-01-01

    Exclusive observables involving Higgs boson in association with jets are often well suited to study the Higgs boson properties. They are rates involving cuts on the final state jets or differential distributions of rapidity, transverse momentum of the observed Higgs boson. While they get dominant contributions from gluon initiated partonic subprocesses, it is important to include the subdominant ones coming from other channels. In this article, we study one such channel namely the Higgs production in association with a jet in bottom anti-bottom annihilation process. We compute relevant amplitude $H\\rightarrow b+\\overline b+g$ up to two loop level in QCD where Higgs couples to bottom quark through Yukawa coupling. We use projection operators to obtain the coefficients for each tensorial structure appearing in this process. We have demonstrated that the renormalized amplitudes do have the right infrared structure predicted by the QCD factorization in dimensional regularization. The finite parts of the one and t...

  14. Experimental Study of Flexible Plate Vibration Control by Using Two-Loop Sliding Mode Control Strategy

    Science.gov (United States)

    Yang, Jingyu; Lin, Jiahui; Liu, Yuejun; Yang, Kang; Zhou, Lanwei; Chen, Guoping

    2016-06-01

    It is well known that intelligent control theory has been used in many research fields, novel modeling method (DROMM) is used for flexible rectangular active vibration control, and then the validity of new model is confirmed by comparing finite element model with new model. In this paper, taking advantage of the dynamics of flexible rectangular plate, a two-loop sliding mode (TSM) MIMO approach is introduced for designing multiple-input multiple-output continuous vibration control system, which can overcome uncertainties, disturbances or unstable dynamics. An illustrative example is given in order to show the feasibility of the method. Numerical simulations and experiment confirm the effectiveness of the proposed TSM MIMO controller.

  15. The Two-Loop Finite-Temperature Effective Potential of the MSSM and Baryogenesis

    CERN Document Server

    Losada, M

    1999-01-01

    We construct an effective three dimensional theory for the MSSM at high temperatures in the limit of large-$m_{A}$. We analyse the two-loop effective potential of the 3D theory for the case of a light right handed stop to determine the precise region in the $m_{h}$-$m_{\\tilde{t}_{R}}$ plane for which the sphaleron constraint for preservation of the baryon asymmetry is satisfied. We also compare with results previously obtained usind 3D and 4D calculations of the effective potential. A two-stage phase transition still persists for a small range of values of $m_{\\tilde{t}_{R}}$. The allowed region requires a value of $m_{\\tilde{t}_{R}} \\lsi m_{t}$ and $m_{h} \\lsi 100$ (110) GeV for $m_{Q} = 300$ GeV (1 TeV).

  16. The Higgs Mass in the MSSM at two-loop order beyond minimal flavour violation

    CERN Document Server

    Goodsell, Mark D; Staub, Florian

    2015-01-01

    Soft supersymmetry-breaking terms provide a wealth of new potential sources of flavour violation, which lead to very tight constraints from precision experiments. This has posed a challenge to construct flavour models to both explain the structure of the Standard Model Yukawa couplings and how their consequent predictions for patterns in the soft supersymmetry-breaking terms do not violate these constraints. While such models have been studied in great detail, the impact of flavour violating soft terms on the Higgs mass at the two-loop level has been assumed to be small or negligible. In this letter, we show that large flavour violation in the up-squark sector can give a positive or negative shift to the SM-like Higgs of several GeV, without being in conflict with any other observation. We investigate in which regions of the parameter space these effects can be expected.

  17. Two-Loop Quantum Gravity Corrections to Cosmological Constant in Landau Gauge

    CERN Document Server

    Hamada, Ken-ji

    2015-01-01

    The anomalous dimensions of the Planck mass and the cosmological constant are calculated in a renormalizable quantum conformal gravity with a single dimensionless coupling, which is formulated using dimensional regularization on the basis of Hathrell's works for conformal anomalies. The dynamics of the traceless tensor field is handled by the Weyl action, while that of the conformal-factor field is described by the induced Wess-Zumino actions, including the Riegert action as the kinetic term. Loop calculations are carried out in Landau gauge in order to reduce the number of Feynman diagrams as well as to avoid some uncertainty. Especially, we calculate two-loop quantum gravity corrections to the cosmological constant. It suggests that there is a dynamical solution to the cosmological constant problem.

  18. The Higgs mass in the MSSM at two-loop order beyond minimal flavour violation

    Science.gov (United States)

    Goodsell, Mark D.; Nickel, Kilian; Staub, Florian

    2016-07-01

    Soft supersymmetry-breaking terms provide a wealth of new potential sources of flavour violation, which are tightly constrained by precision experiments. This has posed a challenge to construct flavour models which both explain the structure of the Standard Model Yukawa couplings and also predict soft-breaking patterns that are compatible with these constraints. While such models have been studied in great detail, the impact of flavour violating soft terms on the Higgs mass at the two-loop level has been assumed to be small or negligible. In this letter, we show that large flavour violation in the up-squark sector can give a positive or negative mass shift to the SM-like Higgs of several GeV, without being in conflict with other observations. We investigate in which regions of the parameter space these effects can be expected.

  19. Experimental Study of Flexible Plate Vibration Control by Using Two-Loop Sliding Mode Control Strategy

    Science.gov (United States)

    Yang, Jingyu; Lin, Jiahui; Liu, Yuejun; Yang, Kang; Zhou, Lanwei; Chen, Guoping

    2017-08-01

    It is well known that intelligent control theory has been used in many research fields, novel modeling method (DROMM) is used for flexible rectangular active vibration control, and then the validity of new model is confirmed by comparing finite element model with new model. In this paper, taking advantage of the dynamics of flexible rectangular plate, a two-loop sliding mode (TSM) MIMO approach is introduced for designing multiple-input multiple-output continuous vibration control system, which can overcome uncertainties, disturbances or unstable dynamics. An illustrative example is given in order to show the feasibility of the method. Numerical simulations and experiment confirm the effectiveness of the proposed TSM MIMO controller.

  20. The Effective Field Theory of Large Scale Structures at two loops

    Energy Technology Data Exchange (ETDEWEB)

    Carrasco, John Joseph M.; Foreman, Simon; Green, Daniel; Senatore, Leonardo, E-mail: jjmc@stanford.edu, E-mail: sfore@stanford.edu, E-mail: drgreen@stanford.edu, E-mail: senatore@stanford.edu [Stanford Institute for Theoretical Physics and Department of Physics, Stanford University, Stanford, CA 94306 (United States)

    2014-07-01

    Large scale structure surveys promise to be the next leading probe of cosmological information. It is therefore crucial to reliably predict their observables. The Effective Field Theory of Large Scale Structures (EFTofLSS) provides a manifestly convergent perturbation theory for the weakly non-linear regime of dark matter, where correlation functions are computed in an expansion of the wavenumber k of a mode over the wavenumber associated with the non-linear scale k{sub NL}. Since most of the information is contained at high wavenumbers, it is necessary to compute higher order corrections to correlation functions. After the one-loop correction to the matter power spectrum, we estimate that the next leading one is the two-loop contribution, which we compute here. At this order in k/k{sub NL}, there is only one counterterm in the EFTofLSS that must be included, though this term contributes both at tree-level and in several one-loop diagrams. We also discuss correlation functions involving the velocity and momentum fields. We find that the EFTofLSS prediction at two loops matches to percent accuracy the non-linear matter power spectrum at redshift zero up to k∼ 0.6 h Mpc{sup −1}, requiring just one unknown coefficient that needs to be fit to observations. Given that Standard Perturbation Theory stops converging at redshift zero at k∼ 0.1 h Mpc{sup −1}, our results demonstrate the possibility of accessing a factor of order 200 more dark matter quasi-linear modes than naively expected. If the remaining observational challenges to accessing these modes can be addressed with similar success, our results show that there is tremendous potential for large scale structure surveys to explore the primordial universe.

  1. Evidence for two-loop interaction from IRIS and SDO observations of penumbral brightenings

    Science.gov (United States)

    Alissandrakis, C. E.; Koukras, A.; Patsourakos, S.; Nindos, A.

    2017-07-01

    Aims: We investigate small scale energy release events which can provide clues on the heating mechanism of the solar corona. Methods: We analyzed spectral and imaging data from the Interface Region Imaging Spectrograph (IRIS), images from the Atmospheric Imaging Assembly (AIA) aboard the Solar Dynamics Observatoty (SDO), and magnetograms from the Helioseismic and Magnetic Imager (HMI) aboard SDO. Results: We report observations of small flaring loops in the penumbra of a large sunspot on July 19, 2013. Our main event consisted of a loop spanning 15'', from the umbral-penumbral boundary to an opposite polarity region outside the penumbra. It lasted approximately 10 min with a two minute impulsive peak and was observed in all AIA/SDO channels, while the IRIS slit was located near its penumbral footpoint. Mass motions with an apparent velocity of 100 km s-1 were detected beyond the brightening, starting in the rise phase of the impulsive peak; these were apparently associated with a higher-lying loop. We interpret these motions in terms of two-loop interaction. IRIS spectra in both the C ii and Si iv lines showed very extended wings, up to about 400 km s-1, first in the blue (upflows) and subsequently in the red wing. In addition to the strong lines, emission was detected in the weak lines of Cl i, O i and C i, as well as in the Mg ii triplet lines. Absorption features in the profiles of the C ii doublet, the Si iv doublet and the Mg ii h and k lines indicate the existence of material with a lower source function between the brightening and the observer. We attribute this absorption to the higher loop and this adds further credibility to the two-loop interaction hypothesis. Tilts were detected in the absorption spectra, as well as in the spectra of Cl i, O i, and C i lines, possibly indicating rotational motions from the untwisting of magnetic flux tubes. Conclusions: We conclude that the absorption features in the C ii, Si iv and Mg ii profiles originate in a higher

  2. Two-Loop QCD Correction to massive spin-2 resonance $\\rightarrow$ 3 gluons

    CERN Document Server

    Ahmed, Taushif; Mathews, Prakash; Rana, Narayan; Ravindran, V

    2014-01-01

    We present the ${\\cal O}(\\alpha_s^3)$ virtual QCD corrections to the process $h \\rightarrow g+g+g$ due to interference of born and two-loop amplitudes, where $h$ is a massive spin-2 particle and $g$ is the gluon. We assume that the SM fields couple to $h$ through the SM energy momentum tensor. Our result constitutes one of the ingredients to full NNLO QCD contribution to production of a massive spin-2 particle along with a jet in the scattering process at the LHC. In particular, this massive spin-2 could be a KK mode of a ADD graviton in large extra dimensional model or a RS KK mode in warped extra dimensional model or a generic massive spin-2. In addition, it provides an opportunity to study the ultraviolet and infrared structures of QCD amplitudes involving tensorial coupling resulting from energy momentum operator. Using dimensional regularization, we find that infrared poles of this amplitude are in agreement with the proposal by Catani confirming the factorization property of QCD amplitudes with tensoria...

  3. Two-loop conformal generators for leading-twist operators in QCD

    Energy Technology Data Exchange (ETDEWEB)

    Braun, V.M.; Strohmaier, M. [Regensburg Univ. (Germany). Inst. fuer Theoretische Physik; Manashov, A.N. [Regensburg Univ. (Germany). Inst. fuer Theoretische Physik; Hamburg Univ. (Germany). 2. Inst. fuer Theoretische Physik; Moch, S. [Hamburg Univ. (Germany). 2. Inst. fuer Theoretische Physik

    2016-01-15

    QCD evolution equations in minimal subtraction schemes have a hidden symmetry: One can construct three operators that commute with the evolution kernel and form an SL(2) algebra, i.e. they satisfy (exactly) the SL(2) commutation relations. In this paper we find explicit expressions for these operators to two-loop accuracy going over to QCD in non-integer d=4-2ε space-time dimensions at the intermediate stage. In this way conformal symmetry of QCD is restored on quantum level at the specially chosen (critical) value of the coupling, and at the same time the theory is regularized allowing one to use the standard renormalization procedure for the relevant Feynman diagrams. Quantum corrections to conformal generators in d=4-2ε effectively correspond to the conformal symmetry breaking in the physical theory in four dimensions and the SL(2) commutation relations lead to nontrivial constraints on the renormalization group equations for composite operators. This approach is valid to all orders in perturbation theory and the result includes automatically all terms that can be identified as due to a nonvanishing QCD β-function (in the physical theory in four dimensions). Our result can be used to derive three-loop evolution equations for flavor-nonsinglet quark-antiquark operators including mixing with the operators containing total derivatives. These equations govern, e.g., the scale dependence of generalized hadron parton distributions and light-cone meson distribution amplitudes.

  4. Two-loop supersymmetric QCD and half-maximal supergravity amplitudes

    Science.gov (United States)

    Johansson, Henrik; Kälin, Gregor; Mogull, Gustav

    2017-09-01

    Using the duality between color and kinematics, we construct two-loop four-point scattering amplitudes in N=2 super-Yang-Mills (SYM) theory coupled to N f fundamental hypermultiplets. Our results are valid in D ≤ 6 dimensions, where the upper bound corresponds to six-dimensional chiral N=(1,0) SYM theory. By exploiting a close connection with N=4 SYM theory — and, equivalently, six-dimensional N=(1,1) SYM theory — we find compact integrands with four-dimensional external vectors in both the maximally-helicity-violating (MHV) and all-chiral-vector sectors. Via the double-copy construction corresponding D-dimensional half-maximal supergravity amplitudes with external graviton multiplets are obtained in the MHV and all-chiral sectors. Appropriately tuning N f enables us to consider both pure and matter-coupled supergravity, with arbitrary numbers of vector multiplets in D = 4. As a bonus, we obtain the integrands of the genuinely six-dimensional supergravities with N=(1,1) and N=(2,0) supersymmetry. Finally, we extract the potential ultraviolet divergence of half-maximal supergravity in D = 5 - 2 ɛ and show that it non-trivially cancels out as expected.

  5. Two-loop stability of a complex singlet extended standard model

    Science.gov (United States)

    Costa, Raul; Morais, António P.; Sampaio, Marco O. P.; Santos, Rui

    2015-07-01

    Motivated by the dark matter and the baryon asymmetry problems, we analyze a complex singlet extension of the Standard Model with a Z2 symmetry (which provides a dark matter candidate). After a detailed two-loop calculation of the renormalization group equations for the new scalar sector, we study the radiative stability of the model up to a high energy scale (with the constraint that the 126 GeV Higgs boson found at the LHC is in the spectrum) and find it requires the existence of a new scalar state mixing with the Higgs with a mass larger than 140 GeV. This bound is not very sensitive to the cutoff scale as long as the latter is larger than 1010 GeV . We then include all experimental and observational constraints/measurements from collider data, from dark matter direct detection experiments, and from the Planck satellite and in addition force stability at least up to the grand unified theory scale, to find that the lower bound is raised to about 170 GeV, while the dark matter particle must be heavier than about 50 GeV.

  6. The Two-Loop Scale Dependence of the Static QCD Potential including Quark Masses

    Energy Technology Data Exchange (ETDEWEB)

    Brodsky, Stanley J.

    1999-06-14

    The interaction potential V(Q{sup 2}) between static test charges can be used to define an effective charge {alpha}{sub V}(Q{sup 2}) and a physically-based renormalization scheme for quantum chromodynamics and other gauge theories. In this paper we use recent results for the finite-mass fermionic corrections to the heavy-quark potential at two-loops to derive the next-to-leading order term for the Gell Mann-Low function of the V-scheme. The resulting effective number of flavors N{sub F}(Q{sup 2}/m{sup 2}) in the {alpha}{sub V} scheme is determined as a gauge-independent and analytic function of the ratio of the momentum transfer to the quark pole mass. The results give automatic decoupling of heavy quarks and are independent of the renormalization procedure. Commensurate scale relations then provide the next-to-leading order connection between all perturbatively calculable observables to the analytic and gauge-invariant {alpha}{sub V} scheme without any scale ambiguity and a well defined number of active flavors. The inclusion of the finite quark mass effects in the running of the coupling is compared with the standard treatment of finite quark mass effects in the {ovr MS} scheme.

  7. Naturalness made easy: two-loop naturalness bounds on minimal SM extensions

    CERN Document Server

    Clarke, Jackson D

    2016-01-01

    The main result of this paper is a collection of conservative naturalness bounds on minimal extensions of the standard model by (vector-like) fermionic or scalar gauge multiplets. Within, we advocate for an intuitive and physical concept of naturalness built upon the renormalisation group equations. In the effective field theory of the standard model plus a gauge multiplet with mass $M$, the low scale Higgs mass parameter is a calculable function of $\\overline{\\rm MS}$ input parameters defined at some high scale $\\Lambda_h > M$. If the Higgs mass is very sensitive to these input parameters, then this signifies a naturalness problem. To sensibly capture the sensitivity, it is shown how a sensitivity measure can be rigorously derived as a Bayesian model comparison, which reduces in a relevant limit to a Barbieri--Giudice-like fine-tuning measure. This measure is fully generalisable to any perturbative EFT. The interesting results of our two-loop renormalisation group study are as follows: for $\\Lambda_h=\\Lambda...

  8. Naturalness made easy: two-loop naturalness bounds on minimal SM extensions

    Science.gov (United States)

    Clarke, Jackson D.; Cox, Peter

    2017-02-01

    The main result of this paper is a collection of conservative naturalness bounds on minimal extensions of the Standard Model by (vector-like) fermionic or scalar gauge multiplets. Within, we advocate for an intuitive and physical concept of naturalness built upon the renormalisation group equations. In the effective field theory of the Standard Model plus a gauge multiplet with mass M , the low scale Higgs mass parameter is a calculable function of overline{MS} input parameters defined at some high scale Λ h > M . If the Higgs mass is very sensitive to these input parameters, then this signifies a naturalness problem. To sensibly capture the sensitivity, it is shown how a sensitivity measure can be rigorously derived as a Bayesian model comparison, which reduces in a relevant limit to a Barbieri-Giudice-like fine-tuning measure. This measure is fully generalisable to any perturbative EFT. The interesting results of our two-loop renormalisation group study are as follows: for Λ h = ΛPl we find "10% fine-tuning" bounds on the masses of various gauge multiplets of M

  9. Avoiding the Goldstone Boson Catastrophe in general renormalisable field theories at two loops

    CERN Document Server

    Braathen, Johannes

    2016-01-01

    We show how the infra-red divergences associated to Goldstone bosons in the minimum condition of the two-loop Landau-gauge effective potential can be avoided in general field theories. This extends the resummation formalism recently developed for the Standard Model and the MSSM, and we give compact, infra-red finite expressions in closed form for the tadpole equations. We also show that the results at this loop order are equivalent to (and are most easily obtained by) imposing an "on-shell" condition for the Goldstone bosons. Moreover, we extend the approach to show how the infra-red divergences in the calculation of the masses of neutral scalars (such as the Higgs boson) can be eliminated. For the mass computation, we specialise to the gaugeless limit and extend the effective potential computation to allow the masses to be determined without needing to solve differential equations for the loop functions -- opening the door to fast, infra-red safe determinations of the Higgs mass in general theories.

  10. Avoiding the Goldstone Boson Catastrophe in general renormalisable field theories at two loops

    Energy Technology Data Exchange (ETDEWEB)

    Braathen, Johannes; Goodsell, Mark D. [LPTHE, UPMC University Paris 06, Sorbonne Universités,4 Place Jussieu, F-75252 Paris (France); LPTHE, CNRS,4 Place Jussieu, F-75252 Paris (France)

    2016-12-14

    We show how the infra-red divergences associated to Goldstone bosons in the minimum condition of the two-loop Landau-gauge effective potential can be avoided in general field theories. This extends the resummation formalism recently developed for the Standard Model and the MSSM, and we give compact, infra-red finite expressions in closed form for the tadpole equations. We also show that the results at this loop order are equivalent to (and are most easily obtained by) imposing an “on-shell” condition for the Goldstone bosons. Moreover, we extend the approach to show how the infra-red divergences in the calculation of the masses of neutral scalars (such as the Higgs boson) can be eliminated. For the mass computation, we specialise to the gaugeless limit and extend the effective potential computation to allow the masses to be determined without needing to solve differential equations for the loop functions — opening the door to fast, infra-red safe determinations of the Higgs mass in general theories.

  11. World-line approach to the Bern-Kosower formalism in two-loop Yang-Mills theory

    CERN Document Server

    Sato, H T; Sato, Haru-Tada; Schmidt, Michael G.

    1999-01-01

    Based on the world-line formalism with a sewing method, we derive the Yang-Mills effective action in a form useful to generate the Bern-Kosower-type master formulae for gluon scattering amplitudes at the two-loop level. It is shown that four-gluon ($\\Phi^4$ type sewing) contributions can be encapsulated in the action with three-gluon ($\\Phi^3$ type) vertices only, the total action thus becoming a simple expression. We then derive a general formula for a two-loop Euler-Heisenberg type action in a pseudo-abelian $su(2)$ background. The ghost loop and fermion loop cases are also studied.

  12. Electron thermal self-energy in a magnetic field

    CERN Document Server

    Persson, D

    1995-01-01

    Using the general form of the static energy solutions to the Dirac equation with a magnetic field, we calculate a general self-energy matrix in the Furry-picture. In the limit of high temperatures, but even higher magnetic fields, a self-consistent dispersion relation is solved. In contrast to the high temperature limit, this merely results in a small mass shift. The electron anomalous magnetic moment is calculated. The contribution from thermal fermions is found to be different from the corresponding contribution using perturbation theory and plane-wave external states. In the low temperature limit the self-energy is shown to exhibit de Haas--van Alphen oscillations. In the limit of low temperatures and high densities, the self-energy becomes very large.

  13. Effective Two-loop Thermodynamic Potential with Fermions in the real-time formalism of thermal field theory

    CERN Document Server

    Xin, W; Xin, Wang; Jiarong, Li

    2000-01-01

    Within the real-time formalism (RTF) of thermal field theory,we apply the hard thermal loop (HTL) resummation technique to calculating effective two-loop thermodynamic potential in quark-gluon plasma (QGP) and its renormalization. The result with collective effects is obtained, which is valid for an arbitrary number of quark flavors with masses.

  14. Momentum-dependent two-loop QCD corrections to the neutral Higgs-boson masses in the MSSM

    Energy Technology Data Exchange (ETDEWEB)

    Borowka, S.; Hahn, T.; Heinrich, G.; Hollik, W. [Max-Planck-Institut fuer Physik (Werner-Heisenberg-Institut), Munich (Germany); Heinemeyer, S. [Instituto de Fisica de Cantabria (CSIC-UC), Santander (Spain)

    2014-08-15

    Results are presented for the momentum-dependent two-loop contributions of O(α{sub t}α{sub s}) to the masses and mixing effects in the Higgs sector of the MSSM. They are obtained in the Feynman-diagrammatic approach using a mixed on-shell/DR renormalization that can directly be matched onto the higher-order corrections included in the code FeynHiggs. The new two-loop diagrams are evaluated with the program SecDec. The combination of the new momentum-dependent two-loop contribution with the existing one- and two-loop corrections in the on-shell/DR scheme leads to an improved prediction of the light MSSM Higgs boson mass and a correspondingly reduced theoretical uncertainty. We find that the corresponding shifts in the lightest Higgs-boson mass M{sub h} are below 1 GeV in all scenarios considered, but they can extend up to the level of the current experimental uncertainty. The results are included in the code FeynHiggs. (orig.)

  15. Self-energy Effects in the Superfluidity of Neutron Matter

    CERN Document Server

    Lombardo, U; Zuo, W

    2001-01-01

    The superfluidity of neutron matter in the channel $^1 S_0$ is studied by taking into account the effect of the ground-state correlations in the self-energy. To this purpose the gap equation has been solved within the generalized Gorkov approach. A sizeable suppression of the energy gap is driven by the quasi-particle strength around the Fermi surface.

  16. Computation of $H\\to gg$ in FDH and DRED: renormalization, operator mixing, and explicit two-loop results

    CERN Document Server

    Broggio, A; Signer, A; Stöckinger, D; Visconti, A

    2015-01-01

    The $H\\to gg$ amplitude relevant for Higgs production via gluon fusion is computed in the four-dimensional helicity scheme (FDH) and in dimensional reduction (DRED) at the two-loop level. The required renormalization is developed and described in detail, including the treatment of evanescent $\\epsilon$-scalar contributions. In FDH and DRED there are additional dimension-5 operators generating the $H g g$ vertices, where $g$ can either be a gluon or an $\\epsilon$-scalar. An appropriate operator basis is given and the operator mixing through renormalization is described. The results of the present paper provide building blocks for further computations, and they allow to complete the study of the infrared divergence structure of two-loop amplitudes in FDH and DRED.

  17. Matching QCD and heavy-quark effective theory heavy-light currents at two loops and beyond

    Science.gov (United States)

    Broadhurst, D. J.; Grozin, A. G.

    1995-10-01

    Heavy-light QCD currents are matched with heavy-quark effective theory (HQET) currents at two loops and leading order in 1/m. A single formula applies to all current matchings. As a by-product, a master formula for the two-loop anomalous dimension of the QCD current q¯γ[μ1...γμn]q is obtained, yielding a new result for the tensor current. The dependence of matching coefficients on γ5 prescriptions is elucidated. Ratios of QCD matrix elements are obtained, independently of the three-loop anomalous dimension of HQET currents. The two-loop coefficient in f*B/fB =1-2αs(mb)/3π-Kbα2s/π2 +O(α3s,1/mb) is Kb=83/12+4/81π2+2/27π2ln2-1/9ζ(3)-19/54Nl +Δc=6.37+Δc, with Nl=4 light flavors, and a correction Δc=0.18+/-0.01 that takes account of the nonzero ratio mc/mb=0.28+/-0.03. Convergence of the perturbative series is poor: the fastest apparent convergence would entail αs(μ) at μ=370 MeV. ``Naive non-Abelianization'' of large-Nl results, via Nl-->Nl-33/2, gives reasonable approximations to exact two-loop results. All-order results for anomalous dimensions and matching coefficients are obtained at large β0=11=2/3Nl. Consistent cancellation between infrared- and ultraviolet-renormalon ambiguities is demonstrated.

  18. Effective field theory of large scale structure at two loops: The apparent scale dependence of the speed of sound

    Science.gov (United States)

    Baldauf, Tobias; Mercolli, Lorenzo; Zaldarriaga, Matias

    2015-12-01

    We study the effective field theory (EFT) of large-scale structure for cosmic density and momentum fields. We show that the finite part of the two-loop calculation and its counterterms introduces an apparent scale dependence for the leading-order parameter cs2 of the EFT starting at k =0.1 h Mpc-1 . These terms limit the range over which one can trust the one-loop EFT calculation at the 1% level to k z =0 . We construct a well-motivated one-parameter ansatz to fix the relative size of the one- and two-loop counterterms using their high-k sensitivity. Although this one-parameter model is a very restrictive choice for the counterterms, it explains the apparent scale dependence of cs2 seen in simulations. It is also able to capture the scale dependence of the density power spectrum up to k ≈0.3 h Mpc-1 at the 1% level at redshift z =0 . Considering a simple scheme for the resummation of large-scale motions, we find that the two-loop calculation reduces the need for this IR resummation at k <0.2 h Mpc-1 . Finally, we extend our calculation to momentum statistics and show that the same one-parameter model can also describe density-momentum and momentum-momentum statistics.

  19. The Effective Field Theory of Large Scale Structure at Two Loops: the apparent scale dependence of the speed of sound

    CERN Document Server

    Baldauf, Tobias; Zaldarriaga, Matias

    2015-01-01

    We study the Effective Field Theory of Large Scale Structure for cosmic density and momentum fields. We show that the finite part of the two-loop calculation and its counterterms introduce an apparent scale dependence for the leading order parameter $c_\\text{s}^2$ of the EFT starting at k=0.1 h/Mpc. These terms limit the range over which one can trust the one-loop EFT calculation at the 1 % level to k<0.1 h/Mpc at redshift z=0. We construct a well motivated one parameter ansatz to fix the relative size of the one- and two-loop counterterms using their high-k sensitivity. Although this one parameter model is a very restrictive choice for the counterterms, it explains the apparent scale dependence of $c_\\text{s}^2$ seen in simulations. It is also able to capture the scale dependence of the density power spectrum up to k$\\approx$ 0.3 h/Mpc at the 1 % level at redshift $z=0$. Considering a simple scheme for the resummation of large scale motions, we find that the two loop calculation reduces the need for this ...

  20. 2D Quantum Gravity on Compact Riemann Surfaces and Two-Loop Partition Function: Circumventing the c=1 Barrier?

    CERN Document Server

    Bilal, Adel

    2014-01-01

    We study two-dimensional quantum gravity on arbitrary genus Riemann surfaces in the Kaehler formalism where the basic quantum field is the (Laplacian of the) Kaehler potential. We do a careful first-principles computation of the fixed-area partition function $Z[A]$ up to and including all two-loop contributions. This includes genuine two-loop diagrams as determined by the Liouville action, one-loop diagrams resulting from the non-trivial measure on the space of metrics, as well as one-loop diagrams involving various counterterm vertices. Contrary to what is often believed, several such counterterms, in addition to the usual cosmological constant, do and must occur. We consistently determine the relevant counterterms from a one-loop computation of the full two-point Green's function of the Kaehler field. Throughout this paper we use the general spectral cutoff regularization developed recently and which is well-suited for multi-loop computations on curved manifolds. At two loops, while all "unwanted" contribut...

  1. Renormalization scheme dependence of the two-loop QCD corrections to the neutral Higgs-boson masses in the MSSM

    Energy Technology Data Exchange (ETDEWEB)

    Borowka, S. [University of Zurich, Institute for Physics, Zurich (Switzerland); Hahn, T.; Heinrich, G.; Hollik, W. [Max-Planck-Institut fuer Physik (Werner-Heisenberg-Institut), Muenchen (Germany); Heinemeyer, S. [Instituto de Fisica de Cantabria (CSIC-UC), Santander (Spain)

    2015-09-15

    Reaching a theoretical accuracy in the prediction of the lightest MSSM Higgs-boson mass, M{sub h}, at the level of the current experimental precision requires the inclusion of momentum-dependent contributions at the two-loop level. Recently two groups presented the two-loop QCD momentum-dependent corrections to M{sub h} (Borowka et al., Eur Phys J C 74(8):2994, 2014; Degrassi et al., Eur Phys J C 75(2):61, 2015), using a hybrid on-shell-DR scheme, with apparently different results. We show that the differences can be traced back to a different renormalization of the top-quark mass, and that the claim in Ref. Degrassi et al. (Eur Phys J C 75(2):61, 2015) of an inconsistency in Ref. Borowka et al. (Eur Phys J C 74(8):2994, 2014) is incorrect. We furthermore compare consistently the results for M{sub h} obtained with the top-quark mass renormalized on-shell and DR. The latter calculation has been added to the FeynHiggs package and can be used to estimate missing higher-order corrections beyond the two-loop level. (orig.)

  2. The pion electromagnetic structure with self-energy

    CERN Document Server

    Mello, Clayton Santos; Frederico, T

    2016-01-01

    We study the electromagnetic structure of the pion in terms of the quantum cromodynamic~(QCD) model on the Breit-frame. We calculated the observables, such as the electromagnetic form factor. The priori to have a calculation covariant need to get the valence term of the eletromagnetic form factor. We use the usual formalism in quantum field theory (QFT) and light-front quantum field theory (LFQFT) in order to test the properties of form factor in nonperturbative QCD. In this particular case, the form factor can be obtained using the pion Light-Front (LF) wave function including self-energy from Lattice-QCD. Specifically, these calculations was performed in LF formalism. We consider a quark-antiquark vertex model having a quark self-energy. Also we can use other models to compare the pion electromagnetic form factor with different wave function and to observe the degree of agreement between them.

  3. Nonrelativistic QED expansion for the electron self-energy

    Science.gov (United States)

    Patkóš, V.; Šimsa, D.; Zamastil, J.

    2017-01-01

    The recently proposed relativistic multipole expansion (RME) of the self-energy effect suggests some observations on the nonrelativistic expansion of the effect. First, the nature of the series for the one-loop self-energy of an electron bound by the Coulomb field of the nucleus is clarified. It is shown that the expansion of the energy shift caused by the self-energy effect contains terms of the form α (Zα ) 7ln(Z α ) , α (Zα ) 8ln3(Z α ) , α (Zα ) 9ln2(Z α ) , α (Zα ) 10ln4(Z α ) , and so on. Here Z is the charge of the nucleus. The origin of these terms is traced back to the logarithmic divergence of the Dirac S -wave function at the origin. These terms eventually lead to breakdown of the nonrelativistic quantum electrodynamics approach. Second, at leading order relativistic multipole expansion requires an evaluation of the "extended Bethe logarithm" (EBL). When expanded in series in Z α EBL reduces at leading order to the ordinary Bethe logarithm. However, it is argued that it is both more accurate and easier to calculate the EBL than the ordinary Bethe logarithm. Both variants of the Bethe logarithm can be calculated by means of the pseudostate method. An improvement of this method is suggested. Finally, the contribution of the combined self-energy vacuum polarization contribution to the Lamb shift in muonic hydrogen for the 1 s -4 s and 2 p -4 p states by means of the EBL is calculated. For cases that had already been calculated the results reported here are more accurate than the previous ones.

  4. Towards a Numerical Unitarity Approach for Two-loop Amplitudes in QCD

    CERN Document Server

    Ita, Harald

    2016-01-01

    The numerical unitarity approach has been important for obtaining reliable QCD predictions for the LHC. Here I discuss the extension of the approach beyond the leading quantum corrections for computing multi-loop amplitudes. The numerical unitarity approach requires a suitable parametrisation of the loop integrands as a sum of terms that integrate to zero (surface terms) and master integrands. The construction and classification of suitable surface terms which match the propagators structures of Feynman amplitudes is the main technical advance discussed. A number of spin-offs for integral reduction and further formal questions are briefly reviewed.

  5. Counting master integrals. Integration by parts vs. functional equations

    Energy Technology Data Exchange (ETDEWEB)

    Kniehl, Bernd A.; Tarasov, Oleg V. [Hamburg Univ. (Germany). II. Inst. fuer Theoretische Physik

    2016-01-15

    We illustrate the usefulness of functional equations in establishing relationships between master integrals under the integration-by-parts reduction procedure by considering a certain two-loop propagator-type diagram as an example.

  6. Sfermion loop contribution to the two-loop level fermion electric dipole moment in R-parity violating supersymmetric models

    CERN Document Server

    Yamanaka, Nodoka

    2012-01-01

    We evaluate the Barr-Zee type two-loop level contribution to the fermion electric and chromo-electric dipole moments with sfermion loop in R-parity violating supersymmetric models. It is found that the Barr-Zee type fermion dipole moment with sfermion loop acts destructively to the currently known fermion loop contribution, and that it has small effect when the mass of squarks or charged sleptons in the loop is larger than or comparable to that of the sneutrinos, but cannot be neglected if the sneutrinos are much heavier than loop sfermions.

  7. Nucleon self-energies for supernova equations of state

    Science.gov (United States)

    Hempel, Matthias

    2015-05-01

    Nucleon self-energies and interaction potentials in supernova (SN) matter, which are known to have an important effect on nucleosynthesis conditions in SN ejecta are investigated. Corresponding weak charged-current interaction rates with unbound nucleons that are consistent with existing SN equations of state (EOSs) are specified. The nucleon self-energies are made available online as electronic tables. The discussion is mostly restricted to relativistic mean-field models. In the first part of the article, the generic properties of this class of models at finite temperature and asymmetry are studied. It is found that the quadratic expansion of the EOS in terms of asymmetry works reasonably well at finite temperatures and deviations originate mostly from the kinetic part. The interaction part of the symmetry energy is found to be almost temperature independent. At low densities, the account of realistic nucleon masses requires the introduction of a linear term in the expansion. Finally, it is shown that the important neutron-to-proton potential difference is given approximately by the asymmetry of the system and the interaction part of the zero-temperature symmetry energy. The results of different interactions are then compared with constraints from nuclear experiments and thereby the possible range of the potential difference is limited. In the second part, for a certain class of SN EOS models, the formation of nuclei is considered. Only moderate modifications are found for the self-energies of unbound nucleons that enter the weak charged-current interaction rates. This is because in the present approach the binding energies of bound states do not contribute to the single-particle energies of unbound nucleons.

  8. Parquet decomposition calculations of the electronic self-energy

    Science.gov (United States)

    Gunnarsson, O.; Schäfer, T.; LeBlanc, J. P. F.; Merino, J.; Sangiovanni, G.; Rohringer, G.; Toschi, A.

    2016-06-01

    The parquet decomposition of the self-energy into classes of diagrams, those associated with specific scattering processes, can be exploited for different scopes. In this work, the parquet decomposition is used to unravel the underlying physics of nonperturbative numerical calculations. We show the specific example of dynamical mean field theory and its cluster extensions [dynamical cluster approximation (DCA)] applied to the Hubbard model at half-filling and with hole doping: These techniques allow for a simultaneous determination of two-particle vertex functions and self-energies and, hence, for an essentially "exact" parquet decomposition at the single-site or at the cluster level. Our calculations show that the self-energies in the underdoped regime are dominated by spin-scattering processes, consistent with the conclusions obtained by means of the fluctuation diagnostics approach [O. Gunnarsson et al., Phys. Rev. Lett. 114, 236402 (2015), 10.1103/PhysRevLett.114.236402]. However, differently from the latter approach, the parquet procedure displays important changes with increasing interaction: Even for relatively moderate couplings, well before the Mott transition, singularities appear in different terms, with the notable exception of the predominant spin channel. We explain precisely how these singularities, which partly limit the utility of the parquet decomposition and, more generally, of parquet-based algorithms, are never found in the fluctuation diagnostics procedure. Finally, by a more refined analysis, we link the occurrence of the parquet singularities in our calculations to a progressive suppression of charge fluctuations and the formation of a resonance valence bond state, which are typical hallmarks of a pseudogap state in DCA.

  9. Constraints on abelian extensions of the Standard Model from two-loop vacuum stability and U(1) B- L

    Science.gov (United States)

    Corianò, Claudio; Rose, Luigi Delle; Marzo, Carlo

    2016-02-01

    We present a renormalization group study of the scalar potential in a minimal U(1) B- L extension of the Standard Model involving one extra heavier Higgs and three heavy right-handed neutrinos with family universal B-L charge assignments. We implement a type-I seesaw for the masses of the light neutrinos of the Standard Model. In particular, compared to a previous study, we perform a two-loop extension of the evolution, showing that two-loop effects are essential for the study of the stability of the scalar potential up to the Planck scale. The analysis includes the contribution of the kinetic mixing between the two abelian gauge groups, which is radiatively generated by the evolution, and the one-loop matching conditions at the electroweak scale. By requiring the stability of the potential up to the Planck mass, significant constraints on the masses of the heavy neutrinos, on the gauge couplings and the mixing in the Higgs sector are identified.

  10. Constraints on Abelian Extensions of the Standard Model from Two-Loop Vacuum Stability and $U(1)_{B-L}$

    CERN Document Server

    Coriano, Claudio; Marzo, Carlo

    2015-01-01

    We present a renormalization group study of the scalar potential in a minimal $U(1)_{B-L}$ extension of the Standard Model involving one extra heavier Higgs and three heavy right-handed neutrinos with family universal B-L charge assignments. We implement a type-I seesaw for the masses of the light neutrinos of the Standard Model. In particular, compared to a previous study, we perform a two-loop extension of the evolution, showing that two-loop effects are essential for the study of the stability of the scalar potential up to the Planck scale. The analysis includes the contribution of the kinetic mixing between the two abelian gauge groups, which is radiatively generated by the evolution, and the one-loop matching conditions at the electroweak scale. By requiring the stability of the potential up to the Planck mass, significant constraints on the masses of the heavy neutrinos, on the gauge couplings and the mixing in the Higgs sector are identified.

  11. A two-loop study of the deconfinement transition in Yang-Mills theories: SU(3) and beyond

    CERN Document Server

    Reinosa, U; Tissier, M; Wschebor, N

    2015-01-01

    We study the confinement-deconfinement phase transition of pure Yang-Mills theories at finite temperature within a simple massive extension of standard background field methods. We generalize our recent next-to-leading-order perturbative calculation of the Polyakov loop and the related background field effective potential for the SU(2) theory to any compact and connex Lie group with a simple Lie algebra. We discuss in detail the SU(3) theory, where the two-loop corrections yield improved values for the first order transition temperature as compared to the one-loop result. We show that certain one-loop artifacts of thermodynamical observables disappear at two-loop order, as was already the case for the SU(2) theory. In particular, the entropy and the pressure are positive for all temperatures. We also discuss the groups SU(4) and Sp(2) which shed interesting light, respectively, on the relation between the (de)confinement of static matter sources in the various representations of the gauge group and on the use...

  12. Severe accident analysis in a two-loop PWR nuclear power plant with the ASTEC code

    Energy Technology Data Exchange (ETDEWEB)

    Sadek, Sinisa; Amizic, Milan; Grgic, Davor [Zagreb Univ. (Croatia). Faculty of Electrical Engineering and Computing

    2013-12-15

    The ASTEC/V2.0 computer code was used to simulate a hypothetical severe accident sequence in the nuclear power plant Krsko, a 2-loop pressurized water reactor (PWR) plant. ASTEC is an integral code jointly developed by Institut de Radioprotection et de Surete Nucleaire (IRSN, France) and Gesellschaft fuer Anlagen- und Reaktorsicherheit (GRS, Germany) to assess nuclear power plant behaviour during a severe accident. The analysis was conducted in 2 steps. First, the steady state calculation was performed in order to confirm the applicability of the plant model and to obtain correct initial conditions for the accident analysis. The second step was the calculation of the station blackout accident with a leakage of the primary coolant through degraded reactor coolant pump seals, which was a small LOCA without makeup capability. Two scenarios were analyzed: one with and one without the auxiliary feedwater (AFW). The latter scenario, without the AFW, resulted in earlier core damage. In both cases, the accident ended with a core melt and a reactor pressure vessel failure with significant release of hydrogen. In addition, results of the ASTEC calculation were compared with results of the RELAP5/SCDAPSIM calculation for the same transient scenario. The results comparison showed a good agreement between predictions of those 2 codes. (orig.)

  13. The static quark self-energy at O($\\alpha^{20}$) in perturbation theory

    CERN Document Server

    Bali, Gunnar S; Pineda, Antonio

    2013-01-01

    In Refs. [1,2] we determined the infinite volume coefficients of the perturbative expansions of the self-energies of static sources in the fundamental and adjoint representations in SU(3) gluodynamics to order $\\alpha^{20}$. We used numerical stochastic perturbation theory [3], where we employed a new second order integrator and twisted boundary conditions. The expansions were obtained in lattice regularization with the Wilson action and two different discretizations of the covariant time derivative within the Polyakov loop. Overall, we obtained four different perturbative series. For all of them the high order coefficients displayed the factorial growth predicted by the conjectured renormalon picture, based on the operator product expansion. This enabled us to determine the normalization constants of the leading infrared renormalons of heavy quark and heavy gluino pole masses. Here we present improved determinations of the normalization constants and the perturbative coefficients by incorporating the four-lo...

  14. Extending two Higgs doublet models for two-loop neutrino mass generation and one-loop neutrinoless double beta decay

    CERN Document Server

    Liu, Zhen

    2016-01-01

    We extend some two Higgs doublet models, where the Yukawa couplings for the charged fermion mass generation only involve one Higgs doublet, by two singlet scalars respectively carrying a singly electric charge and a doubly electric charge. The doublet and singlet scalars together can mediate a two-loop diagram to generate a tiny Majorana mass matrix of the standard model neutrinos. Remarkably, the structure of the neutrino mass matrix is fully determined by the symmetric Yukawa couplings of the doubly charged scalar to the right-handed leptons. Meanwhile, a one-loop induced neutrinoless double beta decay can arrive at a testable level even if the electron neutrino has an extremely small Majorana mass. We also study other experimental constraints and implications including some rare processes and Higgs phenomenology.

  15. Extending two Higgs doublet models for two-loop neutrino mass generation and one-loop neutrinoless double beta decay

    Directory of Open Access Journals (Sweden)

    Zhen Liu

    2017-02-01

    Full Text Available We extend some two Higgs doublet models, where the Yukawa couplings for the charged fermion mass generation only involve one Higgs doublet, by two singlet scalars respectively carrying a singly electric charge and a doubly electric charge. The doublet and singlet scalars together can mediate a two-loop diagram to generate a tiny Majorana mass matrix of the standard model neutrinos. Remarkably, the structure of the neutrino mass matrix is fully determined by the symmetric Yukawa couplings of the doubly charged scalar to the right-handed leptons. Meanwhile, a one-loop induced neutrinoless double beta decay can arrive at a testable level even if the electron neutrino has an extremely small Majorana mass. We also study other experimental constraints and implications including some rare processes and Higgs phenomenology.

  16. The corrections from one loop and two-loop Barr-Zee type diagrams to muon MDM in BLMSSM

    CERN Document Server

    Zhao, Shu-Min; Zhang, Hai-Bin; Yan, Ben; Zhan, Xi-Jie

    2014-01-01

    In a supersymmetric extension of the standard model where baryon and lepton numbers are local gauge symmetries(BLMSSM) and the Yukawa couplings between Higgs doublets and exotic quarks are considered, we study the one loop diagrams and the two-loop Barr-Zee type diagrams with a closed Fermi(scalar) loop between the vector Boson and Higgs. Using the effective Lagrangian method, we deduce the Wilson coefficients of dimension 6 operators contributing to the anomalous magnetic moment of muon, which satisfies the electromagnetic gauge invariance. In the numerical analysis, we consider the experiment constraints from Higgs and neutrino data. In some parameter space, the new physics contribution is large and even reaches $24\\times10^{-10}$, which can remedy the deviation well.

  17. Extending two Higgs doublet models for two-loop neutrino mass generation and one-loop neutrinoless double beta decay

    Science.gov (United States)

    Liu, Zhen; Gu, Pei-Hong

    2017-02-01

    We extend some two Higgs doublet models, where the Yukawa couplings for the charged fermion mass generation only involve one Higgs doublet, by two singlet scalars respectively carrying a singly electric charge and a doubly electric charge. The doublet and singlet scalars together can mediate a two-loop diagram to generate a tiny Majorana mass matrix of the standard model neutrinos. Remarkably, the structure of the neutrino mass matrix is fully determined by the symmetric Yukawa couplings of the doubly charged scalar to the right-handed leptons. Meanwhile, a one-loop induced neutrinoless double beta decay can arrive at a testable level even if the electron neutrino has an extremely small Majorana mass. We also study other experimental constraints and implications including some rare processes and Higgs phenomenology.

  18. The dielectric environment dependent exchange self-energy of the energy structure in graphene

    Energy Technology Data Exchange (ETDEWEB)

    Yang, C.H., E-mail: chyang@nuist.edu.c [Faculty of Maths and Physics, Nanjing University of Information Science and Technology, Nanjing 210044 (China); Xu, W. [Institute of Solid State Physics, Chinese Academy of Sciences, Hefei 230031 (China)

    2010-10-01

    We theoretically calculate the energy dispersion in the presence of the screened exchange self-energy in extrinsic monolayer graphene. It is found that the exchange self-energy enhances the renormalized Fermi velocity. With decreasing the dielectric constant, the screening effect and the electron correlation effect increase which induces the Fermi velocity increasing. The screened exchange energy has an energy shift at the Dirac points. The self-energy from the valance band carriers gives the main contribution to the effective energy. We also discuss the electron density dependence of the self-energy.

  19. Scalar Contribution to the Graviton Self-Energy During Inflation

    Energy Technology Data Exchange (ETDEWEB)

    Park, Sohyun [Univ. of Florida, Gainesville, FL (United States)

    2012-01-01

    We use dimensional regularization to evaluate the one loop contribution to the graviton self-energy from a massless, minimally coupled scalar on a locally de Sitter background. For noncoincident points our result agrees with the stress tensor correlators obtained recently by Perez-Nadal, Roura and Verdaguer. We absorb the ultraviolet divergences using the R2 and C2 counterterms first derived by ’t Hooft and Veltman, and we take the D = 4 limit of the finite remainder. The renormalized result is expressed as the sum of two transverse, 4th order differential operators acting on nonlocal, de Sitter invariant structure functions. In this form it can be used to quantum-correct the linearized Einstein equations so that one can study how the inflationary production of infrared scalars affects the propagation of dynamical gravitons and the force of gravity. We have seen that they have no effect on the propagation of dynamical gravitons. Our computation motivates a conjecture for the first correction to the vacuum state wave functional of gravitons. We comment as well on performing the same analysis for the more interesting contribution from inflationary gravitons, and on inferring one loop corrections to the force of gravity.

  20. Finding new relationships between hypergeometric functions by evaluating Feynman integrals

    Energy Technology Data Exchange (ETDEWEB)

    Kniehl, Bernd A. [Santa Barbara Univ., CA (United States). Kavli Inst. for Theoretical Physics; Tarasov, Oleg V. [Hamburg Univ. (Germany). 2. Inst. fuer Theoretische Physik

    2011-08-15

    Several new relationships between hypergeometric functions are found by comparing results for Feynman integrals calculated using different methods. A new expression for the one-loop propagator-type integral with arbitrary masses and arbitrary powers of propagators is derived in terms of only one Appell hypergeometric function F{sub 1}. From the comparison of this expression with a previously known one, a new relation between the Appell functions F{sub 1} and F{sub 4} is found. By comparing this new expression for the case of equal masses with another known result, a new formula for reducing the F{sub 1} function with particular arguments to the hypergeometric function {sub 3}F{sub 2} is derived. By comparing results for a particular one-loop vertex integral obtained using different methods, a new relationship between F{sub 1} functions corresponding to a quadratic transformation of the arguments is established. Another reduction formula for the F{sub 1} function is found by analysing the imaginary part of the two-loop self-energy integral on the cut. An explicit formula relating the F{sub 1} function and the Gaussian hypergeometric function {sub 2}F{sub 1} whose argument is the ratio of polynomials of degree six is presented. (orig.)

  1. Local mirror symmetry and the sunset Feynman integral

    CERN Document Server

    Bloch, Spencer; Vanhove, Pierre

    2016-01-01

    We study the sunset Feynman integral defined as the scalar two-point self-energy at two-loop order in a two dimensional space-time. We firstly compute the Feynman integral, for arbitrary internal masses, in terms of the regulator of a class in the motivic cohomology of a 1-parameter family of open elliptic curves. Using an Hodge theoretic (B-model) approach, we show that the integral is given by a sum of elliptic dilogarithms evaluated at the divisors determined by the punctures. Secondly we associate to the sunset elliptic curve a local non-compact Calabi-Yau 3-fold, obtained as a limit of elliptically fibered compact Calabi-Yau 3-folds. By considering the limiting mixed Hodge structure of the Batyrev dual A-model, we arrive at an expression for the sunset Feynman integral in terms of the local Gromov-Witten prepotential of the del Pezzo surface of degree 6. This expression is obtained by proving a strong form of local mirror symmetry which identifies this prepotential with the second regulator period of the...

  2. Two--Loop Anomalous Dimension Matrix for $\\Delta S=1$ Weak Non-Leptonic Decays; 2, ${\\cal O}(\\alpha_e \\alpha_s)$

    CERN Document Server

    Buras, Andrzej J; Lautenbacher, M E; Buras, Andrzej J.; Jamin, Matthias; Lautenbacher, Markus E.

    1993-01-01

    We calculate the $10\\times 10$ two--loop anomalous dimension matrix to order $\\ord(\\alpha_e \\alpha_s)$ in the dimensional regularization scheme with anticommuting $\\gamma_5$ (NDR) which is necessary for the extension of the $\\Delta S=1$ weak Hamiltonian involving electroweak penguins beyond the leading logarithmic approximation. We demonstrate, how a direct calculation of penguin diagrams involving $\\gamma_5$ in closed fermion loops can be avoided thus allowing a consistent calculation of two--loop anomalous dimensions in the simplest renormalization scheme with anticommuting $\\gamma_5$ in $D$ dimensions. We give the necessary one--loop finite terms which allow to obtain the corresponding two--loop anomalous dimension matrix in the HV scheme with non--anticommuting $\\gamma_5$.

  3. Validity of the local self-energy approximation: Application to coupled quantum impurities

    NARCIS (Netherlands)

    Mitchell, A.

    2015-01-01

    We examine the quality of the local self-energy approximation, applied here to models of multiple quantum impurities coupled to an electronic bath. The local self-energy is obtained by solving a single-impurity Anderson model in an effective medium that is determined self-consistently, similar to

  4. The calculation of the two-loop spin splitting functions P{sub ij}{sup (1)}(x)

    Energy Technology Data Exchange (ETDEWEB)

    Mertig, R. [Nationaal Inst. voor Kernfysica en Hoge-Energiefysica (NIKHEF), Amsterdam (Netherlands). Sectie H; Neerven, W.L. van [Rijksuniversiteit Leiden (Netherlands). Inst. Lorentz voor Theoretische Natuurkunde

    1995-06-01

    We present the calculation of the two-loop spin splitting functions P{sub ij}{sup (1)}(x) (i, j=q, g) contributing to the next-to-leading order corrected spin structure function g{sub 1}(x, Q{sup 2}). These splitting functions, which are presented in the anti M anti S scheme, are derived from the order {alpha}{sub s}{sup 2} contribution to the anomalous dimensions {gamma}{sup m}{sub ij} (i, j=q, g). The latter correspond to the local operators which appear in the operator product expansion of two electromagnetic currents. Some of the properties of the anomalous dimensions will be discussed. In particular we find that in order {alpha}{sub s}{sup 2} the supersymmetric relation {gamma}{sup m}{sub qq}+{gamma}{sup m}{sub qg}-{gamma}{sup m}{sub qg}-{gamma}{sup m}{sub gg}=0 is violated. (orig.).

  5. Thermodynamics and phase transition of the O(N) model from the two-loop Phi-derivable approximation

    CERN Document Server

    Markó, Gergely; Szép, Zsolt

    2013-01-01

    We discuss the thermodynamics of the O(N) model across the corresponding phase transition using the two-loop Phi-derivable approximation of the effective potential and compare our results to those obtained in the literature within the Hartree-Fock approximation. In particular, we find that in the chiral limit the transition is of the second order, whereas it was found to be of the first order in the Hartree-Fock case. These features are manifest at the level of the thermodynamical observables. We also compute the thermal sigma and pion masses from the curvature of the effective potential. In the chiral limit, this guarantees that the Goldstone theorem is obeyed in the broken phase. A realistic parametrization of the model in the N=4 case, based on the vacuum values of the curvature masses, shows that a sigma mass of around 450 MeV can be obtained. The equations are renormalized after extending our previous results for the N=1 case by means of the general procedure described in [J. Berges et al., Annals Phys. ...

  6. The 1-loop self-energy of an electron in a strong external magnetic field revisited

    CERN Document Server

    Machet, Bruno

    2015-01-01

    I revisit the 1-loop self-energy of an electron in a strong, constant and uniform external magnetic field B. First, I show, after Tsai (1974), how, for an electron in the lowest Landau level, Schwinger's techniques, as explained by Dittrich and Reuter (1985) lead to the same integral deduced by Demeur (1953) and used later by Jancovici (1969). Then, I calculate the Demeur-Jancovici integral in the range $75 \\leq L\\equiv\\frac{|e|B}{m^2} \\leq 10\\,000$, which yields $\\delta m \\simeq \\frac{\\alpha m}{4\\pi} \\left[\\left(\\ln L-\\gamma_E-\\frac32\\right)^2 -\\frac94 +\\frac{\\pi}{\\beta-1} +\\frac{\\pi^2}{6} +\\frac{\\pi\\;\\Gamma[1-\\beta]}{L^{\\beta-1}} +\\frac{1}{L}\\left(\\frac{\\pi}{2-\\beta}-5\\right) +{\\cal O}(\\frac{1}{L^{\\geq 2}})\\right],\\ \\beta \\simeq 1.175$, close to Jancovici's last estimate $\\delta m \\simeq \\frac{\\alpha m}{4\\pi}\\left[\\left(\\ln 2L-\\gamma_E-\\frac32\\right)^2 +A+\\ldots\\right]$ with $A\\simeq 3.5$ (previously undetermined). The term proportional to $(\\ln\\frac{|e|B}{m^2})^2$ can never be considered to be leading and ...

  7. Two-loop RGE of a general renormalizable Yang-Mills theory in a renormalization scheme with an explicit UV cutoff

    CERN Document Server

    Chankowski, Piotr H; Meissner, Krzysztof A

    2016-01-01

    We perform a systematic one-loop renormalization of a general renormalizable Yang-Mills theory coupled to scalars and fermions using a regularization scheme with an explicit UV momentum cutoff $\\Lambda$. We construct the necessary finite counterterms restoring the BRST invariance of the effective action by analyzing the relevant Slavnov-Taylor identities. We find the relation between the renormalized parameters in our scheme and in the conventional $\\overline{\\rm MS}$ scheme which allow us to obtain the explicit two-loop renormalization group equations in our scheme from the known two-loop ones in the $\\overline{\\rm MS}$ scheme. We calculate in our scheme the divergences of two-loop vacuum graphs in the presence of a constant scalar background field which allow us to rederive the two-loop beta functions for parameters of the scalar potential. We also prove that consistent application of the proposed regularization leads to counterterms which, together with the original action, combine to a bare action express...

  8. Two-loop RGE of a general renormalizable Yang-Mills theory in a renormalization scheme with an explicit UV cutoff

    Energy Technology Data Exchange (ETDEWEB)

    Chankowski, Piotr H. [Institute of Theoretical Physics, Faculty of Physics, University of Warsaw,Pasteura 5, 02-093 Warsaw (Poland); Lewandowski, Adrian [Max-Planck-Institut für Gravitationsphysik (Albert-Einstein-Institut),Mühlenberg 1, D-14476 Potsdam (Germany); Institute of Theoretical Physics, Faculty of Physics, University of Warsaw,Pasteura 5, 02-093 Warsaw (Poland); Meissner, Krzysztof A. [Institute of Theoretical Physics, Faculty of Physics, University of Warsaw,Pasteura 5, 02-093 Warsaw (Poland)

    2016-11-18

    We perform a systematic one-loop renormalization of a general renormalizable Yang-Mills theory coupled to scalars and fermions using a regularization scheme with a smooth momentum cutoff Λ (implemented through an exponential damping factor). We construct the necessary finite counterterms restoring the BRST invariance of the effective action by analyzing the relevant Slavnov-Taylor identities. We find the relation between the renormalized parameters in our scheme and in the conventional (MS)-bar scheme which allow us to obtain the explicit two-loop renormalization group equations in our scheme from the known two-loop ones in the (MS)-bar scheme. We calculate in our scheme the divergences of two-loop vacuum graphs in the presence of a constant scalar background field which allow us to rederive the two-loop beta functions for parameters of the scalar potential. We also prove that consistent application of the proposed regularization leads to counterterms which, together with the original action, combine to a bare action expressed in terms of bare parameters. This, together with treating Λ as an intrinsic scale of a hypothetical underlying finite theory of all interactions, offers a possibility of an unconventional solution to the hierarchy problem if no intermediate scales between the electroweak scale and the Planck scale exist.

  9. Two-loop RGE of a general renormalizable Yang-Mills theory in a renormalization scheme with an explicit UV cutoff

    Science.gov (United States)

    Chankowski, Piotr H.; Lewandowski, Adrian; Meissner, Krzysztof A.

    2016-11-01

    We perform a systematic one-loop renormalization of a general renormalizable Yang-Mills theory coupled to scalars and fermions using a regularization scheme with a smooth momentum cutoff Λ (implemented through an exponential damping factor). We construct the necessary finite counterterms restoring the BRST invariance of the effective action by analyzing the relevant Slavnov-Taylor identities. We find the relation between the renormalized parameters in our scheme and in the conventional overline{MS} scheme which allow us to obtain the explicit two-loop renormalization group equations in our scheme from the known two-loop ones in the overline{MS} scheme. We calculate in our scheme the divergences of two-loop vacuum graphs in the presence of a constant scalar background field which allow us to rederive the two-loop beta functions for parameters of the scalar potential. We also prove that consistent application of the proposed regularization leads to counterterms which, together with the original action, combine to a bare action expressed in terms of bare parameters. This, together with treating Λ as an intrinsic scale of a hypothetical underlying finite theory of all interactions, offers a possibility of an unconventional solution to the hierarchy problem if no intermediate scales between the electroweak scale and the Planck scale exist.

  10. Quark self-energy in an ellipsoidally anisotropic quark-gluon plasma

    CERN Document Server

    Kasmaei, Babak S; Strickland, Michael

    2016-01-01

    We calculate the quark self-energy in a quark-gluon plasma that possesses an ellipsoidal momentum-space anisotropy in the local rest frame. By introducing additional transverse momentum anisotropy parameters into the parton distribution functions, we generalize previous results which were obtained for the case of a spheroidal anisotropy. Our results demonstrate that the presence of anisotropies in the transverse directions affects the real and imaginary parts of quark self-energy and, consequently, the self-energy depends on both the polar and azimuthal angles in the local rest frame of the matter. Our results for the quark self-energy set the stage for the calculation of the effects of ellipsoidal momentum-space anisotropy on quark-gluon plasma photon spectra and collective flow.

  11. Complete Form of Fermion Self-energy in NJL Model with External Magnetic Field

    CERN Document Server

    Shi, Song; Cui, Zhu-Fang; Xia, Yong-Hui; Zong, Hong-Shi

    2016-01-01

    In this paper, we aim to study the complete form of self-energy in fermion propagator within two-flavor NJL model in the case of finite temperature, chemical potential and external magnetic field. Through self-consistency analysis we prove that the self-energy is not simply proportional to dynamical mass in the presence of chemical potential, moreover, it could be more complicated after introducing external magnetic field. We find out the appropriate and complete form of self-energy and establish new gap equations. The numerical results show that the dynamical mass only has small quantitative modification rather than qualitative change by using these new gap equations, but the new self-energy does generate split in the dispersion relation with fixed momentum and Landau level.

  12. The 1-loop self-energy of an electron in a strong external magnetic field revisited

    Science.gov (United States)

    Machet, B.

    2016-05-01

    I calculate the 1-loop self-energy of the lowest Landau level of an electron of mass m in a strong, constant and uniform external magnetic field B, beyond its always used truncation at (ln L)2, L = |e|B m2. This is achieved by evaluating the integral deduced in 1953 by Demeur and incompletely calculated in 1969 by Jancovici, which I recover from Schwinger’s techniques of calculation. It yields δm ≃ αm 4π ln L - γE -3 22 -9 4 + π β-1 + π2 6 + πΓ[1-β] Lβ-1 + 1 L π 2-β - 5 + 𝒪 1 L≥2 with β ≃ 1.175 for 75 ≤ L ≤ 10, 000. The (ln L)2 truncation exceeds the precise estimate by 45% at L = 100 and by more at lower values of L, due to neglecting, among others, the single logarithmic contribution. This is doubly unjustified because it is large and because it is needed to fulfill appropriate renormalization conditions. Technically challenging improvements look therefore necessary, for example, when resumming higher loops and incorporating the effects of large B on the photonic vacuum polarization, like investigated in recent years.

  13. Multiple Scattering Expansion of the Self-Energy at Finite Temperature

    CERN Document Server

    Jeon, S; Jeon, Sangyong; Ellis, Paul J.

    1998-01-01

    An often used rule that the thermal correction to the self-energy is the thermal phase-space times the forward scattering amplitude from target particles is shown to be the leading term in an exact multiple scattering expansion. Starting from imaginary-time finite-temperature field theory, a rigorous expansion for the retarded self-energy is derived. The relationship to the thermodynamic potential is briefly discussed.

  14. Self-energy Effects on Nuclear Magnetic Resonance Parameters within Quantum Electrodynamics Perturbation Theory

    Directory of Open Access Journals (Sweden)

    Gustavo A. Aucar

    2002-08-01

    Full Text Available Abstract: A theory for the calculation of self-energy corrections to the nuclear magnetic parameters is given in this paper. It is based on the S-matrix formulation of bound-state quantum electrodynamics (QED. Explicit expressions for the various terms of the S-matrix are given. The interpretation of the self-energy, one- and two-vertex terms and some perspective for possible future developments are discussed.

  15. The Two-Loop Anomalous Dimension Matrix for $\\Delta S=1$ Weak Non-Leptonic Decays; 1, ${\\cal O}(\\alpha_s^2)$

    CERN Document Server

    Buras, Andrzej J; Lautenbacher, M E; Weisz, P; Buras, Andrzej J.; Jamin, Matthias; Lautenbacher, Markus E.; Weisz, Peter H.

    1993-01-01

    We calculate the two-loop $10 \\times 10$ anomalous dimension matrix ${\\cal O}(\\alpha_s^{2})$ involving current-current operators, QCD penguin operators, and electroweak penguin operators especially relevant for $\\Delta S=1$ weak non-leptonic decays, but also important for $\\Delta B=1$ decays. The calculation is performed in two schemes for $\\gamma_{5}$: the dimensional regularization scheme with anticommuting $\\gamma_{5}$ (NDR), and in the 't Hooft-Veltman scheme. We demonstrate how a direct calculation of diagrams involving $\\gamma_{5}$ in closed fermion loops can be avoided thus allowing a consistent calculation in the NDR scheme. The compatibility of the results obtained in the two schemes considered is verified and the properties of the resulting matrices are discussed. The two-loop corrections are found to be substantial. The two-loop anomalous dimension matrix ${\\cal O}(\\alpha_e\\alpha_s)$, required for a consistent inclusion of electroweak penguin operators, is presented in a subsequent publication.

  16. The Imaginary Part of Nucleon Self-energy in hot nuclear matter

    CERN Document Server

    Alvarez-Ruso, L; Oset, E

    1996-01-01

    A semiphenomenological approach to the nucleon self-energy in nuclear matter at finite temperatures is followed. It combines elements of Thermo Field Dynamics for the treatment of finite temperature with a model for the self-energy, which evaluates the second order diagrams taking the needed dynamics of the NN interaction from experiment. The approach proved to be accurate at zero temperature to reproduce Im(Sigma) and other properties of nucleons in matter. In the present case we apply it to determine Im(Sigma) at finite temperatures. An effective NN cross section is deduced which can be easily used in analyses of heavy ion reactions.

  17. Anomalous scaling and large-scale anisotropy in magnetohydrodynamic turbulence: two-loop renormalization-group analysis of the Kazantsev-Kraichnan kinematic model.

    Science.gov (United States)

    Antonov, N V; Gulitskiy, N M

    2012-06-01

    The field theoretic renormalization group and operator product expansion are applied to the Kazantsev-Kraichnan kinematic model for the magnetohydrodynamic turbulence. The anomalous scaling emerges as a consequence of the existence of certain composite fields ("operators") with negative dimensions. The anomalous exponents for the correlation functions of arbitrary order are calculated in the two-loop approximation (second order of the renormalization-group expansion), including the anisotropic sectors. The anomalous scaling and the hierarchy of anisotropic contributions become stronger due to those second-order contributions.

  18. Effect of spray system on fission product distribution in containment during a severe accident in a two-loop pressurized water reactor

    Energy Technology Data Exchange (ETDEWEB)

    Dehjourian, Mehdi; Rahgoshay, Mohammad; Jahanfamia, Gholamreza [Dept. of Nuclear Engineering, Science and Research Branch, Islamic Azad University of Tehran, Tehran (Iran, Islamic Republic of); Sayareh, Reza [Faculty of Electrical and Computer Engineering, Kerman Graduate University of Technology, Kerman (Iran, Islamic Republic of); Shirani, Saied [Faculty of Engineering, Shahid Beheshti University, Tehran (Iran, Islamic Republic of)

    2016-08-15

    The containment response during the first 24 hours of a low-pressure severe accident scenario in a nuclear power plant with a two-loop Westinghouse-type pressurized water reactor was simulated with the CONTAIN 2.0 computer code. The accident considered in this study is a large-break loss-of-coolant accident, which is not successfully mitigated by the action of safety systems. The analysis includes pressure and temperature responses, as well as investigation into the influence of spray on the retention of fission products and the prevention of hydrogen combustion in the containment.

  19. Effect of Spray System on Fission Product Distribution in Containment During a Severe Accident in a Two-Loop Pressurized Water Reactor

    Directory of Open Access Journals (Sweden)

    Mehdi Dehjourian

    2016-08-01

    Full Text Available The containment response during the first 24 hours of a low-pressure severe accident scenario in a nuclear power plant with a two-loop Westinghouse-type pressurized water reactor was simulated with the CONTAIN 2.0 computer code. The accident considered in this study is a large-break loss-of-coolant accident, which is not successfully mitigated by the action of safety systems. The analysis includes pressure and temperature responses, as well as investigation into the influence of spray on the retention of fission products and the prevention of hydrogen combustion in the containment.

  20. Non-transversality of the gluon self-energy and the DDT analysis

    Science.gov (United States)

    Konetschny, W.

    1982-12-01

    It is found that the one-loop corrections to the propagator induced by the non-transversality of the gluon self energy in the planar gauge are not kinematically suppressed in the leading logarithm approximation. As a consequence the multiplicative renormalization of the bare gluon propagator assumed by Dokshitzer, Dyakonov and Troyan is lost.

  1. SINGLE-PARTICLE SELF-ENERGY AND OPTICAL CONDUCTIVITY OF THE SIMPLIFIED HUBBARD-MODEL

    NARCIS (Netherlands)

    de Vries, Pedro; Michielsen, Kristel; Raedt, Hans De

    1994-01-01

    It is shown that the single-particle self-energy of the one and two-dimensional simplified Hubbard model exhibits different behavior characterized by Fermi-liquid, non-Fermi-liquid quasiparticle, or non-quasiparticle excitations, as a function of the strength of the on-site Coulomb repulsion U, temp

  2. Krylov subspace method for evaluating the self-energy matrices in electron transport calculations

    DEFF Research Database (Denmark)

    Sørensen, Hans Henrik Brandenborg; Hansen, Per Christian; Petersen, D. E.;

    2008-01-01

    We present a Krylov subspace method for evaluating the self-energy matrices used in the Green's function formulation of electron transport in nanoscale devices. A procedure based on the Arnoldi method is employed to obtain solutions of the quadratic eigenvalue problem associated with the infinite...

  3. Consistent off-shell pi NN vertex and nucleon self-energy

    NARCIS (Netherlands)

    Kondratyuk, S; Scholten, O

    1999-01-01

    We present a consistent calculation of half-off-shell form factors in the pion-nucleon vertex and the nucleon self-energy. Numerical results are presented. Near the on-shell point the pion-nucleon vertex is dominated by the pseudovector coupling, while at large nucleon invariant masses we find a siz

  4. Consistent off-shell πNN vertex and nucleon self-energy

    NARCIS (Netherlands)

    Kondratyuk, S.; Scholten, O.

    1999-01-01

    We present a consistent calculation of half-off-shell form factors in the pion-nucleon vertex and the nucleon self-energy. Numerical results are presented. Near the on-shell point the pion-nucleon vertex is dominated by the pseudovector coupling, while at large nucleon invariant masses we find a siz

  5. Two-loop electroweak corrections to the A{sup 0}{gamma}{gamma} and A{sup 0}gg couplings of the CP-odd Higgs boson

    Energy Technology Data Exchange (ETDEWEB)

    Brod, J. [Karlsruhe Univ. (T.H.) (Germany). Inst. fuer Theoretische Teilchenphysik; Fugel, F. [Paul Scherrer Inst. (PSI), Villigen (Switzerland); Kniehl, B.A. [Hamburg Univ. (Germany). 2. Inst. fuer Theoretische Physik

    2008-06-15

    Using the asymptotic-expansion technique, we compute the dominant two-loop electroweak corrections, of O(G{sub F}m{sup 2}{sub t}), to production and decay via a pair of photons or gluons of the CP-odd Higgs boson A{sup 0} in a two-Higgs-doublet model with low- to intermediate values of the Higgs-boson masses and ratio tan {beta}=v{sub 2}/v{sub 1} of the vacuum expectation values. We also study the influence of a sequential heavyfermion generation. The appearance of three {gamma}{sub 5} matrices in closed fermion loops requires special care in the dimensional regularisation of ultraviolet divergences. The finite renormalisation constant for the pseudoscalar current effectively restoring the anticommutativity of the {gamma}{sub 5} matrix, familiar from perturbative quantum chromodynamics, is found not to receive a correction in this order. We also revisit the dominant two-loop electroweak correction to the H{yields}{gamma}{gamma} decay width in the standard model with a fourth fermion generation. (orig.)

  6. Breakdown of Fermi liquid behavior near the hot spots in a two-dimensional model: A two-loop renormalization group analysis

    Energy Technology Data Exchange (ETDEWEB)

    Carvalho, Vanuildo S. de [Instituto de Física, Universidade Federal de Goiás, 74.001-970 Goiânia, GO (Brazil); Freire, Hermann, E-mail: hfreire@mit.edu [Instituto de Física, Universidade Federal de Goiás, 74.001-970 Goiânia, GO (Brazil); Department of Physics, Massachusetts Institute of Technology, Cambridge, MA 02139 (United States)

    2013-10-21

    Motivated by a recent experimental observation of a nodal liquid on both single crystals and thin films of Bi{sub 2}Sr{sub 2}CaCu{sub 2}O{sub 8+} {sub δ} by Chatterjee et al. [Nature Phys. 6 (2010) 99], we perform a field-theoretical renormalization group (RG) analysis of a two-dimensional model such that only eight points located near the “hot spots” on the Fermi surface are retained, which are directly connected by spin density wave ordering wavevector. We derive RG equations up to two-loop order describing the flow of renormalized couplings, quasiparticle weight, several order-parameter response functions, and uniform spin and charge susceptibilities of the model. We find that while the order-parameter susceptibilities investigated here become non-divergent at two loops, the quasiparticle weight vanishes in the low-energy limit, indicating a breakdown of Fermi liquid behavior at this RG level. Moreover, both uniform spin and charge susceptibilities become suppressed in the scaling limit which indicate gap openings in both spin and charge excitation spectra of the model.

  7. Constraints on abelian extensions of the Standard Model from two-loop vacuum stability and U(1){sub B−L}

    Energy Technology Data Exchange (ETDEWEB)

    Corianò, Claudio [STAG Research Centre and Mathematical Sciences,University of Southampton, Southampton SO17 1BJ (United Kingdom); Dipartimento di Matematica e Fisica “Ennio De Giorgi' ,Università del Salento and INFN - Sezione di Lecce,Via Arnesano, 73100 Lecce (Italy); Rose, Luigi Delle; Marzo, Carlo [Dipartimento di Matematica e Fisica “Ennio De Giorgi' ,Università del Salento and INFN - Sezione di Lecce,Via Arnesano, 73100 Lecce (Italy)

    2016-02-19

    We present a renormalization group study of the scalar potential in a minimal U(1){sub B−L} extension of the Standard Model involving one extra heavier Higgs and three heavy right-handed neutrinos with family universal B-L charge assignments. We implement a type-I seesaw for the masses of the light neutrinos of the Standard Model. In particular, compared to a previous study, we perform a two-loop extension of the evolution, showing that two-loop effects are essential for the study of the stability of the scalar potential up to the Planck scale. The analysis includes the contribution of the kinetic mixing between the two abelian gauge groups, which is radiatively generated by the evolution, and the one-loop matching conditions at the electroweak scale. By requiring the stability of the potential up to the Planck mass, significant constraints on the masses of the heavy neutrinos, on the gauge couplings and the mixing in the Higgs sector are identified.

  8. Displacement fields and self-energies of circular and polygonal dislocation loops in homogeneous and layered anisotropic solids

    Science.gov (United States)

    Gao, Yanfei; Larson, Bennett C.

    2015-10-01

    There are large classes of materials problems that involve the solutions of stress, displacement, and strain energy of dislocation loops in elastically anisotropic solids, including increasingly detailed investigations of the generation and evolution of irradiation induced defect clusters ranging in sizes from the micro- to meso-scopic length scales. Based on a two-dimensional Fourier transform and Stroh formalism that are ideal for homogeneous and layered anisotropic solids, we have developed robust and computationally efficient methods to calculate the displacement fields for circular and polygonal dislocation loops. Using the homogeneous nature of the Green tensor of order -1, we have shown that the displacement and stress fields of dislocation loops can be obtained by numerical quadrature of a line integral. In addition, it is shown that the sextuple integrals associated with the strain energy of loops can be represented by the product of a pre-factor containing elastic anisotropy effects and a universal term that is singular and equal to that for elastic isotropic case. Furthermore, we have found that the self-energy pre-factor of prismatic loops is identical to the effective modulus of normal contact, and the pre-factor of shear loops differs from the effective indentation modulus in shear by only a few percent. These results provide a convenient method for examining dislocation reaction energetic and efficient procedures for numerical computation of local displacements and stresses of dislocation loops, both of which play integral roles in quantitative defect analyses within combined experimental-theoretical investigations.

  9. Integrability of orbifold ABJM theories

    Science.gov (United States)

    Bai, Nan; Chen, Hui-Huang; Ding, Xiao-Chen; Li, De-Sheng; Wu, Jun-Bao

    2016-11-01

    Integrable structure has played a very important role in the study of various non-perturbative aspects of planar Aharony-Bergman-Jafferis-Maldacena (ABJM) theories. In this paper, we showed that this remarkable structure survives after orbifold operation with discrete group Γ < SU(4) R × U(1) b . For general Γ(≃ ℤ n ), we prove the integrability in the scalar sector at the planar two-loop order and get the Bethe ansatz equations (BAEs). The eigenvalues of the anomalous dimension matrix are also obtained. For Γ < SU(4), two-loop all-sector and all-loop BAEs are proposed. Supersymmetric orbifolds are discussed in this framework.

  10. Evaluation of two loop-mediated isothermal amplification methods for the detection of Salmonella Enteritidis and Listeria monocytogenes in artificially contaminated ready-to-eat fresh products

    Directory of Open Access Journals (Sweden)

    Angeliki Birmpa

    2015-08-01

    Full Text Available In the present study, the effectiveness of two loop-mediated isothermal amplification (LAMP assays was evaluated. Samples of romaine lettuce, strawberries, cherry tomatoes, green onions and sour berries were inoculated with known dilutions (100-108 CFU/g of produce of S. Enteritidis and L. monocytogenes. With LAMP assay, pathogens can be detected in less than 60 min. The limits of detection of S. Enteritidis and L. monocytogenes depended on the food sample tested and on the presence of enrichment step. After enrichment steps, all food samples were found positive even at low initial pathogen levels. The developed LAMP, assays, are expected to become a valuable, robust, innovative, powerful, cheap and fast monitoring tool, which can be extensively used for routine analysis, and screening of contaminated foods by the food industry and the Public Food Health Authorities.

  11. Behavior of three modes of decay channels and their self-energies of elliptic dielectric microcavity

    Science.gov (United States)

    Park, Kyu-Won; Kim, Jaewan; Jeong, Kabgyun

    2016-09-01

    The Lamb shift (self-energy) of an elliptic dielectric microcavity is studied. We show that the size of the Lamb shift, which is a small energy shift due to the system-environment coupling in the quantum regime, is dependent on the geometry of the boundary conditions. It shows a global transition depending on the eccentricity of the ellipsis. These transitions can be classified into three types of decay channels known as whispering-gallery modes, stable-bouncing-ball modes, and unstable-bouncing-ball modes. These modes are manifested through the Poincaré surface of section with the Husimi distribution function in classical phase space. It is found that the similarity (measured in Bhattacharyya distance) between the Husimi distributions below critical lines of two different modes increases as the difference of their self-energies decreases when the quality factors of the modes are on the same order of magnitude.

  12. Thermal right-handed neutrino self-energy in the non-relativistic regime

    CERN Document Server

    Laine, M

    2012-01-01

    Recently the issue of radiative corrections to leptogenesis has been raised. Considering the "strong washout" regime, in which OPE-techniques permit to streamline the setup, we report the thermal self-energy matrix of heavy right-handed neutrinos at NLO (resummed 2-loop level) in Standard Model couplings. The renormalized expression describes flavour transitions and "inclusive" decays of chemically decoupled right-handed neutrinos. Although CP-violation is not addressed, the result may find use in existing leptogenesis frameworks.

  13. Towards ab initio self-energy embedding theory in quantum chemistry

    CERN Document Server

    Lan, Tran Nguyen; Zgid, Dominika

    2015-01-01

    The self-energy embedding theory (SEET), in which the active space self-energy is embedded in the self-energy obtained from a perturbative method treating the non-local correlation effects, was recently developed in our group. In SEET the double counting problem does not appear and the accuracy can be improved either by increasing the perturbation order or by enlarging the active space. This method was first calibrated for the 2D Hubbard lattice showing promising results. In this paper, we report an extension of SEET to quantum chemical ab initio Hamiltonians for applications to molecular systems. The self-consistent second-order Green's function (GF2) method is used to describe the non-local correlations, while the full configuration interaction (FCI) method is carried out to capture strong correlation within the active space. Using few proof-of-concept examples, we show that SEET yields results of comparable quality to $n-$electron valence state second-order perturbation theory (NEVPT2) with the same active...

  14. Communication: Towards ab initio self-energy embedding theory in quantum chemistry

    Energy Technology Data Exchange (ETDEWEB)

    Lan, Tran Nguyen, E-mail: latran@umich.edu [Department of Chemistry, University of Michigan, Ann Arbor, Michigan 48109 (United States); Department of Physics, University of Michigan, Ann Arbor, Michigan 48109 (United States); Kananenka, Alexei A.; Zgid, Dominika [Department of Chemistry, University of Michigan, Ann Arbor, Michigan 48109 (United States)

    2015-12-28

    The self-energy embedding theory (SEET), in which the active space self-energy is embedded in the self-energy obtained from a perturbative method treating the non-local correlation effects, was recently developed in our group. In SEET, the double counting problem does not appear and the accuracy can be improved either by increasing the perturbation order or by enlarging the active space. This method was first calibrated for the 2D Hubbard lattice showing promising results. In this paper, we report an extension of SEET to quantum chemical ab initio Hamiltonians for applications to molecular systems. The self-consistent second-order Green’s function method is used to describe the non-local correlations, while the full configuration interaction method is carried out to capture strong correlation within the active space. Using few proof-of-concept examples, we show that SEET yields results of comparable quality to n-electron valence state second-order perturbation theory with the same active space, and furthermore, the full active space can be split into smaller active spaces without further implementation. Moreover, SEET avoids intruder states and does not require any high-order reduced density matrices. These advantages show that SEET is a promising method to describe physical and chemical properties of challenging molecules requiring large active spaces.

  15. Communication: Towards ab initio self-energy embedding theory in quantum chemistry.

    Science.gov (United States)

    Lan, Tran Nguyen; Kananenka, Alexei A; Zgid, Dominika

    2015-12-28

    The self-energy embedding theory (SEET), in which the active space self-energy is embedded in the self-energy obtained from a perturbative method treating the non-local correlation effects, was recently developed in our group. In SEET, the double counting problem does not appear and the accuracy can be improved either by increasing the perturbation order or by enlarging the active space. This method was first calibrated for the 2D Hubbard lattice showing promising results. In this paper, we report an extension of SEET to quantum chemical ab initio Hamiltonians for applications to molecular systems. The self-consistent second-order Green's function method is used to describe the non-local correlations, while the full configuration interaction method is carried out to capture strong correlation within the active space. Using few proof-of-concept examples, we show that SEET yields results of comparable quality to n-electron valence state second-order perturbation theory with the same active space, and furthermore, the full active space can be split into smaller active spaces without further implementation. Moreover, SEET avoids intruder states and does not require any high-order reduced density matrices. These advantages show that SEET is a promising method to describe physical and chemical properties of challenging molecules requiring large active spaces.

  16. System-Level Heat Transfer Analysis, Thermal- Mechanical Cyclic Stress Analysis, and Environmental Fatigue Modeling of a Two-Loop Pressurized Water Reactor. A Preliminary Study

    Energy Technology Data Exchange (ETDEWEB)

    Mohanty, Subhasish [Argonne National Lab. (ANL), Argonne, IL (United States); Soppet, William [Argonne National Lab. (ANL), Argonne, IL (United States); Majumdar, Saurin [Argonne National Lab. (ANL), Argonne, IL (United States); Natesan, Ken [Argonne National Lab. (ANL), Argonne, IL (United States)

    2015-01-03

    This report provides an update on an assessment of environmentally assisted fatigue for light water reactor components under extended service conditions. This report is a deliverable in April 2015 under the work package for environmentally assisted fatigue under DOE's Light Water Reactor Sustainability program. In this report, updates are discussed related to a system level preliminary finite element model of a two-loop pressurized water reactor (PWR). Based on this model, system-level heat transfer analysis and subsequent thermal-mechanical stress analysis were performed for typical design-basis thermal-mechanical fatigue cycles. The in-air fatigue lives of components, such as the hot and cold legs, were estimated on the basis of stress analysis results, ASME in-air fatigue life estimation criteria, and fatigue design curves. Furthermore, environmental correction factors and associated PWR environment fatigue lives for the hot and cold legs were estimated by using estimated stress and strain histories and the approach described in NUREG-6909. The discussed models and results are very preliminary. Further advancement of the discussed model is required for more accurate life prediction of reactor components. This report only presents the work related to finite element modelling activities. However, in between multiple tensile and fatigue tests were conducted. The related experimental results will be presented in the year-end report.

  17. $\\Delta$ self-energy at finite temperature and density and the $\\pi N$ cross-section

    CERN Document Server

    Ghosh, Snigdha; Sarkar, Sourav

    2016-01-01

    The self energy of $\\Delta$-baryon is evaluated at finite temperature and density using the real time formalism of thermal field theory. The Dyson-Schwinger equation is used to get the exact thermal propagator followed by the spectral function of $\\Delta$. The $\\pi N$ scattering cross section obtained using explicit $\\Delta$ exchange is normalized to the experimental data in vacuum and its medium modification is implemented by means of the exact thermal propagator. A significant suppression of the peak is observed at higher temperature and baryon density.

  18. Self-Energy Closure for Inhomogeneous Turbulent Flows and Subgrid Modeling

    Directory of Open Access Journals (Sweden)

    Jorgen S. Frederiksen

    2012-04-01

    Full Text Available A new statistical dynamical closure theory for general inhomogeneous turbulent flows and subgrid modeling is presented. This Self-Energy (SE closure represents all eddy interactions through nonlinear dissipation or forcing ‘self-energy’ terms in the mean-field, covariance and response function equations. This makes the renormalization of the bare dissipation and forcing, and the subgrid modeling problem, transparent. The SE closure generalizes the quasi-diagonal direct interaction closure to allow for more complex interactions. The SE closure is applicable to flows in different geometries, is exact near maximum entropy states corresponding to canonical equilibrium, and provides a framework for deriving simpler realizable closures.

  19. Where is the electrostatic self-energy localized in general relativity?

    CERN Document Server

    Barcelo, Carlos

    2011-01-01

    We discuss an alternative way of prescribing the spacetime geometry associated with a non-radiating distribution of charged matter. It is based on the possibility that the electrostatic self-energy does not reside on the Coulombian field but in a matter pressure term of electromagnetic origin localized at the sources. We work out completely the well controlled spherically symmetric case, questioning the realization of Reissner-Nordstrom geometry in nature. Finally, we sketch an experiment that could distinguish between the standard and the alternative scenario.

  20. Validity of the local self-energy approximation: Application to coupled quantum impurities

    Science.gov (United States)

    Mitchell, Andrew K.; Bulla, Ralf

    2015-10-01

    We examine the quality of the local self-energy approximation, applied here to models of multiple quantum impurities coupled to an electronic bath. The local self-energy is obtained by solving a single-impurity Anderson model in an effective medium that is determined self-consistently, similar to the dynamical mean-field theory (DMFT) for correlated lattice systems. By comparing to exact results obtained by using the numerical renormalization group, we determine situations where "impurity-DMFT" is able to capture the physics of highly inhomogeneous systems and those cases where it fails. For two magnetic impurities separated in real space, the onset of the dilute limit is captured, but RKKY-dominated interimpurity singlet formation cannot be described. For parallel quantum dot devices, impurity-DMFT succeeds in capturing the underscreened Kondo physics by self-consistent generation of a critical pseudogapped effective medium. However, the quantum phase transition between high- and low-spin states upon tuning interdot coupling cannot be described.

  1. Scalar and vector self-energies of heavy baryons in nuclear medium

    Science.gov (United States)

    Azizi, K.; Er, N.; Sundu, H.

    2017-04-01

    The in-medium sum rules are employed to calculate the shifts in the mass and residue as well as the scalar and vector self-energies of the heavy ΛQ ,ΣQ and ΞQ baryons, with Q being b or c quark. The maximum shift in mass due to nuclear matter belongs to the Σc baryon and it is found to be ΔmΣc = - 936 MeV. In the case of residue, it is obtained that the residue of Σb baryon is maximally affected by the nuclear medium with the shift ΔλΣb = - 0.014 GeV3. The scalar and vector self-energies are found to be ΣΛbS = 653 MeV, ΣΣbS = - 614 MeV, ΣΞbS = - 17 MeV, ΣΛcS = 272 MeV, ΣΣcS = - 936 MeV, ΣΞcS = - 5 MeV and ΣΛbν = 436 ± 148 MeV, ΣΣbν = 382 ± 129 MeV, ΣΞbν = 15 ± 5 MeV, ΣΛcν = 151 ± 45 MeV, ΣΣcν = 486 ± 144 MeV and ΣΞcν = 1.391 ± 0.529 MeV.

  2. Second-order many-body perturbation expansions of vibrational Dyson self-energies.

    Science.gov (United States)

    Hermes, Matthew R; Hirata, So

    2013-07-21

    Second-order many-body perturbation theories for anharmonic vibrational frequencies and zero-point energies of molecules are formulated, implemented, and tested. They solve the vibrational Dyson equation self-consistently by taking into account the frequency dependence of the Dyson self-energy in the diagonal approximation, which is expanded in a diagrammatic perturbation series up to second order. Three reference wave functions, all of which are diagrammatically size consistent, are considered: the harmonic approximation and diagrammatic vibrational self-consistent field (XVSCF) methods with and without the first-order Dyson geometry correction, i.e., XVSCF[n] and XVSCF(n), where n refers to the truncation rank of the Taylor-series potential energy surface. The corresponding second-order perturbation theories, XVH2(n), XVMP2[n], and XVMP2(n), are shown to be rigorously diagrammatically size consistent for both total energies and transition frequencies, yield accurate results (typically within a few cm(-1) at n = 4 for water and formaldehyde) for both quantities even in the presence of Fermi resonance, and have access to fundamentals, overtones, and combinations as well as their relative intensities as residues of the vibrational Green's functions. They are implemented into simple algorithms that require only force constants and frequencies of the reference methods (with no basis sets, quadrature, or matrix diagonalization at any stage of the calculation). The rules for enumerating and algebraically interpreting energy and self-energy diagrams are elucidated in detail.

  3. Self-energies, renormalization factor, Luttinger sum rule and quasiparticle structure of the Hubbard systems

    Energy Technology Data Exchange (ETDEWEB)

    Lopez-Aguilar, F.; Costa-Quintana, J. (Dept. de Fisica, Grupo de Electromagnetismo, Univ. Autonoma de Barcelona, Bellaterra, E-08193 Barcelona (ES))

    1992-07-10

    In this paper, the authors give a method for obtaining the renormalized electronic structure of the Hubbard systems. The first step is the determination of the self-energy beyond the Hartree-Fock approximation. This self-energy is constructed from several dielectric response functions. The second step is the determination of the quasiparticle band structure calculation which is performed from an appropriate modification of the augmented plane wave method. The third step consists in the determination of the renormalized density of states deduced from the spectral functions. The analysis of the renormalized density of states of the strongly correlated systems leads to the conclusion that there exist three types of resonances in their electronic structures, the lower energy resonances (LER), the middle energy resonances (MER) and the upper energy resonances (UER). In addition, the authors analyze the conditions for which the Luttinger theorem is satisfied. All of these questions are determined in a characteristic example which allows to test the theoretical method.

  4. Improved GWγ scheme for the first-principles calculation of the electron self-energy

    Science.gov (United States)

    Takada, Yasutami

    2010-03-01

    Improvements are made on the self-consistent calculation scheme for the electron self-energy with the vertex function γ satisfying the Ward identity, originally proposed in 2001 [1]. Although it is basically equivalent to the original one, this improved scheme not only shortens the computational time by about one hundredth but also opens new horizons in its applications: (i) If it is applied to semiconductors and insulators, the obtained quasiparticle dispersion is virtually the same as that in the one-shot GW approximation (or G0W0A), indicating that the G0W0A actually takes proper account of both vertex and high-order self-energy corrections in a mutually cancelling manner [2]. (ii) If it is applied to the Tomonaga-Luttinger model, it is reduced to the Dzyaloshinskii-Larkin theory, implying that it is a unified theory to treat both Fermi- and Luttinger-liquids on the same footing. (iii) In contrast with the original one, it can provide the convergent self-consistent solution for the low-density electron liquid where an intrinsic difficulty arises due the dielectric catastrophe associated with the negative electronic compressibility. [1]YT, PRL87, 226402 (2001). [2] S. Ishii, H. Maebashi, and YT, unpublished.

  5. Self-energy effects in the Polchinski and Wick-ordered renormalization-group approaches

    Energy Technology Data Exchange (ETDEWEB)

    Katanin, A, E-mail: katanin@mail.ru [Institute of Metal Physics, 620041, Ekaterinburg (Russian Federation); Ural Federal University, 620002, Ekaterinburg (Russian Federation)

    2011-12-09

    I discuss functional renormalization group (fRG) schemes, which allow for non-perturbative treatment of the self-energy effects and do not rely on the one-particle irreducible functional. In particular, I consider the Polchinski or Wick-ordered scheme with amputation of full (instead of bare) Green functions, as well as more general schemes, and establish their relation to the 'dynamical adjustment propagator' scheme by Salmhofer (2007 Ann. Phys., Lpz. 16 171). While in the Polchinski scheme the amputation of full (instead of bare) Green functions improves treatment of the self-energy effects, the structure of the corresponding equations is not suitable to treat strong-coupling problems; it is also not evident how the mean-field solution of these problems is recovered in this scheme. For the Wick-ordered scheme, fully or partly excluding tadpole diagrams one can obtain forms of fRG hierarchy, which are suitable to treat strong-coupling problems. In particular, I emphasize the usefulness of the schemes, which are local in the cutoff parameter, and compare them to the one-particle irreducible approach. (paper)

  6. The GW space-time method for the self-energy of large systems

    Science.gov (United States)

    Rieger, Martin M.; Steinbeck, L.; White, I. D.; Rojas, H. N.; Godby, R. W.

    1999-03-01

    We present a detailed account of the GW space-time method. The method increases the size of systems whose electronic structure can be studied with a computational implementation of Hedin's GW approximation. At the heart of the method is a representation of the Green function G and the screened Coulomb interaction W in the real-space and imaginary-time domain, which allows a more efficient computation of the self-energy approximation Σ = iGW. For intermediate steps we freely change between representations in real and reciprocal space on the one hand, and imaginary time and imaginary energy on the other, using fast Fourier transforms. The power of the method is demonstrated using the example of Si with artificially increased unit cell sizes.

  7. Classical electrodynamics with vacuum polarization: electron self-energy and radiation reaction

    Science.gov (United States)

    Blinder, S. M.

    2001-04-01

    The region very close to an electron ( r ⪅ r0 = e2/ mc2 ≈ 2.8 × 10 -13 cm) is, according to quantum electrodynamics, a seething maelstrom of virtual electron-positron pairs flashing in and out of existence. To take account of this well-established physical reality, a phenomenological representation for vacuum polarization is introduced into the framework of classical electrodynamics. Such a model enables a consistent picture of classical point charges with finite electromagnetic self-energy. It is further conjectured that the reaction of a point charge to its own electromagnetic field is tantamount to interaction with its vacuum polarization charge or "aura." This leads to a modification of the Lorentz-Dirac equation for the force on an accelerating electron, a new differential-difference equation which avoids the pathologies of preacceleration and runaway solutions.

  8. Series expansion of the photon self-energy in QED and the photon anomalous magnetic moment

    CERN Document Server

    Rojas, H Perez; Chavez, S Villalba

    2008-01-01

    We start from the analytical expression of the eigenvalues $\\kappa^{(i)}$ of the photon self-energy tensor in an external constant magnetic field $B$ calculated by Batalin Shabad in the Furry representation, and in the one-loop approximation. We expand in power series of the external field and in terms of the squared photon transverse momentum $z_2$ and (minus) transverse energy $z_1=k^2-z_2$, in terms of which are expressed $\\kappa^{(i)}$. A general expression is given for the photon anomalous magnetic moment $\\mu_{\\gamma}>0$ in the region of transparency, below the first threshold for pair creation, and it is shown that it is positive, i.e. paramagnetic. The results of the numerical calculation for $\\mu_{\\gamma}>0$ are displayed in a region close to the threshold.

  9. Relationship between Population Dynamics and the Self-Energy in Driven Non-Equilibrium Systems

    Directory of Open Access Journals (Sweden)

    Alexander F. Kemper

    2016-05-01

    Full Text Available We compare the decay rates of excited populations directly calculated within a Keldysh formalism to the equation of motion of the population itself for a Hubbard-Holstein model in two dimensions. While it is true that these two approaches must give the same answer, it is common to make a number of simplifying assumptions, within the differential equation for the populations, that allows one to interpret the decay in terms of hot electrons interacting with a phonon bath. Here, we show how care must be taken to ensure an accurate treatment of the equation of motion for the populations due to the fact that there are identities that require cancellations of terms that naively look like they contribute to the decay rates. In particular, the average time dependence of the Green’s functions and self-energies plays a pivotal role in determining these decay rates.

  10. Unraveling the interlayer-related phonon self-energy renormalization in bilayer graphene

    Science.gov (United States)

    Araujo, Paulo T.; Mafra, Daniela L.; Sato, Kentaro; Saito, Riichiro; Kong, Jing; Dresselhaus, Mildred S.

    2012-01-01

    In this letter, we present a step towards understanding the bilayer graphene (2LG) interlayer (IL)-related phonon combination modes and overtones as well as their phonon self-energy renormalizations by using both gate-modulated and laser-energy dependent inelastic scattering spectroscopy. We show that although the IL interactions are weak, their respective phonon renormalization response is significant. Particularly special, the IL interactions are mediated by Van der Waals forces and are fundamental for understanding low-energy phenomena such as transport and infrared optics. Our approach opens up a new route to understanding fundamental properties of IL interactions which can be extended to any graphene-like material, such as MoS2, WSe2, oxides and hydroxides. Furthermore, we report a previously elusive crossing between IL-related phonon combination modes in 2LG, which might have important technological applications. PMID:23264879

  11. Self-Energy in the Lorentzian ERPL-FK Spin Foam Model of Quantum Gravity

    CERN Document Server

    Riello, Aldo

    2013-01-01

    We calculate the most divergent contribution to the self-energy (or "melonic") graph in the context of the Lorentzian EPRL-FK Spin Foam model of Quantum Gravity. We find that such a contribution is logarithmically divergent in the cut-off over the SU(2)-representation spins when one chooses the face amplitude guaranteeing the face-splitting invariance of the foam.We also find that the dependence on the boundary data is different from that of the bare propagator. This fact has its origin in the non-commutativity of the EPRL-FK Y-map with the projector onto SL(2,C)-invariant states. In the course of the paper, we discuss in detail the approximations used during the calculations, its geometrical interpretation as well as the physical consequences of our result.

  12. [pi][sup 0] electromagnetic self-energy and its implications for incorporating electromagnetism in few-body systems

    Energy Technology Data Exchange (ETDEWEB)

    Maltman, K. (Department of Mathematics and Statistics, York University, 4700 Keele St., North York, Ontario, M3J 1P3 (Canada) Physics Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545 (United States))

    1994-08-01

    By investigating the electromagnetic (EM) chiral series for the pseudoscalar mesons at next-to-leading order, it is shown that the [pi][sup 0] EM self-energy is [ital O]([alpha][sub EM][ital m][sub [ital u],][ital d]), and hence small. This observation completes the crucial step in an earlier argument, which employed previously the vanishing of the [pi][sup 0] EM self-energy in the chiral limit, and which demonstrates that the effects of not only one-photon-exchange- but also one-photon-loop graphs must be included in order to incorporate the effects of electromagnetism in hadronic systems.

  13. Weak-coupling approach to the semi-infinite Hubbard model: Non-locality of the self-energy

    OpenAIRE

    Potthoff, M.; Nolting, W.

    1997-01-01

    The Hubbard model on a semi-infinite three-dimensional lattice is considered to investigate electron-correlation effects at single-crystal surfaces. The standard second-order perturbation theory in the interaction U is used to calculate the electronic self-energy and the quasi-particle density of states (QDOS) in the bulk as well as in the vicinity of the surface. Within a real-space representation we fully account for the non-locality of the self-energy and examine the quality of the local a...

  14. Lowest-order corrections to the RPA polarizability and GW self-energy of a semiconducting wire

    Science.gov (United States)

    de Groot, H. J.; Ummels, R. T. M.; Bobbert, P. A.; van Haeringen, W.

    1996-07-01

    We present the results of the addition of lowest-order vertex and self-consistency corrections to the RPA polarizability and the GW self-energy for a semiconducting wire. It is found that, when starting from a local density approximation zeroth-order Green function and systematically including these corrections in both the polarizability and the self-energy, the correction to the non-self-consistent RPA-GW band gap is small. Partial inclusion of these corrections leads to very different band gaps. This sheds new light on the puzzling question why non-self-consistent RPA-GW calculations of band gaps have been so very successful.

  15. Integration

    DEFF Research Database (Denmark)

    Emerek, Ruth

    2004-01-01

    Bidraget diskuterer de forskellige intergrationsopfattelse i Danmark - og hvad der kan forstås ved vellykket integration......Bidraget diskuterer de forskellige intergrationsopfattelse i Danmark - og hvad der kan forstås ved vellykket integration...

  16. Quantum fluctuations in semiconductor quantum dots and their contributions to the self-energy functions of exciton states

    Science.gov (United States)

    Mutygullina, A. A.; Khamadeev, M. A.; Blum, D. O.; Shirdelhavar, A. H.

    2017-06-01

    Influence of quantum fluctuations in a system consisting of a quantum dot and the reservoir of acoustic phonons on processes in which the quantum dot takes part is investigated. Under some conditions this influence is shown to be very strong. We find a contribution from the quantum fluctuations to the self-energy function of the exciton coupled to the quantum dot.

  17. Electrostatic Self-energy of a Charged Particle in the Surroundings of a Topologically Charged Black Hole in the Brane

    CERN Document Server

    Larranaga, Alexis; Torres, Daniel Alexdy

    2014-01-01

    We determine the self-energy for a point charge held stationary in a topologically charged black hole spacetime arising from the Randall-Sundrum II braneworld model, showing that it has two contributions, one of geometric origin and the other of topological one.

  18. [Integrity].

    Science.gov (United States)

    Gómez Rodríguez, Rafael Ángel

    2014-01-01

    To say that someone possesses integrity is to claim that that person is almost predictable about responses to specific situations, that he or she can prudentially judge and to act correctly. There is a closed interrelationship between integrity and autonomy, and the autonomy rests on the deeper moral claim of all humans to integrity of the person. Integrity has two senses of significance for medical ethic: one sense refers to the integrity of the person in the bodily, psychosocial and intellectual elements; and in the second sense, the integrity is the virtue. Another facet of integrity of the person is la integrity of values we cherish and espouse. The physician must be a person of integrity if the integrity of the patient is to be safeguarded. The autonomy has reduced the violations in the past, but the character and virtues of the physician are the ultimate safeguard of autonomy of patient. A field very important in medicine is the scientific research. It is the character of the investigator that determines the moral quality of research. The problem arises when legitimate self-interests are replaced by selfish, particularly when human subjects are involved. The final safeguard of moral quality of research is the character and conscience of the investigator. Teaching must be relevant in the scientific field, but the most effective way to teach virtue ethics is through the example of the a respected scientist.

  19. Automatic numerical integration methods for Feynman integrals through 3-loop

    Science.gov (United States)

    de Doncker, E.; Yuasa, F.; Kato, K.; Ishikawa, T.; Olagbemi, O.

    2015-05-01

    We give numerical integration results for Feynman loop diagrams through 3-loop such as those covered by Laporta [1]. The methods are based on automatic adaptive integration, using iterated integration and extrapolation with programs from the QUADPACK package, or multivariate techniques from the ParInt package. The Dqags algorithm from QuadPack accommodates boundary singularities of fairly general types. PARINT is a package for multivariate integration layered over MPI (Message Passing Interface), which runs on clusters and incorporates advanced parallel/distributed techniques such as load balancing among processes that may be distributed over a network of nodes. Results are included for 3-loop self-energy diagrams without IR (infra-red) or UV (ultra-violet) singularities. A procedure based on iterated integration and extrapolation yields a novel method of numerical regularization for integrals with UV terms, and is applied to a set of 2-loop self-energy diagrams with UV singularities.

  20. $\\phi$ meson self-energy in nuclear matter from $\\phi N$ resonant interactions

    CERN Document Server

    Cabrera, D; Vacas, M J Vicente

    2016-01-01

    The $\\phi$-meson properties in cold nuclear matter are investigated by implementing resonant $\\phi N$ interactions as described in effective approaches including the unitarization of scattering amplitudes. Several $N^*$-like states are dynamically generated in these models around $2$ GeV, in the vicinity of the $\\phi N$ threshold. We find that both these states and the non-resonant part of the amplitude contribute sizably to the $\\phi$ collisional self-energy at finite nuclear density. These contributions are of a similar strength as the widely studied medium effects from the $\\bar K K$ cloud. Depending on model details (position of the resonances and strength of the coupling to $\\phi N$) we report a $\\phi$ broadening up to about $40$-$50$ MeV, to be added to the $\\phi\\to\\bar K K$ in-medium decay width, and an attractive optical potential at threshold up to about $35$ MeV at normal matter density. The $\\phi$ spectral function develops a double peak structure as a consequence of the mixing of resonance-hole mo...

  1. ϕ meson self-energy in nuclear matter from ϕ N resonant interactions

    Science.gov (United States)

    Cabrera, D.; Hiller Blin, A. N.; Vicente Vacas, M. J.

    2017-01-01

    The ϕ -meson properties in cold nuclear matter are investigated by implementing resonant ϕ N interactions as described in effective approaches including the unitarization of scattering amplitudes. Several N*-like states are dynamically generated in these models around 2 GeV, in the vicinity of the ϕ N threshold. We find that both these states and the non-resonant part of the amplitude contribute sizably to the ϕ collisional self-energy at finite nuclear density. These contributions are of a similar strength as the widely studied medium effects from the K ¯K cloud. Depending on model details (position of the resonances and strength of the coupling to ϕ N ) we report a ϕ broadening up to about 40-50 MeV, to be added to the ϕ →K ¯K in-medium decay width, and an attractive optical potential at threshold up to about 35 MeV at normal matter density. The ϕ spectral function develops a double peak structure as a consequence of the mixing of resonance-hole modes with the ϕ quasiparticle peak. The former results point in the direction of making up for missing absorption as reported in ϕ nuclear production experiments.

  2. Generalizations of polylogarithms for Feynman integrals

    Science.gov (United States)

    Bogner, Christian

    2016-10-01

    In this talk, we discuss recent progress in the application of generalizations of polylogarithms in the symbolic computation of multi-loop integrals. We briefly review the Maple program MPL which supports a certain approach for the computation of Feynman integrals in terms of multiple polylogarithms. Furthermore we discuss elliptic generalizations of polylogarithms which have shown to be useful in the computation of the massive two-loop sunrise integral.

  3. Baryon Self-Energy With QQQ Bethe-Salpeter Dynamics In The Non-Perturbative QCD Regime n-p Mass Difference

    CERN Document Server

    Mitra, A N

    1999-01-01

    A qqq BSE formalism based on DB{\\chi}S of an input 4-fermion Lagrangian of `current' u,d quarks interacting pairwise via gluon-exchange-propagator in its self-energy via quark-loop integrals. To that end the baryon-qqq vertex function is derived under Covariant Instantaneity Ansatz (CIA), using Green's function techniques. This is a 3-body extension of an earlier q{\\bar q} (2-body) result on the exact 3D-4D interconnection for the respective BS wave functions under 3D kernel support, precalibrated to both q{\\bar q} and qqq spectra plus other observables. The quark loop integrals for the neutron (n) - proton (p) mass difference receive contributions from : i) the strong SU(2) effect arising from the d-u mass difference (4 MeV); ii) the e.m. effect of the respective quark charges. The resultant n-p difference comes dominantly from d-u effect (+1.71 Mev), which is mildly offset by e.m.effect (-0.44), subject to gauge corrections. To that end, a general method for QED gauge corrections to an arbitrary momentum de...

  4. Explaining the apparent arbitrariness of the LDA-1/2 self-energy correction method applied to purely covalent systems

    CERN Document Server

    Xue, Kan-Hao; Miao, Xiang-Shui

    2016-01-01

    The LDA-1/2 method expands Slater's half occupation technique to infinite solid state materials by introducing a self-energy potential centered at the anions to cancel the energy associated with electron-hole self-interaction. To avoid an infinite summation of long-ranged self-energy potentials they must be trimmed at a variationally-defined cutoff radius. The method has been successful in predicting accurate band gaps for a large number of elementary and binary semiconductors. Nevertheless, there has been some confusion regarding carbon and silicon, both in the cubic diamond structure, which require different ionizations of the valence charge, 1/2 for carbon and 1/4 for silicon respectively, to yield band gaps in agreement with experimental data. We here analyze the spatial distribution of the valence electrons of these two materials to conclude that in silicon and in carbon LDA-1/4 and LDA-1/2, respectively, must be adopted for the proper cancellation of the self-energies. Such analysis should be applied to...

  5. Efficient Numerical Evaluation of Feynman Integral

    CERN Document Server

    Li, Zhao; Yan, Qi-Shu; Zhao, Xiaoran

    2016-01-01

    Feynman loop integral is the key ingredient of high order radiation effect, which is responsible for reliable and accurate theoretical prediction. We improve the efficiency of numerical integration in sector decomposition by implementing quasi-Monte Carlo method associated with the technique of CUDA/GPU. For demonstration we present the results of several Feynman integrals up to two loops in both Euclidean and physical kinematic regions in comparison with those obtained from FIESTA3. It is shown that both planar and non-planar two-loop master integrals in physical kinematic region can be evaluated in less than half minute with $\\mathcal{O}(10^{-3})$ accuracy, which makes the direct numerical approach viable for the precise investigation on the high order effect in multi-loop processes, e.g. the next-to-leading order QCD effect in Higgs pair production via gluon fusion with finite top quark mass.

  6. Investigation of a hydrogen mitigation system during large break loss-of-coolant accident for a two-loop pressurized water reactor

    Energy Technology Data Exchange (ETDEWEB)

    Dehjourian, Mehdi; Rahgoshay, Mohmmad; Jahanfamia, Gholamreza [Dept. of Nuclear Engineering, Science and Research Branch, Islamic Azad University of Tehran, Tehran (Iran, Islamic Republic of); Sayareh, Reza [Faculty of Electrical and Computer Engineering, Kerman Graduate University of Technology, Kerman (Iran, Islamic Republic of); Shirani, Amir Saied [Faculty of Engineering, Shahid Beheshti University, Tehran (Iran, Islamic Republic of)

    2016-10-15

    Hydrogen release during severe accidents poses a serious threat to containment integrity. Mitigating procedures are necessary to prevent global or local explosions, especially in large steel shell containments. The management of hydrogen safety and prevention of over-pressurization could be implemented through a hydrogen reduction system and spray system. During the course of the hypothetical large break loss-of-coolant accident in a nuclear power plant, hydrogen is generated by a reaction between steam and the fuel-cladding inside the reactor pressure vessel and also core concrete interaction after ejection of melt into the cavity. The MELCOR 1.8.6 was used to assess core degradation and containment behavior during the large break loss-of-coolant accident without the actuation of the safety injection system except for accumulators in Beznau nuclear power plant. Also, hydrogen distribution in containment and performance of hydrogen reduction system were investigated.

  7. Evidence of a short-range incommensurate d-wave charge order from a fermionic two-loop renormalization group calculation of a 2D model with hot spots

    Energy Technology Data Exchange (ETDEWEB)

    Carvalho, Vanuildo S de [Instituto de Física, Universidade Federal de Goiás, 74.001-970, Goiânia-GO (Brazil); Freire, Hermann, E-mail: hfreire@mit.edu [Instituto de Física, Universidade Federal de Goiás, 74.001-970, Goiânia-GO (Brazil); Department of Physics, Massachusetts Institute of Technology, Cambridge, MA 2139 (United States)

    2014-09-15

    The two-loop renormalization group (RG) calculation is considerably extended here for the two-dimensional (2D) fermionic effective field theory model, which includes only the so-called “hot spots” that are connected by the spin-density-wave (SDW) ordering wavevector on a Fermi surface generated by the 2D t−t{sup ′} Hubbard model at low hole doping. We compute the Callan–Symanzik RG equation up to two loops describing the flow of the single-particle Green’s function, the corresponding spectral function, the Fermi velocity, and some of the most important order-parameter susceptibilities in the model at lower energies. As a result, we establish that–in addition to clearly dominant SDW correlations–an approximate (pseudospin) symmetry relating a short-range incommensurated-wave charge order to the d-wave superconducting order indeed emerges at lower energy scales, which is in agreement with recent works available in the literature addressing the 2D spin-fermion model. We derive implications of this possible electronic phase in the ongoing attempt to describe the phenomenology of the pseudogap regime in underdoped cuprates.

  8. Toward high-precision values of the self energy of non-S states in hydrogen and hydrogen-like ions

    CERN Document Server

    Le Bigot, E O; Jentschura, U D; Mohr, P J; Bigot, Eric-Olivier Le; Indelicato, Paul; Jentschura, Ulrich D.; Mohr, Peter J.; ccsd-00003072, ccsd

    2004-01-01

    The method and status of a study to provide numerical, high-precision values of the self-energy level shift in hydrogen and hydrogen-like ions is described. Graphs of the self energy in hydrogen-like ions with nuclear charge number between 20 and 110 are given for a large number of states. The self-energy is the largest contribution of Quantum Electrodynamics (QED) to the energy levels of these atomic systems. These results greatly expand the number of levels for which the self energy is known with a controlled and high precision. Applications include the adjustment of the Rydberg constant and atomic calculations that take into account QED effects.

  9. 'Integration'

    DEFF Research Database (Denmark)

    Olwig, Karen Fog

    2011-01-01

    After a long history dominated by out-migration, Denmark, Norway and Sweden have, in the past 50 years, become immigration societies. This article compares how these Scandinavian welfare societies have sought to incorporate immigrants and refugees into their national communities. It suggests that......, while the countries have adopted disparate policies and ideologies, differences in the actual treatment and attitudes towards immigrants and refugees in everyday life are less clear, due to parallel integration programmes based on strong similarities in the welfare systems and in cultural notions...... of equality in the three societies. Finally, it shows that family relations play a central role in immigrants’ and refugees’ establishment of a new life in the receiving societies, even though the welfare society takes on many of the social and economic functions of the family....

  10. Multiple Bosonic Mode Coupling in Electron Self-Energy of (La_2-xSr_x)CuO_4

    Energy Technology Data Exchange (ETDEWEB)

    Zhou, X.J.

    2010-06-02

    High resolution angle-resolved photoemission spectroscopy data with significantly improved statistics reveal tne structure in the electron self-energy of the underdoped (La{sub 2-x}Sr{sub x}) CuO{sub 4} (x=0.03, 0.036 and 0.07) samples in the normal state. Four fine structure have been identified near 27, 45, 61 and 75 meV. These features show good correspondence to the structure in the phonon density of states as measured from neutron scattering.

  11. Eikonal field theory description of interacting pomerons. [Total cross sections, Feynman graphs, self-energy radiative correction, unitarity

    Energy Technology Data Exchange (ETDEWEB)

    Fried, H. M.

    1976-01-01

    Starting from an underlying field theory in Eikonal approximation, interacting Pomerons are produced by retaining those Feynman graphs that correspond to self-energy and related radiative corrections. Multiple Reggeon t-channel thresholds may be viewed in a simple s-channel field theory framework, while the degree of s-channel unitarity required depends upon the spin content of the underlying field theory and the classes of permitted processes. An approximate Eikonal calculation suggests how restricted triple-Pomeron interactions can serve to remove the bare Pomeron, and substitute an alternate asymptotic expression for o/sub TOT/.

  12. Time-dependent scattering of a composite particle: A local self-energy approach for internal excitations

    Science.gov (United States)

    Grasselli, Federico; Bertoni, Andrea; Goldoni, Guido

    2016-09-01

    When composite particles—such as small molecules, nuclei, or photogenerated excitons in semiconductors—are scattered by an external potential, energy may be transferred between the c.m. and the internal degrees of freedom. An accurate dynamical modeling of this effect is pivotal in predicting diverse scattering quantities and reaction cross sections, and allows us to rationalize time-resolved energy and localization spectra. Here, we show that time-dependent scattering of a quantum composite particle with an arbitrary, nonperturbative external potential can be obtained by propagating the c.m. degrees of freedom with a properly designed local self-energy potential. The latter embeds the effect of internal virtual transitions and can be obtained by the knowledge of the stationary internal states. The case is made by simulating Wannier-Mott excitons in one- and two-dimensional semiconductor heterostructures. The self-energy approach shows very good agreement with numerically exact Schrödinger propagation for scattering potentials where a mean-field model cannot be applied, at a dramatically reduced computational cost.

  13. Perturbative expansions from Monte Carlo simulations at weak coupling Wilson loops and the static-quark self-energy

    CERN Document Server

    Trottier, H D; Lepage, G P; MacKenzie, P B

    2002-01-01

    Perturbative coefficients for Wilson loops and the static-quark self-energy are extracted from Monte Carlo simulations at weak coupling. The lattice volumes and couplings are chosen to ensure that the lattice momenta are all perturbative. Twisted boundary conditions are used to eliminate the effects of lattice zero modes and to suppress nonperturbative finite-volume effects due to Z(3) phases. Simulations of the Wilson gluon action are done with both periodic and twisted boundary conditions, and over a wide range of lattice volumes (from $3^4$ to $16^4$) and couplings (from $\\beta \\approx 9$ to $\\beta \\approx 60$). A high precision comparison is made between the simulation data and results from finite-volume lattice perturbation theory. The Monte Carlo results are shown to be in excellent agreement with perturbation theory through second order. New results for third-order coefficients for a number of Wilson loops and the static-quark self-energy are reported.

  14. A note on two-loop superloop

    CERN Document Server

    Belitsky, A V

    2012-01-01

    We explore the duality between supersymmetric Wilson loop on null polygonal contours in maximally supersymmetric Yang-Mills theory and next-to-maximal helicity violating (NMHV) scattering amplitudes. Earlier analyses demonstrated that the use of a dimensional regulator for ultraviolet divergences, induced due to presence of the cusps on the loop, yields anomalies that break both conformal symmetry and supersymmetry. At one-loop order, these are present only in Grassmann components localized in the vicinity of a single cusp and result in a universal function for any number of sites of the polygon that can be subtracted away in a systematic manner leaving a well-defined supersymmetric remainder dual to corresponding components of the superamplitude. The question remains though whether components which were free from the aforementioned supersymmetric anomaly at leading order of perturbation theory remain so once computed at higher orders. Presently we verify this fact by calculating a particular component of the...

  15. Quantum electrodynamics and the electron self-energy in a deformed space with a minimal length scale

    CERN Document Server

    Silva, Apollo V; Neves, M J

    2016-01-01

    The main motivation to study models in the presence of a minimal length is to obtain a quantum field theory free of the divergences. In this way, in this paper, we have constructed a new framework for quantum electrodynamics embedded in a minimal length scale background. New operators are introduced and the Green function method was used for the solution of the field equations, i.e., the Maxwell, Klein-Gordon and Dirac equations. We have analyzed specifically the scalar field and its one loop propagator. The mass of the scalar field regularized by the minimal length was obtained. The QED Lagrangian containing a minimal length was also constructed and the divergences were analyzed. The electron and photon propagators, and the electron self-energy at one loop as a function of the minimal length was also obtained.

  16. The Electromagnetic Self-Energy Contribution to M_p - M_n and the Isovector Nucleon Magnetic Polarizability

    Energy Technology Data Exchange (ETDEWEB)

    Andre Walker-Loud, Carl E. Carlson, Gerald A. Miller

    2012-06-01

    We update the determination of the isovector nucleon electromagnetic self-energy, valid to leading order in QED. A technical oversight in the literature concerning the elastic contribution to Cottingham's formula is corrected and modern knowledge of the structure functions is used to precisely determine the inelastic contribution. We find {delta}M{sub p-n}{sup {gamma}} = 1.30(03)(47) MeV. The largest uncertainty arises from a subtraction term required in the dispersive analysis, which can be related to the isovector magnetic polarizability. With plausible model assumptions, we can combine our calculation with additional input from lattice QCD to constrain this polarizability as: {beta}{sub p-n} = -0.87(85) x 10{sup -4} fm{sup 3}.

  17. Self-Energy Correction to the Two-Photon Decay Width in Hydrogenlike Atoms

    CERN Document Server

    Jentschura, U D

    2004-01-01

    We investigate the gauge invariance of the leading logarithmic radiative correction to the two-photon decay width in hydrogenlike atoms. It is shown that an effective treatment of the correction using a Lamb-shift "potential" leads to equivalent results in both the length as well as the velocity gauges provided all relevant correction terms are taken into account. Specifically, the relevant radiative corrections are related to the energies that enter into the propagator denominators, to the Hamiltonian, to the wave functions, and to the energy conservation condition that holds between the two photons; the form of all of these effects is different in the two gauges, but the final result is shown to be gauge invariant, as it should be. Although the actual calculation only involves integrations over nonrelativistic hydrogenic Green functions, the derivation of the leading logarithmic correction can be regarded as slightly more complex than that of other typical logarithmic terms. The dominant radiative correctio...

  18. Rigorous ab initio quantum embedding for quantum chemistry using Green's function theory: screened interaction, non-local self-energy relaxation, orbital basis, and chemical accuracy

    CERN Document Server

    Lan, Tran Nguyen; Zgid, Dominika

    2016-01-01

    We present a detailed discussion of self-energy embedding theory (SEET) which is a quantum embedding scheme allowing us to describe a chosen subsystem very accurately while keeping the description of the environment at a lower cost. We apply SEET to molecular examples where commonly our chosen subsystem is made out of a set of strongly correlated orbitals while the weakly correlated orbitals constitute an environment. Such a self-energy separation is very general and to make this procedure applicable to multiple systems a detailed and practical procedure for the evaluation of the system and environment self-energy is necessary. We list all the intricacies for one of the possible procedures while focusing our discussion on many practical implementation aspects such as the choice of best orbital basis, impurity solver, and many steps necessary to reach chemical accuracy. Finally, on a set of carefully chosen molecular examples, we demonstrate that SEET which is a controlled, systematically improvable Green's fu...

  19. Testing high-Z QED with SuperEBIT: An estimate of the U{sup 91+}1s two-loop Lamb shift based on a measurement of the 2s{sub 1/2}-2p{sub 1/2} transition in U{sup 89+}

    Energy Technology Data Exchange (ETDEWEB)

    Beiersdorfer, Peter [University of California Lawrence Livermore National Laboratory, Livermore, CA 94550 (United States)]. E-mail: beiersdorfer@llnl.gov

    2006-11-15

    Starting from the results of a recent measurement of the 2s{sub 1/2}-2p{sub 1/2} transition in U{sup 89+} made on the SuperEBIT electron beam ion trap, which provided a determination of the 2s two-loop QED contribution, we estimate 1.27+/-0.45eV for the two-loop contribution to the 1s level in U{sup 91+}. This estimate could be improved by a factor of two or more, if the uncertainties associated with the three-photon exchange in the theoretical calculations were eliminated in the future.

  20. The Pentabox Master Integrals with the Simplified Differential Equations approach

    CERN Document Server

    Papadopoulos, Costas G; Wever, Christopher

    2015-01-01

    We present the calculation of massless two-loop Master Integrals relevant to five-point amplitudes with one off-shell external leg and derive the complete set of planar Master Integrals with five on-mass-shell legs, that contribute to many $2\\to 3$ amplitudes of interest at the LHC, as for instance three jet production, $\\gamma, V, H +2$ jets etc., based on the Simplified Differential Equations approach.

  1. Self-energy and interaction energy of stacking fault in fcc metals calculated by embedded-atom method

    Institute of Scientific and Technical Information of China (English)

    何刚; 戎咏华; 徐祖耀

    2000-01-01

    The stacking fault energies of five fcc metals (Cu, Ag, Au, Ni and Al) with various quan-tivalences have been calculated by embedded-atom method (EAM). It indicated that the stacking fault energy is mainly determined by the metallic bond-energy and the lattice constant. Thus, monovalent fcc metals should have different stacking fault energies, contrary to Attree’s conclusion. The interaction energy between stacking faults one I 111 I layer apart in a fcc metal is found to be 1/40-1/250 of its self-energy, while it becomes zero when the two stacking faults are two layers apart. The twin energy is just half of the energy of intrinsic stacking fault energy without the consideration of lattice relaxation and the energy of a single intrinsic stacking fault is almost the same as that of extrinsic stacking fault, which are consistent with the results from the calculation of Lennard-Jones force between atoms, but differ from Attree’s result.

  2. On the Integrability of Planar N=2 Superconformal Gauge Theories

    CERN Document Server

    Gadde, Abhijit; Rastelli, Leonardo; Yan, Wenbin

    2012-01-01

    We study the integrability properties of planar N=2 superconformal field theories in four dimensions. We show that the spin chain associated to the planar dilation operator of N=2 superconformal QCD fails to be integrable at two loops. In our analysis we focus on a closed SU(2|1) sector, whose two-loop spin chain we fix by symmetry arguments (up to a few undetermined coefficients). It turns out that the Yang-Baxter equation for magnon scattering is not satisfied in this sector. On the other hand, we suggest that the closed SU(2,1|2) sector, which exists in any N=2 superconformal gauge theory, may be integrable to all loops.

  3. Further explorations of Skyrme-Hartree-Fock-Bogoliubov mass formulas. XVI. Inclusion of self-energy effects in pairing

    Science.gov (United States)

    Goriely, S.; Chamel, N.; Pearson, J. M.

    2016-03-01

    Extending our earlier work, a new family of three Hartree-Fock-Bogoliubov (HFB) mass models, labeled HFB-30, HFB-31, and HFB-32, is presented, along with their underlying interactions, BSk30, BSk31, and BSk32, respectively. The principle new feature is a purely phenomenological pairing term that depends on the density gradient. This enables us to have a bulk pairing term that is fitted to realistic nuclear-matter calculations in which for the first time the self-energy corrections are included, while the behavior of the nucleon effective masses in asymmetric homogeneous nuclear matter is significantly improved. Furthermore, in the particle-hole channel all the highly realistic constraints of our earlier work are retained. In particular, the unconventional Skyrme forces containing t4 and t5 terms are still constrained to fit realistic equations of state of neutron matter stiff enough to support the massive neutron stars PSR J1614-2230 and PSR J0348+0432. All unphysical long-wavelength spin and spin-isospin instabilities of nuclear matter, including the unphysical transition to a polarized state in neutron-star matter, are eliminated. Our three interactions are characterized by values of the symmetry coefficient J of 30, 31, and 32 MeV, respectively. The best fit to the database of 2353 nuclear masses is found for model HFB-31 (J =31 MeV ) with a model error of 0.561 MeV. This model also fits the charge-radius data with an root-mean-square error of 0.027 fm.

  4. Integrability in Yang-Mills theory on the light cone beyond leading order

    CERN Document Server

    Belitsky, A V; Müller, D

    2004-01-01

    The one-loop dilatation operator in Yang-Mills theory possesses a hidden integrability symmetry in the sector of maximal helicity Wilson operators. We calculate two-loop corrections to the dilatation operator and demonstrate that while integrability is broken for matter in the fundamental representation of the SU(3) gauge group, for the adjoint SU(N_c) matter it survives the conformal symmetry breaking and persists in supersymmetric N=1, N=2 and N=4 Yang-Mills theories.

  5. New results for loop integrals. AMBRE, CSectors, hexagon

    Energy Technology Data Exchange (ETDEWEB)

    Gluza, Janusz; Kajda, Krzysztof [Silesia Univ., Katowice (Poland). Dept. of Field Theory and Particle Physics, Inst. of Physics; Riemann, Tord; Yundin, Valery [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany)

    2009-03-15

    We report on the three Mathematica packages hexagon, CSectors, AMBRE. They are useful for the evaluation of one- and two-loop Feynman integrals with a dependence on several kinematical scales. These integrals are typically needed for LHC and ILC applications, but also for higher order corrections at meson factories. hexagon is a new package for the tensor reduction of one-loop 5-point and 6-point functions with rank R=3 and R=4, respectively; AMBRE is a tool for derivations of Mellin-Barnes representations; CSectors is an interface for the package sectordecomposition and allows a convenient, direct evaluation of tensor Feynman integrals. (orig.)

  6. New results for loop integrals: AMBRE, CSectors, hexagon

    CERN Document Server

    Gluza, Janusz; Riemann, Tord; Yundin, Valery

    2009-01-01

    We report on the three Mathematica packages hexagon, CSectors, AMBRE. They are useful for the evaluation of one- and two-loop Feynman integrals with a dependence on several kinematical scales. These integrals are typically needed for LHC and ILC applications, but also for higher order corrections at meson factories. hexagon is a new package for the tensor reduction of one-loop 5-point and 6-point functions with rank R=3 and R=4, respectively; AMBRE is a tool for derivations of Mellin-Barnes representations; CSectors is an interface for the package sector_decomposition and allows a convenient, direct evaluation of tensor Feynman integrals.

  7. Efficient numerical evaluation of Feynman integrals

    Science.gov (United States)

    Li, Zhao; Wang, Jian; Yan, Qi-Shu; Zhao, Xiaoran

    2016-03-01

    Feynman loop integrals are a key ingredient for the calculation of higher order radiation effects, and are responsible for reliable and accurate theoretical prediction. We improve the efficiency of numerical integration in sector decomposition by implementing a quasi-Monte Carlo method associated with the CUDA/GPU technique. For demonstration we present the results of several Feynman integrals up to two loops in both Euclidean and physical kinematic regions in comparison with those obtained from FIESTA3. It is shown that both planar and non-planar two-loop master integrals in the physical kinematic region can be evaluated in less than half a minute with accuracy, which makes the direct numerical approach viable for precise investigation of higher order effects in multi-loop processes, e.g. the next-to-leading order QCD effect in Higgs pair production via gluon fusion with a finite top quark mass. Supported by the Natural Science Foundation of China (11305179 11475180), Youth Innovation Promotion Association, CAS, IHEP Innovation (Y4545170Y2), State Key Lab for Electronics and Particle Detectors, Open Project Program of State Key Laboratory of Theoretical Physics, Institute of Theoretical Physics, Chinese Academy of Sciences, China (Y4KF061CJ1), Cluster of Excellence Precision Physics, Fundamental Interactions and Structure of Matter (PRISMA-EXC 1098)

  8. Screened self-energy correction to the 2p3/2-2s transition energy in Li-like ions

    CERN Document Server

    Yerokhin, V A; Shabaev, V M; Plunien, G; Soff, G

    2004-01-01

    We present an ab initio calculation of the screened self-energy correction for (1s)^2 2p3/2 and (1s)^2 2s states of Li-like ions with nuclear charge numbers in the range Z = 12-100. The evaluation is carried out to all orders in the nuclear-strength parameter Z \\alpha. This investigation concludes our calculations of all two-electron QED corrections for the 2p3/2-2s transition energy in Li-like ions and thus considerably improves theoretical predictions for this transition for high-Z ions.

  9. Theory and Measures of Self-energy Development of Vocational Students%高职学生自能发展的理论与措施研究

    Institute of Scientific and Technical Information of China (English)

    刘先法

    2011-01-01

    目前,高职教育十分重视教育的基本功能,注重专业技能的提高,但缺乏对高职学生的整体关心和终身关怀,学生的发展受到很大的制约.要使高职学生从根本上提高,必须提高高职学生的自能发展能力.笔者就高职学生的知识结构、心理缺陷、发展后劲等问题,提出自能发展的概念、自能发展的培养措施等.%At present the vocational education attaches great importance to the basic functions of education. pays attention to improvement of professional skills, but it is lack of overall concem and lifelong care for vocational students, so the development of students has been greatly restricted. To radically improve the development of vocational students, we need to improve the self-energy development of vocational students. Based on the issues in the knawledge structure, psychological defects development potential of vocational students. the writer proposed the concept and measures of self-energy development.

  10. Direct observation of self-energy signatures of the resonant collective mode in Bi2Sr2CaCu2O8 +δ

    Science.gov (United States)

    Mou, Daixiang; Kaminski, Adam; Gu, Genda

    2017-05-01

    We use high-resolution angle-resolved photoemission spectroscopy to study the resonant, collective excitation mode in the superconducting state of Bi2212. By collecting very high-quality data we found noteworthy features in the self-energy in the antinodal region, where the interaction of electrons with the mode is the strongest. This interaction leads to a pronounced peak in the scattering rate and we demonstrate that this feature is directly responsible for the well-known peak-dip-hump structure in cuprates. By studying how the weight of this peak changes with temperature we unequivocally demonstrate that interaction of electrons with the resonant mode in cuprates vanishes at Tc and is very much localized in the momentum space close to the antinode. These findings present a consistent picture of line shape and self-energy signatures of the electron-boson coupling in cuprates and resolve long-standing controversy surrounding this issue. The momentum dependence of the strength of electron-mode interaction enables development of quantitative theory of this phenomenon in cuprates.

  11. Momentum-resolved electron-phonon coupling and self-energy effects in YBa{sub 2}Cu{sub 3}O{sub 7}: an LDA study

    Energy Technology Data Exchange (ETDEWEB)

    Heid, Rolf; Bohnen, Klaus-Peter [Forschungszentrum Karlsruhe, Institut fuer Festkoerperphysik (Germany); Zeyher, Roland; Manske, Dirk [Max-Planck-Institut fuer Festkoerperforschung, Stuttgart (Germany)

    2008-07-01

    The observation of kinks in the electronic dispersion of high-T{sub c} cuprates by angle resolved photoemission experiments has revived the discussion about the importance of electron-phonon interaction in the cuprates. Here we determine the effect of the electron-phonon coupling on the electronic self-energy in the normal state within the local-density approximation. Using a realistic phonon spectrum we determine the momentum and frequency dependence of {alpha}{sup 2}F(k,{omega}) in YBa{sub 2}Cu{sub 3}O{sub 7} for the bonding, antibonding, and chain band. We find that the maximum in the real part of the self-energy at low frequencies is about a factor 5 too small compared to the experiment. The renormalization factor Z(k,{omega}), which determines the change in the slope of the electronic dispersion due to the interaction, varies smoothly as a function of frequency and momentum. These findings show that, at least within the LDA, phonons cannot produce well-pronounced kinks in YBa{sub 2}Cu{sub 3}O{sub 7}.

  12. Cross-Order Integral Relations from Maximal Cuts

    CERN Document Server

    Johansson, Henrik; Larsen, Kasper J.; Søgaard, Mads

    2015-01-01

    We study the ABDK relation using maximal cuts of one- and two-loop integrals with up to five external legs. We show how to find a special combination of integrals that allows the relation to exist, and how to reconstruct the terms with one-loop integrals squared. The reconstruction relies on the observation that integrals across different loop orders can have support on the same generalized unitarity cuts and can share global poles. We discuss the appearance of nonhomologous integration contours in multivariate residues. Their origin can be understood in simple terms, and their existence enables us to distinguish contributions from different integrals. Our analysis suggests that maximal and near-maximal cuts can be used to infer the existence of integral identities more generally.

  13. Minimal Standard Model self-energies at finite temperature in the presence of weak magnetic fields: towards a full symmetry restoration study

    CERN Document Server

    Tejeda-Yeomans, Maria E; Sanchez, Angel; Piccinelli, Gabriella; Ayala, Alejandro

    2008-01-01

    The study of the universe's primordial plasma at high temperature plays an important role when tackling different questions in cosmology, such as the origin of the matter-antimatter asymmetry. In the Minimal Standard Model (MSM) neither the amount of CP violation nor the strength of the phase transition are enough to produce and preserve baryon number during the Electroweak Phase Transition (EWPT), which are two of the three ingredients needed to develop baryon asymmetry. In this talk we present the first part of the analysis done within a scenario where it is viable to have improvements to the aforementioned situation: we work with the degrees of freedom in the broken symmetry phase of the MSM and analyze the development of the EWPT in the presence of a weak magnetic field. More specifically, we calculate the particle self-energies that include the effects of the weak magnetic field, needed for the MSM effective potential up to ring diagrams.

  14. CdSe/CdTe interface band gaps and band offsets calculated using spin-orbit and self-energy corrections

    Energy Technology Data Exchange (ETDEWEB)

    Ribeiro, M. [Centro de Pesquisas Avancadas Wernher von Braun, Av. Alice de Castro P.N. Mattosinho 301, CEP 13098-392 Campinas, SP (Brazil); Ferreira, L.G. [Departamento de Fisica dos Materiais e Mecanica, Instituto de Fisica, Universidade de Sao Paulo, 05315-970 Sao Paulo, SP (Brazil); Fonseca, L.R.C. [Center for Semiconductor Components, State University of Campinas, R. Pandia Calogeras 90, 13083-870 Campinas, SP (Brazil); Ramprasad, R. [Department of Chemical, Materials and Biomolecular Engineering, Institute of Materials Science, University of Connecticut, 97 North Eagleville Road, Storrs, CT 06269 (United States)

    2012-09-20

    We performed ab initio calculations of the electronic structures of bulk CdSe and CdTe, and their interface band alignments on the CdSe in-plane lattice parameters. For this, we employed the LDA-1/2 self-energy correction scheme to obtain corrected band gaps and band offsets. Our calculations include the spin-orbit effects for the bulk cases, which have shown to be of importance for the equilibrium systems and are possibly degraded in these strained semiconductors. Therefore, the SO showed reduced importance for the band alignment of this particular system. Moreover, the electronic structure calculated along the transition region across the CdSe/CdTe interface shows an interesting non-monotonic variation of the band gap in the range 0.8-1.8 eV, which may enhance the absorption of light for corresponding frequencies at the interface between these two materials in photovoltaic applications.

  15. Numerical approach to multi-loop integrals

    CERN Document Server

    Kato, K; Hamaguchi, N; Ishikawa, T; Koike, T; Kurihara, Y; Shimizu, Y; Yuasa, F

    2012-01-01

    For the calculation of multi-loop Feynman integrals, a novel numerical method, the Direct Computation Method (DCM) is developed. It is a combination of a numerical integration and a series extrapolation. In principle, DCM can handle diagrams of arbitrary internal masses and external momenta, and can calculate integrals with general numerator function. As an example of the performance of DCM, a numerical computation of two-loop box diagrams is presented. Further discussion is given on the choice of control parameters in DCM. This method will be an indispensable tool for the higher order radiative correction when it is tested for a wider class of physical parameters and the separation of divergence is done automatically.

  16. Numerical multi-loop calculations via finite integrals and one-mass EW-QCD Drell-Yan master integrals

    Science.gov (United States)

    von Manteuffel, Andreas; Schabinger, Robert M.

    2017-04-01

    We study a recently-proposed approach to the numerical evaluation of multi-loop Feynman integrals using available sector decomposition programs. As our main example, we consider the two-loop integrals for the αα s corrections to Drell-Yan lepton production with up to one massive vector boson in physical kinematics. As a reference, we evaluate these planar and non-planar integrals by the method of differential equations through to weight five. Choosing a basis of finite integrals for the numerical evaluation with SecDec 3 leads to tremendous performance improvements and renders the otherwise problematic seven-line topologies numerically accessible. As another example, basis integrals for massless QCD three loop form factors are evaluated with FIESTA 4. Here, employing a basis of finite integrals results in an overall speedup of more than an order of magnitude.

  17. Numerical multi-loop integrals and applications

    CERN Document Server

    Freitas, Ayres

    2016-01-01

    Higher-order radiative corrections play an important role in precision studies of the electroweak and Higgs sector, as well as for the detailed understanding of large backgrounds to new physics searches. For corrections beyond the one-loop level and involving many independent mass and momentum scales, it is in general not possible to find analytic results, so that one needs to resort to numerical methods instead. This article presents an overview over a variety of numerical loop integration techniques, highlighting their range of applicability, suitability for automatization, and numerical precision and stability. In a second part of this article, the application of numerical loop integration methods in the area of electroweak precision tests is illustrated. Numerical methods were essential for obtaining full two-loop predictions for the most important precision observables within the Standard Model. The theoretical foundations for these corrections will be described in some detail, including aspects of the r...

  18. Integrable spin chains and scattering amplitudes

    Energy Technology Data Exchange (ETDEWEB)

    Bartels, J.; Prygarin, A. [Hamburg Univ. (Germany). 2. Inst. fuer Theoretische Physik; Lipatov, L.N. [Hamburg Univ. (Germany). 2. Inst. fuer Theoretische Physik; Petersburg Nuclear Physics Institute (Russian Federation); Sankt-Peterburgskij Univ., St. Petersburg (Russian Federation)

    2011-04-15

    In this review we show that the multi-particle scattering amplitudes in N=4 SYM at large N{sub c} and in the multi-Regge kinematics for some physical regions have the high energy behavior appearing from the contribution of the Mandelstam cuts in the complex angular momentum plane of the corresponding t-channel partial waves. These Mandelstam cuts or Regge cuts are resulting from gluon composite states in the adjoint representation of the gauge group SU(N{sub c}). In the leading logarithmic approximation (LLA) their contribution to the six point amplitude is in full agreement with the known two-loop result. The Hamiltonian for the Mandelstam states constructed from n gluons in LLA coincides with the local Hamiltonian of an integrable open spin chain. We construct the corresponding wave functions using the integrals of motion and the Baxter-Sklyanin approach. (orig.)

  19. Momentum dependence of the electron-phonon coupling and self-energy effects in superconducting YBa2Cu3O7 within the local density approximation.

    Science.gov (United States)

    Heid, Rolf; Bohnen, Klaus-Peter; Zeyher, Roland; Manske, Dirk

    2008-04-04

    Using the local density approximation and a realistic phonon spectrum we determine the momentum and frequency dependence of alpha(2)F(k,omega) in YBa(2)Cu(3)O(7) for the bonding, antibonding, and chain band. The resulting self-energy Sigma is rather small near the Fermi surface. For instance, for the antibonding band the maximum of ReSigma as a function of frequency is about 7 meV at the nodal point in the normal state and the ratio of bare and renormalized Fermi velocities is 1.18. These values are a factor of 3-5 too small compared to the experiment showing that only a small part of Sigma can be attributed to phonons. Furthermore, the frequency dependence of the renormalization factor Z(k,omega) is smooth and has no anomalies at the observed kink frequencies which means that phonons cannot produce well-pronounced kinks in stoichiometric YBa(2)Cu()3)O(7), at least, within the local density approximation.

  20. Coherent neutrino radiation in supernovae at two loops

    NARCIS (Netherlands)

    Sedrakian, A; Dieperink, AEL

    2000-01-01

    We develop a neutrino transport theory, in terms of the real-time nonequilibrium Green's functions, which is applicable to physical conditions arbitrary far from thermal equilibrium. We compute the coherent neutrino radiation in cores of supernovae by evaluating the two-particle-two-hole (2p-2h) pol

  1. Numerical Approach to Calculation of Feynman Loop Integrals

    CERN Document Server

    Yuasa, F; Kurihara, Y; Fujimoto, J; Shimizu, Y; Hamaguchi, N; de Doncker, E; Kato, K

    2011-01-01

    In this paper, we describe a numerical approach to evaluate Feynman loop integrals. In this approach the key technique is a combination of a numerical integration method and a numerical extrapolation method. Since the computation is carried out in a fully numerical way, our approach is applicable to one-, two- and multi-loop diagrams. Without any analytic treatment it can compute diagrams with not only real masses but also complex masses for the internal particles. As concrete examples we present numerical results of a scalar one-loop box integral with complex masses and two-loop planar and non-planar box integrals with masses. We discuss the quality of our numerical computation by comparisons with other methods and also propose a self consistency check.

  2. Integrable modification of the critical Chalker-Coddington network model

    Science.gov (United States)

    Ikhlef, Yacine; Fendley, Paul; Cardy, John

    2011-10-01

    We consider the Chalker-Coddington network model for the integer quantum Hall effect, and examine the possibility of solving it exactly. In the supersymmetric path integral framework, we introduce a truncation procedure, leading to a series of well-defined two-dimensional loop models with two loop flavors. In the phase diagram of the first-order truncated model, we identify four integrable branches related to the dilute Birman-Wenzl-Murakami braid-monoid algebra and parameterized by the loop fugacity n. In the continuum limit, two of these branches (1,2) are described by a pair of decoupled copies of a Coulomb-gas theory, whereas the other two branches (3,4) couple the two loop flavors, and relate to an SU(2)r×SU(2)r/SU(2)2r Wess-Zumino-Witten (WZW) coset model for the particular values n=-2cos[π/(r+2)], where r is a positive integer. The truncated Chalker-Coddington model is the n=0 point of branch 4. By numerical diagonalization, we find that its universality class is neither an analytic continuation of the WZW coset nor the universality class of the original Chalker-Coddington model. It constitutes rather an integrable, critical approximation to the latter.

  3. Constant External Fields in Gauge Theory and the Spin 0, 1/2, 1 Path Integrals

    CERN Document Server

    Reuter, M; Schubert, C; Reuter, Martin; Schmidt, Michael G.; Schubert, Christian

    1996-01-01

    We investigate the usefulness of the ``string-inspired technique'' for gauge theory calculations in a constant external field background. Our approach is based on Strassler's worldline path integral approach to the Bern-Kosower formalism, and on the construction of worldline (super--) Green's functions incorporating external fields as well as internal propagators. The worldline path integral representation of the gluon loop is reexamined in detail. We calculate the two-loop effective actions induced for a constant external field by a scalar and spinor loop, and the corresponding one-loop effective action in the gluon loop case.

  4. Equivalence of Recurrence Relations for Feynman Integrals with the Same Total Number of External and Loop Momenta

    CERN Document Server

    Baikov, P A

    2000-01-01

    We show that the problem of solving recurrence relations for L-loop (R+1)-point Feynman integrals within the method of integration by parts is equivalent to the corresponding problem for (L+R)-loop vacuum or (L+R-1)-loop propagator-type integrals. Using this property we solve recurrence relations for two-loop massless vertex diagrams, with arbitrary numerators and integer powers of propagators in the case when two legs are on the light cone, by reducing the problem to the well-known solution of the corresponding recurrence relations for massless three-loop propagator diagrams with specific boundary conditions.

  5. A Feynman integral via higher normal functions

    CERN Document Server

    Bloch, Spencer; Vanhove, Pierre

    2014-01-01

    We study the Feynman integral for the three-banana graph defined as the scalar two-point self-energy at three-loop order. The Feynman integral is evaluated for all identical internal masses in two space-time dimensions. Two calculations are given for the Feynman integral; one based on an interpretation of the integral as an inhomogeneous solution of a classical Picard-Fuchs differential equation, and the other using arithmetic algebraic geometry, motivic cohomology, and Eisenstein series. Both methods use the rather special fact that the Feynman integral is a family of regulator periods associated to a family of K3 surfaces. We show that the integral is given by a sum of elliptic trilogarithms evaluated at sixth roots of unity. This elliptic trilogarithm value is related to the regulator of a class in the motivic cohomology of the K3 family. We prove a conjecture by David Broadhurst that at a special kinematical point the Feynman integral is given by a critical value of the Hasse-Weil L-function of the K3 sur...

  6. Cavalieri integration

    CSIR Research Space (South Africa)

    Ackermann, ER

    2012-09-01

    Full Text Available We use Cavalieri’s principle to develop a novel integration technique which we call Cavalieri integration. Cavalieri integrals differ from Riemann integrals in that non-rectangular integration strips are used. In this way we can use single Cavalieri...

  7. Filling- and interaction-driven Mott transition. Quantum cluster calculations within self-energy-functional theory; Fuellungs- und wechselwirkungsabhaengiger Mott-Uebergang. Quanten-Cluster-Rechnungen im Rahmen der Selbstenergiefunktional-Theorie

    Energy Technology Data Exchange (ETDEWEB)

    Balzer, Matthias

    2008-07-01

    The central goal of this thesis is the examination of strongly correlated electron systems on the basis of the two-dimensional Hubbard model. We analyze how the properties of the Mott insulator change upon doping and with interaction strength. The numerical evaluation is done using quantum cluster approximations, which allow for a thermodynamically consistent description of the ground state properties. The framework of self-energy-functional theory offers great flexibility for the construction of cluster approximations. A detailed analysis sheds light on the quality and the convergence properties of different cluster approximations within the self-energy-functional theory. We use the one-dimensional Hubbard model for these examinations and compare our results with the exact solution. In two dimensions the ground state of the particle-hole symmetric model at half-filling is an antiferromagnetic insulator, independent of the interaction strength. The inclusion of short-range spatial correlations by our cluster approach leads to a considerable improvement of the antiferromagnetic order parameter as compared to dynamical mean-field theory. In the paramagnetic phase we furthermore observe a metal-insulator transition as a function of the interaction strength, which qualitatively differs from the pure mean-field scenario. Starting from the antiferromagnetic Mott insulator a filling-controlled metal-insulator transition in a paramagnetic metallic phase can be observed. Depending on the cluster approximation used an antiferromagnetic metallic phase may occur at first. In addition to long-range antiferromagnetic order, we also considered superconductivity in our calculations. The superconducting order parameter as a function of doping is in good agreement with other numerical methods, as well as with experimental results. (orig.)

  8. Numerical multi-loop integrals and applications

    Science.gov (United States)

    Freitas, A.

    2016-09-01

    Higher-order radiative corrections play an important role in precision studies of the electroweak and Higgs sector, as well as for the detailed understanding of large backgrounds to new physics searches. For corrections beyond the one-loop level and involving many independent mass and momentum scales, it is in general not possible to find analytic results, so that one needs to resort to numerical methods instead. This article presents an overview of a variety of numerical loop integration techniques, highlighting their range of applicability, suitability for automatization, and numerical precision and stability. In a second part of this article, the application of numerical loop integration methods in the area of electroweak precision tests is illustrated. Numerical methods were essential for obtaining full two-loop predictions for the most important precision observables within the Standard Model. The theoretical foundations for these corrections will be described in some detail, including aspects of the renormalization, resummation of leading log contributions, and the evaluation of the theory uncertainty from missing higher orders.

  9. A development of an accelerator board dedicated for multi-precision arithmetic operations and its application to Feynman loop integrals

    CERN Document Server

    Motoki, Shinji; Nakasato, Naohito; Ishikawa, Tadashi; Yuasa, Fukuko; Fukushige, Toshiyuki; Kawai, Atsushi; Makino, Junichiro

    2014-01-01

    Higher order corrections in perturbative quantum field theory are required for precise theoretical analysis to investigate new physics beyond the Standard Model. This indicates that we need to evaluate Feynman loop diagram with multi-loop integral which may require multi-precision calculation. We developed a dedicated accelerator system for multi-precision calculation (GRAPE9-MPX). We present performance results of our system for the case of Feynman two-loop box and three-loop selfenergy diagrams with multi-precision.

  10. Integral trees and integral graphs

    NARCIS (Netherlands)

    Wang, Ligong

    2005-01-01

    This monograph deals with integral graphs, Laplacian integral regular graphs, cospectral graphs and cospectral integral graphs. The organization of this work, which consists of eight chapters, is as follows.

  11. The One-Loop Six-Dimensional Hexagon Integral and its Relation to MHV Amplitudes in N=4 SYM

    Energy Technology Data Exchange (ETDEWEB)

    Dixon, Lance J.; /CERN /SLAC; Drummond, James M.; /CERN /Annecy, LAPTH; Henn, Johannes M.; /Humboldt U., Berlin

    2011-08-19

    We provide an analytic formula for the (rescaled) one-loop scalar hexagon integral {tilde {Phi}}{sub 6} with all external legs massless, in terms of classical polylogarithms. We show that this integral is closely connected to two integrals appearing in one- and two-loop amplitudes in planar N = 4 super-Yang-Mills theory, {Omega}{sup (1)} and {Omega}{sup (2)}. The derivative of {Omega}{sup (2)} with respect to one of the conformal invariants yields {tilde {Phi}}{sub 6}, while another first-order differential operator applied to {tilde {Phi}}{sub 6} yields {Omega}{sup (1)}. We also introduce some kinematic variables that rationalize the arguments of the polylogarithms, making it easy to verify the latter differential equation. We also give a further example of a six-dimensional integral relevant for amplitudes in N = 4 super-Yang-Mills.

  12. Network integration; Network integration

    Energy Technology Data Exchange (ETDEWEB)

    NONE

    2000-02-29

    Together with the rapid spread of information network, a shift is seen from the conventional original network to the system based on the standard network also in the monitoring/control field. In the network construction in the monitoring/control field, Meidensha uses internet/intranet technology and multimedia technology and is working on the construction of multimedia network into which sound/image/data are integrated. The paper indicates an example of constructing a large-scale network based on the ATM network constructed by the company and an example of constructing a network based on the Ethernet. The image system is coded/decoded by MPEG2 encoder/decoder and delivered by ATM switch. The sound system is connected to ATM network via CLAD and constructs PBX net. The data system which intercommunicates among terminals interconnects routers on ATM network using TCP/IP. Further, it copes with difficulties such as cable cut by making a detour for the ATM network. (translated by NEDO)

  13. Teaching Integrity

    Science.gov (United States)

    Saunders, Sue; Butts, Jennifer Lease

    2011-01-01

    Integrity is one of those essential yet highly ambiguous concepts. For the purpose of this chapter, integrity is defined as that combination of both attributes and actions that makes entities appear to be whole and ethical, as well as consistent. Like the concepts of leadership or wisdom or community or collaboration, integrity is a key element of…

  14. Integrated Toys

    DEFF Research Database (Denmark)

    Petersson, Eva

    2005-01-01

    the theoretical foundations of play and learning. In this presentation, we explore pedagogical potentials of new technologies and traditional toys integrated into a physical and virtual toy (hereinafter called integrated toy) with specific focus on the open-ended toy and non-formal learning. The integrated toy...... and interaction with the integrated toy as a virtual experience without attachment or wearable on the body, which in context would not be appropriate. In the field of rehabilitation integrated toys are still at an embryonic stage and as such an under used resource for rehabilitation. Qualitative method...

  15. The one-loop six-dimensional hexagon integral with three massive corners

    Energy Technology Data Exchange (ETDEWEB)

    Del Duca, Vittorio; /INFN /KIPAC, Menlo Park; Dixon, Lance J.; /SLAC /CERN; Drummond, James M.; /aff CERN /LAPTH, Annecy-le-Vieux; Duhr, Claude; /Durham U., IPPP /KIPAC, Menlo Park; Henn, Johannes M.; /Humboldt U., Berlin /KIPAC, Menlo Park; Smirnov, Vladimir A.; /Moscow State U.

    2011-11-04

    We compute the six-dimensional hexagon integral with three non-adjacent external masses analytically. After a simple rescaling, it is given by a function of six dual conformally invariant cross-ratios. The result can be expressed as a sum of 24 terms involving only one basic function, which is a simple linear combination of logarithms, dilogarithms, and trilogarithms of uniform degree three transcendentality. Our method uses differential equations to determine the symbol of the function, and an algorithm to reconstruct the latter from its symbol. It is known that six-dimensional hexagon integrals are closely related to scattering amplitudes in N = 4 super Yang-Mills theory, and we therefore expect our result to be helpful for understanding the structure of scattering amplitudes in this theory, in particular at two loops.

  16. Self-energy production applied to buildings

    Energy Technology Data Exchange (ETDEWEB)

    Carlo, Fabricio Ramos del; Balestieri, Jose Antonio Perrella [Sao Paulo State University Julio de Mesquita Filho (UNESP), Guaratingueta, SP (Brazil)], E-mail: perrella@feg.unesp.br; Holanda, Marcelo Rodrigues de [Sao Paulo Univ. (EEL/USP), Lorena, SP (Brazil). Engineering School], E-mail: marcelo@debas.eel.usp.br

    2010-07-01

    The decentralization of energy production in order to obtain better environmental conditions, reducing greenhouse gas emissions and the cost reduction of electricity and thermal energy consumed in residential buildings has been proposed in the literature. This paper proposes to demonstrate what are the chances of having a microcogeneration system toward the residential application. In this study, we contemplate the technologies involved and their possible inputs that are arranged in a superstructure to be studied. As a first step we obtain the cost of the products generated by the configuration that consists basically of two sources of power generation, and through optimization calculations intended to obtain the best configuration, taking into consideration the selection between four fuels, two equipment generators (Fuel Cell and Internal Combustion Engine)and three levels of energy production for each one. An economic analysis is also presented to evaluate the opportunity of selling the energy generated considering the fluctuations of the residential building consumption needs. (author)

  17. Interorganisational Integration

    DEFF Research Database (Denmark)

    Lyngsø, Anne Marie; Godtfredsen, Nina Skavlan; Frølich, Anne

    2016-01-01

    at a university hospital in the Capital Region of Denmark. RESULTS AND DISCUSSION: Our results can be grouped into five influencing areas for interorganisational integration: communication/information transfer, committed leadership, patient engagement, the role and competencies of the general practitioner......INTRODUCTION: Despite many initiatives to improve coordination of patient pathways and intersectoral cooperation, Danish health care is still fragmented, lacking intra- and interorganisational integration. This study explores barriers to and facilitators of interorganisational integration...... and organisational culture. Proposed solutions to barriers in each area hold the potential to improve care integration as experienced by individuals responsible for supporting and facilitating it. Barriers and facilitators to integrating care relate to clinical, professional, functional and normative integration...

  18. Integral equations

    CERN Document Server

    Moiseiwitsch, B L

    2005-01-01

    Two distinct but related approaches hold the solutions to many mathematical problems--the forms of expression known as differential and integral equations. The method employed by the integral equation approach specifically includes the boundary conditions, which confers a valuable advantage. In addition, the integral equation approach leads naturally to the solution of the problem--under suitable conditions--in the form of an infinite series.Geared toward upper-level undergraduate students, this text focuses chiefly upon linear integral equations. It begins with a straightforward account, acco

  19. Integrated Design

    DEFF Research Database (Denmark)

    Lenau, Torben Anker

    1999-01-01

    A homepage on the internet with course material, lecture plan, student exercises, etc. Continuesly updated during the course Integrated Design (80402, 80403)......A homepage on the internet with course material, lecture plan, student exercises, etc. Continuesly updated during the course Integrated Design (80402, 80403)...

  20. Integrated Design

    DEFF Research Database (Denmark)

    Lenau, Torben Anker

    1999-01-01

    A homepage on the internet with course material, lecture plan, student exercises, etc. Continuesly updated during the course Integrated Design (80402, 80403)......A homepage on the internet with course material, lecture plan, student exercises, etc. Continuesly updated during the course Integrated Design (80402, 80403)...

  1. The integration of immigrants

    OpenAIRE

    Bauböck, Rainer

    1995-01-01

    from the Table of Contents: Migration and integration - Basic concepts and definitions; Immigration and Integration policies; The legal framework for integration; Dimension of social integration; Cultural integration; Conclusions;

  2. Organising integration

    DEFF Research Database (Denmark)

    Axelsson, Runo

    2013-01-01

    an increasing lack of integration in the health and welfare system. In the 2000’s, there has been a re-centralisation through mergers of hospitals, regions and state agencies. It has become clear, however, that mergers do not promote integration but rather increase the bureaucratisation of the system. Model......Background: In Sweden, as in many other countries, there has been a succession of trends in the organisation of health care and other welfare services. These trends have had different implications for the integration of services in the health and welfare system. Aims: One aim is to discuss...... the implications of different organisational trends for the integration of health and welfare services. Another aim is to introduce a Swedish model of financial coordination as a flexible way to organise integration. Organisational trends: In the 1960’s there was an expansion of health and welfare services leading...

  3. Stochastic integrals

    CERN Document Server

    McKean, Henry P

    2005-01-01

    This little book is a brilliant introduction to an important boundary field between the theory of probability and differential equations. -E. B. Dynkin, Mathematical Reviews This well-written book has been used for many years to learn about stochastic integrals. The book starts with the presentation of Brownian motion, then deals with stochastic integrals and differentials, including the famous Itô lemma. The rest of the book is devoted to various topics of stochastic integral equations, including those on smooth manifolds. Originally published in 1969, this classic book is ideal for supplemen

  4. Integrated assessment

    Energy Technology Data Exchange (ETDEWEB)

    Nakicenovic, N.; Amann, M.; Fischer, G.

    1995-12-31

    Integrated assessment aims to develop a framework for the analysis of mitigation and adaption strategies to deal with the impacts of global change. It is a recent, rapidly evolving field, IIASA has been an active contributor to its development through in-house research as well as collaborative activities. The latter includes a series of influential conferences on economic aspects and integrated assessment of climate change, as well as the Energy Modeling Forum on integrated assessment models comparison, organized jointly with Stanford University. Various impacts including those of energy use are discussed. 8 refs., 1 fig.

  5. Integral cryptanalysis

    DEFF Research Database (Denmark)

    Knudsen, Lars Ramkilde; Wagner, David

    2002-01-01

    This paper considers a cryptanalytic approach called integral cryptanalysis. It can be seen as a dual to differential cryptanalysis and applies to ciphers not vulnerable to differential attacks. The method is particularly applicable to block ciphers which use bijective components only.......This paper considers a cryptanalytic approach called integral cryptanalysis. It can be seen as a dual to differential cryptanalysis and applies to ciphers not vulnerable to differential attacks. The method is particularly applicable to block ciphers which use bijective components only....

  6. Functional Integration

    Science.gov (United States)

    Cartier, Pierre; DeWitt-Morette, Cecile

    2010-06-01

    Acknowledgements; List symbols, conventions, and formulary; Part I. The Physical and Mathematical Environment: 1. The physical and mathematical environment; Part II. Quantum Mechanics: 2. First lesson: gaussian integrals; 3. Selected examples; 4. Semiclassical expansion: WKB; 5. Semiclassical expansion: beyond WKB; 6. Quantum dynamics: path integrals and operator formalism; Part III. Methods from Differential Geometry: 7. Symmetries; 8. Homotopy; 9. Grassmann analysis: basics; 10. Grassmann analysis: applications; 11. Volume elements, divergences, gradients; Part IV. Non-Gaussian Applications: 12. Poisson processes in physics; 13. A mathematical theory of Poisson processes; 14. First exit time: energy problems; Part V. Problems in Quantum Field Theory: 15. Renormalization 1: an introduction; 16. Renormalization 2: scaling; 17. Renormalization 3: combinatorics; 18. Volume elements in quantum field theory Bryce DeWitt; Part VI. Projects: 19. Projects; Appendix A. Forward and backward integrals: spaces of pointed paths; Appendix B. Product integrals; Appendix C. A compendium of gaussian integrals; Appendix D. Wick calculus Alexander Wurm; Appendix E. The Jacobi operator; Appendix F. Change of variables of integration; Appendix G. Analytic properties of covariances; Appendix H. Feynman's checkerboard; Bibliography; Index.

  7. Integrated Reporting og Integrated Thinking

    DEFF Research Database (Denmark)

    Pontoppidan, Caroline Aggestam; Sonnerfeldt, Amanda

    2017-01-01

    I løbet af de sidste to måneder af 2016, havde vi mulighed for at deltage i to konferencer, med fokus på at udvikle og fremme ‘Integrated Reporting’ (IR) og ‘Integrated Thinking’. Denne artikel søger at videregive nogle af de interessante emner og spørgsmål, der blev drøftet ved disse to begivenh......I løbet af de sidste to måneder af 2016, havde vi mulighed for at deltage i to konferencer, med fokus på at udvikle og fremme ‘Integrated Reporting’ (IR) og ‘Integrated Thinking’. Denne artikel søger at videregive nogle af de interessante emner og spørgsmål, der blev drøftet ved disse...

  8. Classical integrability

    Science.gov (United States)

    Torrielli, Alessandro

    2016-08-01

    We review some essential aspects of classically integrable systems. The detailed outline of the sections consists of: 1. Introduction and motivation, with historical remarks; 2. Liouville theorem and action-angle variables, with examples (harmonic oscillator, Kepler problem); 3. Algebraic tools: Lax pairs, monodromy and transfer matrices, classical r-matrices and exchange relations, non-ultralocal Poisson brackets, with examples (non-linear Schrödinger model, principal chiral field); 4. Features of classical r-matrices: Belavin-Drinfeld theorems, analyticity properties, and lift of the classical structures to quantum groups; 5. Classical inverse scattering method to solve integrable differential equations: soliton solutions, spectral properties and the Gel’fand-Levitan-Marchenko equation, with examples (KdV equation, Sine-Gordon model). Prepared for the Durham Young Researchers Integrability School, organised by the GATIS network. This is part of a collection of lecture notes.

  9. Lebesgue integration

    CERN Document Server

    Williamson, JH

    2014-01-01

    This concise introduction to Lebesgue integration is geared toward advanced undergraduate math majors and may be read by any student possessing some familiarity with real variable theory and elementary calculus. The self-contained treatment features exercises at the end of each chapter that range from simple to difficult. The approach begins with sets and functions and advances to Lebesgue measure, including considerations of measurable sets, sets of measure zero, and Borel sets and nonmeasurable sets. A two-part exploration of the integral covers measurable functions, convergence theorems, co

  10. Integral equations

    CERN Document Server

    Tricomi, Francesco Giacomo

    1957-01-01

    This classic text on integral equations by the late Professor F. G. Tricomi, of the Mathematics Faculty of the University of Turin, Italy, presents an authoritative, well-written treatment of the subject at the graduate or advanced undergraduate level. To render the book accessible to as wide an audience as possible, the author has kept the mathematical knowledge required on the part of the reader to a minimum; a solid foundation in differential and integral calculus, together with some knowledge of the theory of functions is sufficient. The book is divided into four chapters, with two useful

  11. The Integrated Hazard Analysis Integrator

    Science.gov (United States)

    Morris, A. Terry; Massie, Michael J.

    2009-01-01

    Hazard analysis addresses hazards that arise in the design, development, manufacturing, construction, facilities, transportation, operations and disposal activities associated with hardware, software, maintenance, operations and environments. An integrated hazard is an event or condition that is caused by or controlled by multiple systems, elements, or subsystems. Integrated hazard analysis (IHA) is especially daunting and ambitious for large, complex systems such as NASA s Constellation program which incorporates program, systems and element components that impact others (International Space Station, public, International Partners, etc.). An appropriate IHA should identify all hazards, causes, controls and verifications used to mitigate the risk of catastrophic loss of crew, vehicle and/or mission. Unfortunately, in the current age of increased technology dependence, there is the tendency to sometimes overlook the necessary and sufficient qualifications of the integrator, that is, the person/team that identifies the parts, analyzes the architectural structure, aligns the analysis with the program plan and then communicates/coordinates with large and small components, each contributing necessary hardware, software and/or information to prevent catastrophic loss. As viewed from both Challenger and Columbia accidents, lack of appropriate communication, management errors and lack of resources dedicated to safety were cited as major contributors to these fatalities. From the accident reports, it would appear that the organizational impact of managers, integrators and safety personnel contributes more significantly to mission success and mission failure than purely technological components. If this is so, then organizations who sincerely desire mission success must put as much effort in selecting managers and integrators as they do when designing the hardware, writing the software code and analyzing competitive proposals. This paper will discuss the necessary and

  12. Memory integration

    NARCIS (Netherlands)

    Sweegers, C.C.G.

    2014-01-01

    The aim of this thesis was to characterize the neural mechanisms underlying memory integration. In chapter 2, we studied the neural underpinnings of regularity extraction across hippocampus-dependent episodic memories. We found higher connectivity between the hippocampus and the mPFC for the

  13. Scientific integrity

    DEFF Research Database (Denmark)

    Merlo, Domenico Franco; Vahakangas, Kirsi; Knudsen, Lisbeth E.

    2008-01-01

    consent was obtained.Integrity is central to environmental health research searching for causal relations. It requires open communication and trust and any violation (i.e., research misconduct, including fabrication or falsification of data, plagiarism, conflicting interests, etc.) may endanger...

  14. Information Integrity

    Science.gov (United States)

    Graves, Eric

    2013-01-01

    This dissertation introduces the concept of Information Integrity, which is the detection and possible correction of information manipulation by any intermediary node in a communication system. As networks continue to grow in complexity, information theoretic security has failed to keep pace. As a result many parties whom want to communicate,…

  15. Numerical Integration

    Science.gov (United States)

    Sozio, Gerry

    2009-01-01

    Senior secondary students cover numerical integration techniques in their mathematics courses. In particular, students would be familiar with the "midpoint rule," the elementary "trapezoidal rule" and "Simpson's rule." This article derives these techniques by methods which secondary students may not be familiar with and an approach that…

  16. Information Integrity

    Science.gov (United States)

    Graves, Eric

    2013-01-01

    This dissertation introduces the concept of Information Integrity, which is the detection and possible correction of information manipulation by any intermediary node in a communication system. As networks continue to grow in complexity, information theoretic security has failed to keep pace. As a result many parties whom want to communicate,…

  17. Integral cryptanalysis

    DEFF Research Database (Denmark)

    Knudsen, Lars Ramkilde; Wagner, David

    2002-01-01

    This paper considers a cryptanalytic approach called integral cryptanalysis. It can be seen as a dual to differential cryptanalysis and applies to ciphers not vulnerable to differential attacks. The method is particularly applicable to block ciphers which use bijective components only....

  18. Integrated Design

    DEFF Research Database (Denmark)

    Jørgensen, Michael; Nielsen, M. W.; Strømann-Andersen, Jakob Bjørn

    2011-01-01

    This paper presents a case study of the implementation of integrated design in an actual architectural competition. The design process was carried out at a highly esteemed architectural office and attended by both engineers and architects working towards mutual goals of architectural excellence......, low-energy consumption, and high-quality indoor environment. We use this case study to investigate how technical knowledge about building performance can be integrated into the conceptual design stage. We have selected certain points during the design process that represented design challenges...... and describe the decision process. Specific attention is given to how the engineering input was presented and how it was able to facilitate the design development. Site and context, building shape, organization of functions and HVAC-systems were all included to obtain a complete picture of the building...

  19. Two-Loop Control of Redundant Manipulators: Analysis and Experiments on a 3-DOF Planar Arm

    Directory of Open Access Journals (Sweden)

    Israel Soto

    2013-01-01

    Full Text Available A redundant robot has more degrees of freedom (DOF than those required to accomplish a given motion task. This fact allows the possibility of achieving an additional task, such as avoidance of joint limits or singularities, besides the primary one. Different criteria have been proposed in the literature for the selection of such a secondary task. This paper first recalls some of those criteria and then proposes a two‐loop scheme for the motion control of redundant robots. In order to validate the proposed scheme, some experiments are carried out in a direct‐drive redundant planar arm which has been designed and built in our laboratory.

  20. Two-loop thermodynamics of warm and dense (isospin and baryo-chemical potential) perturbative QCD

    Energy Technology Data Exchange (ETDEWEB)

    Graf, Thorben [Institut fuer Theoretische Physik, Goethe Universitaet, Frankfurt am Main (Germany); Schaffner-Bielich, Juergen [Institut fuer Theoretische Physik, Goethe Universitaet, Frankfurt am Main (Germany); Fraga, Eduardo S. [Instituto de Fisica, Universidade Federal do Rio de Janeiro, Rio de Janeiro (Brazil)

    2014-07-01

    We present a perturbative calculation of the thermodynamical potential of quantum chromodynamics at nonvanishing temperatures for different values of the isospin and baryo-chemical potential. A comparison to recent lattice calculations at nonvanishing isospin is performed and the region of the break-down of the perturbative calculations are delineated. Finally, we study the thermodynamic potential at high chemical potentials and low temperatures where the perturbative scheme should be also applicable.

  1. Higgs boson mass in the Standard Model at two-loop order and beyond

    Energy Technology Data Exchange (ETDEWEB)

    Martin, Stephen P. [Northern Illinois U.; Robertson, David G. [Otterbein Coll.

    2014-10-23

    We calculate the mass of the Higgs boson in the standard model in terms of the underlying Lagrangian parameters at complete 2-loop order with leading 3-loop corrections. A computer program implementing the results is provided. The program also computes and minimizes the standard model effective potential in Landau gauge at 2-loop order with leading 3-loop corrections.

  2. Two-point Functions at Two Loops in Three Flavour Chiral Perturbation Theory

    CERN Document Server

    Amorós, G; Talavera, P; Amoros, Gabriel; Bijnens, Johan; Talavera, Pere

    2000-01-01

    The vector and axial-vector two-point functions are calculated to next-to-next-to-leading order in Chiral Perturbation Theory for three light flavours. We also obtain expressions at the same order for the masses, $m_\\pi^2$, $m_K^2$ and $m_\\eta^2$, and the decay constants, $F_\\pi$, $F_K$ and $F_\\eta$. We present some numerical results after a simple resonance estimate of some of the new ${\\cal O}(p^6)$ constants.

  3. Two-loop corrections to the triple Higgs boson production cross section

    CERN Document Server

    de Florian, Daniel

    2016-01-01

    In this paper we compute the QCD corrections for the triple Higgs boson production cross section via gluon fusion, within the heavy-top approximation. We present, for the first time, analytical results for the next-to-leading order corrections, and also compute the soft and virtual contributions of the next-to-next-to-leading order cross section. We provide predictions for the total cross section and the triple Higgs invariant mass distribution. We find that the QCD corrections are large at both perturbative orders, and that the scale uncertainty is substantially reduced when the second order perturbative corrections are included.

  4. Two-loop dimensional reduction and effective potential without temperature expansions

    CERN Document Server

    Laine, Mikko

    2000-01-01

    In many extensions of the Standard Model, finite temperature computations are complicated by a hierarchy of zero temperature mass scales, in addition to the usual thermal mass scales. We extend the standard thermal resummations to such a situation, and discuss the 2-loop computations of the Higgs effective potential, and an effective 3d field theory for the electroweak phase transition, without carrying out high or low temperature expansions for the heavy masses. We also estimate the accuracy of the temperature expansions previously used for the MSSM electroweak phase transition in the presence of a heavy left-handed stop. We find that the low temperature limit of dealing with the left-handed stop is accurate up to surprisingly high temperatures.

  5. Two-loop dimensional reduction and effective potential without temperature expansions

    OpenAIRE

    M. Laine; Losada, M.

    2000-01-01

    In many extensions of the Standard Model, finite temperature computations are complicated by a hierarchy of zero temperature mass scales, in addition to the usual thermal mass scales. We extend the standard thermal resummations to such a situation, and discuss the 2-loop computations of the Higgs effective potential, and an effective 3d field theory for the electroweak phase transition, without carrying out high or low temperature expansions for the heavy masses. We also estimate the accuracy...

  6. Dominant two-loop corrections to the trilinear Higgs couplings in the complex NMSSM

    Energy Technology Data Exchange (ETDEWEB)

    Hoffmann, Hanna; Muehlleitner, Margarete [Karlsruhe Institute of Technology (KIT), Karlsruhe (Germany); Thi Dao, Nhung [Institute of Physics, Vietnam Academy of Science and Technology (Viet Nam)

    2015-07-01

    In this talk I present our results on the O(α{sub t},α{sub s}) corrections to the trilinear Higgs couplings in the complex NMSSM. I give insight into our calculation using the Feynman-diagramatic approach and our renormalization procedure. Furthermore I discuss phenomenological implications of our results.

  7. Two-loop renormalization of fermion bilinear operators on the lattice

    CERN Document Server

    Skouroupathis, A

    2010-01-01

    We compute the renormalization functions on the lattice, in the RI' scheme, of local bilinear quark operators $\\bar{\\psi}\\Gamma\\psi$, where $\\Gamma= 1, \\gamma_5, \\gamma_\\mu, \\gamma_5\\gamma_\\mu, \\gamma_5\\sigma_{\\mu\

  8. Multidimensional singular integrals and integral equations

    CERN Document Server

    Mikhlin, Solomon Grigorievich; Stark, M; Ulam, S

    1965-01-01

    Multidimensional Singular Integrals and Integral Equations presents the results of the theory of multidimensional singular integrals and of equations containing such integrals. Emphasis is on singular integrals taken over Euclidean space or in the closed manifold of Liapounov and equations containing such integrals. This volume is comprised of eight chapters and begins with an overview of some theorems on linear equations in Banach spaces, followed by a discussion on the simplest properties of multidimensional singular integrals. Subsequent chapters deal with compounding of singular integrals

  9. Integrable Bogoliubov Transform and Integrable Model

    Institute of Scientific and Technical Information of China (English)

    王宁

    2003-01-01

    By defining Bogoliubov transform as a function of parameters, the integrability of the Bogoliubov transform in parameter space is investigated. It is shown that integrable Bogoliubov transform is closely related to the known integrable model. The relation between the integrable Bogoliubov transform and geometric phase of vacuum induced by the Bogoliubov transform is also discussed.

  10. Nonplanar integrability

    Science.gov (United States)

    Carlson, Warren; de Mello Koch, Robert; Lin, Hai

    2011-03-01

    In this article we study operators with a dimension Δ ˜ O( N) and show that simple analytic expressions for the action of the dilatation operator can be found. The operators we consider are restricted Schur polynomials. There are two distinct classes of operators that we consider: operators labeled by Young diagrams with two long columns or two long rows. The main complication in working with restricted Schur polynomials is in building a projector from a given S n+ m irreducible representation to an S n × S m irreducible representation (both specified by the labels of the restricted Schur polynomial). We give an explicit construction of these projectors by reducing it to the simple problem of addition of angular momentum in ordinary non-relativistic quantum mechanics. The diagonalization of the dilatation operator reduces to solving three term recursion relations. The fact that the recursion relations have only three terms is a direct consequence of the weak mixing at one loop of the restricted Schur polynomials. The recursion relations can be solved exactly in terms of symmetric Kravchuk polynomials or in terms of Clebsch-Gordan coefficients. This proves that the dilatation operator reduces to a decoupled set of harmonic oscillators and therefore it is integrable.

  11. Simplification of integrity constraints for data integration

    DEFF Research Database (Denmark)

    Christiansen, Henning; Martinenghi, Davide

    2004-01-01

    When two or more databases are combined into a global one, integrity may be violated even when each database is consistent with its own local integrity constraints. Efficient methods for checking global integrity in data integration systems are called for: answers to queries can then be trusted...... together with given a priori constraints on the combination, so that only a minimal number of tuples needs to be considered. Combination from scratch, integration of a new source, and absorption of local updates are dealt with for both the local-as-view and global-as-view approaches to data integration....

  12. Strong vector valued integrals

    CERN Document Server

    Beckmann, Ralf

    2011-01-01

    Strong Bochner type integrals with values in locally convex spaces are introduced. It is shown that the strong integral exists in the same cases as the weak (Gelfand-Pettis) integral is known to exist. The strong integral has better continuity properties that the weak integral.

  13. Discrete integrable system and its integrable coupling

    Institute of Scientific and Technical Information of China (English)

    LI Zhu

    2009-01-01

    This paper derives new discrete integrable system based on discrete isospectral problem. It shows that the hierarchy is completely integrable in the Liouville sense and possesses bi-Hamiltonian structure. Finally, integrable couplings of the obtained system is given by means of semi-direct sums of Lie algebras.

  14. Data integration technologies to support integrated modelling

    NARCIS (Netherlands)

    Knapen, M.J.R.; Roosenschoon, O.R.; Lokers, R.M.; Janssen, S.J.C.; Randen, van Y.; Verweij, P.J.F.M.

    2013-01-01

    Over the recent years the scientific activities of our organisation in large research projects show a shifting priority from model integration to the integration of data itself. Our work in several large projects on integrated modelling for impact assessment studies has clearly shown the importance

  15. Data integration technologies to support integrated modelling

    NARCIS (Netherlands)

    Knapen, M.J.R.; Roosenschoon, O.R.; Lokers, R.M.; Janssen, S.J.C.; Randen, van Y.; Verweij, P.J.F.M.

    2013-01-01

    Over the recent years the scientific activities of our organisation in large research projects show a shifting priority from model integration to the integration of data itself. Our work in several large projects on integrated modelling for impact assessment studies has clearly shown the importance

  16. Hydrography - Integrated List Attaining

    Data.gov (United States)

    NSGIC GIS Inventory (aka Ramona) — This layer shows only attaining segments of the Integrated List. The Streams Integrated List represents stream assessments in an integrated format for the Clean...

  17. Simplification of integrity constraints for data integration

    DEFF Research Database (Denmark)

    Christiansen, Henning; Martinenghi, Davide

    2004-01-01

    When two or more databases are combined into a global one, integrity may be violated even when each database is consistent with its own local integrity constraints. Efficient methods for checking global integrity in data integration systems are called for: answers to queries can then be trusted......, because either the global database is known to be consistent or suitable actions have been taken to provide consistent views. The present work generalizes simplification techniques for integrity checking in traditional databases to the combined case. Knowledge of local consistency is employed, perhaps...... together with given a priori constraints on the combination, so that only a minimal number of tuples needs to be considered. Combination from scratch, integration of a new source, and absorption of local updates are dealt with for both the local-as-view and global-as-view approaches to data integration....

  18. Tactical Systems Integration Laboratory

    Data.gov (United States)

    Federal Laboratory Consortium — The Tactical Systems Integration Laboratory is used to design and integrate computer hardware and software and related electronic subsystems for tactical vehicles....

  19. Pro Spring Integration

    CERN Document Server

    Lui, M; Chan, Andy; Long, Josh

    2011-01-01

    Pro Spring Integration is an authoritative book from the experts that guides you through the vast world of enterprise application integration (EAI) and application of the Spring Integration framework towards solving integration problems. The book is:. * An introduction to the concepts of enterprise application integration * A reference on building event-driven applications using Spring Integration * A guide to solving common integration problems using Spring Integration What makes this book unique is its coverage of contemporary technologies and real-world information, with a focus on common p

  20. Numerical Integration with Derivatives

    Institute of Scientific and Technical Information of China (English)

    Hu Cheng

    2006-01-01

    A new formula with derivatives for numerical integration was presented. Based on this formula and the Richardson extrapolation process, a numerical integration method was established. It can converge faster than the Romberg's. With the same accuracy, the computation of the new numerical integration with derivatives is only half of that of Romberg's numerical integration.

  1. The integrated PWR; Les REP integres

    Energy Technology Data Exchange (ETDEWEB)

    Gautier, G.M. [CEA Cadarache, 13 - Saint-Paul-lez-Durance (France). Dept. d' Etudes des Reacteurs

    2002-07-01

    This document presents the integrated reactors concepts by a presentation of four reactors: PIUS, SIR, IRIS and CAREM. The core conception, the operating, the safety, the economical aspects and the possible users are detailed. From the performance of the classical integrated PWR, the necessity of new innovative fuels utilization, the research of a simplified design to make easier the safety and the KWh cost decrease, a new integrated reactor is presented: SCAR 600. (A.L.B.)

  2. Slimplectic Integrators: Variational Integrators for Nonconservative systems

    Science.gov (United States)

    Tsang, David

    2016-05-01

    Symplectic integrators are widely used for long-term integration of conservative astrophysical problems due to their ability to preserve the constants of motion; however, they cannot in general be applied in the presence of nonconservative interactions. Here we present the “slimplectic” integrator, a new type of numerical integrator that shares many of the benefits of traditional symplectic integrators yet is applicable to general nonconservative systems. We utilize a fixed-time-step variational integrator formalism applied to a newly developed principle of stationary nonconservative action (Galley, 2013, Galley et al 2014). As a result, the generalized momenta and energy (Noether current) evolutions are well-tracked. We discuss several example systems, including damped harmonic oscillators, Poynting-Robertson drag, and gravitational radiation reaction, by utilizing our new publicly available code to demonstrate the slimplectic integrator algorithm. Slimplectic integrators are well-suited for integrations of systems where nonconservative effects play an important role in the long-term dynamical evolution. As such they are particularly appropriate for cosmological or celestial N-body dynamics problems where nonconservative interactions, e.g., gas interactions or dissipative tides, can play an important role.

  3. Some new nystrom integrators

    Science.gov (United States)

    Lear, W. M.

    1978-01-01

    Nystrom integrators were self starting integrators used to integrate the second order, vector, differential equations the second derivative of x factorial = f factorial (t, x factorial) and the second derivative of x factorial = f factorial (t, x factorial, first derivative of x factorial). Nystrom integrator parameters were defined by a set of nonlinear constraint equations and frequently there were more parameters than there were equations. Additions are included for higher order integrations when the second derivative of x factorial = f factorial (t).

  4. Variational path-integral approach to back-reactions of composite mesons in the Nambu-Jona-Lasinio model

    Science.gov (United States)

    Blaschke, D.; Ebert, D.

    2017-08-01

    For the investigation of back-reactions of composite mesons in the NJL model, a variational path-integral treatment is formulated which yields an effective action Aeff [Dσ ,Dπ ; S ], depending on the propagators Dσ, Dπ of σ- and π-mesons and on the full quark propagator S. The stationarity conditions δAeff / δS = 0, δAeff / δDσ = 0, δAeff / δDπ = 0, then lead to coupled Schwinger-Dyson (SD) equations for the quark self-energy and the meson polarization functions. These results reproduce and extend results of the so-called ;Φ-derivable; approach and provide a functional formulation for diagrammatic resummations of 1 /Nc -corrections in the NJL model. Finally, we perform a low-momentum estimate of the quark and meson loop contributions to the polarization function of the pion and on this basis discuss the Goldstone theorem.

  5. Feynman integrals and hyperlogarithms

    CERN Document Server

    Panzer, Erik

    2015-01-01

    We study Feynman integrals in the representation with Schwinger parameters and derive recursive integral formulas for massless 3- and 4-point functions. Properties of analytic (including dimensional) regularization are summarized and we prove that in the Euclidean region, each Feynman integral can be written as a linear combination of convergent Feynman integrals. This means that one can choose a basis of convergent master integrals and need not evaluate any divergent Feynman graph directly. Secondly we give a self-contained account of hyperlogarithms and explain in detail the algorithms needed for their application to the evaluation of multivariate integrals. We define a new method to track singularities of such integrals and present a computer program that implements the integration method. As our main result, we prove the existence of infinite families of massless 3- and 4-point graphs (including the ladder box graphs with arbitrary loop number and their minors) whose Feynman integrals can be expressed in ...

  6. Cavalieri Integration - CSIR Technical report

    CSIR Research Space (South Africa)

    Grobler, TL

    2011-10-01

    Full Text Available The authors use Cavalieri's principle to develop a novel integration technique which they call Cavalieri integration. Cavalieri integrals differ from Riemann integrals in that non-rectangular integration strips are used. In this way they can use...

  7. One loop integrals reduction

    Institute of Scientific and Technical Information of China (English)

    SUN Yi; CHANG Hao-Ran

    2012-01-01

    By further examining the symmetry of external momenta and masses in Feynman integrals,we fulfilled the method proposed by Battistel and Dallabona,and showed that recursion relations in this method can be applied to simplify Feynman integrals directly.

  8. Integrated resource planning

    DEFF Research Database (Denmark)

    Østergaard, Poul Alberg

    2004-01-01

    The chapter describes two cases where the principles of Integrated Resouce Plannning (IRP) has been applied to simplified systems.......The chapter describes two cases where the principles of Integrated Resouce Plannning (IRP) has been applied to simplified systems....

  9. Spring integration essentials

    CERN Document Server

    Pandey, Chandan

    2015-01-01

    This book is intended for developers who are either already involved with enterprise integration or planning to venture into the domain. Basic knowledge of Java and Spring is expected. For newer users, this book can be used to understand an integration scenario, what the challenges are, and how Spring Integration can be used to solve it. Prior experience of Spring Integration is not expected as this book will walk you through all the code examples.

  10. Entrepreneurial Integration Skills

    DEFF Research Database (Denmark)

    Bauer, Florian; Schriber, Svante; King, David R.

    2016-01-01

    effect relationships by investigating the effect of integration related decisions on intermediate goals. Additionally, we argue that entrepreneurial integration skills, or proactivity under ambiguity, are needed to keep pace with the dynamism inherent in acquisition integration. Based on primary data...... on 116 acquisitions, we find that entrepreneurial integration skills can display both advantages and disadvantages. While it helps to realize expected and serendipitous synergies, it can also trigger employee uncertainty due to decreased transparency. In supplementary analysis, we show measures...

  11. Boolean integral calculus

    Science.gov (United States)

    Tucker, Jerry H.; Tapia, Moiez A.; Bennett, A. Wayne

    1988-01-01

    The concept of Boolean integration is developed, and different Boolean integral operators are introduced. Given the changes in a desired function in terms of the changes in its arguments, the ways of 'integrating' (i.e. realizing) such a function, if it exists, are presented. The necessary and sufficient conditions for integrating, in different senses, the expression specifying the changes are obtained. Boolean calculus has applications in the design of logic circuits and in fault analysis.

  12. Boolean integral calculus

    Science.gov (United States)

    Tucker, Jerry H.; Tapia, Moiez A.; Bennett, A. Wayne

    1988-01-01

    The concept of Boolean integration is developed, and different Boolean integral operators are introduced. Given the changes in a desired function in terms of the changes in its arguments, the ways of 'integrating' (i.e. realizing) such a function, if it exists, are presented. The necessary and sufficient conditions for integrating, in different senses, the expression specifying the changes are obtained. Boolean calculus has applications in the design of logic circuits and in fault analysis.

  13. Integrated vs. Federated Search

    DEFF Research Database (Denmark)

    Løvschall, Kasper

    2009-01-01

    Oplæg om forskelle og ligheder mellem integrated og federated search i bibliotekskontekst. Holdt ved temadag om "Integrated Search - samsøgning i alle kilder" på Danmarks Biblioteksskole den 22. januar 2009.......Oplæg om forskelle og ligheder mellem integrated og federated search i bibliotekskontekst. Holdt ved temadag om "Integrated Search - samsøgning i alle kilder" på Danmarks Biblioteksskole den 22. januar 2009....

  14. Electromechanical integrated magnetic gear

    OpenAIRE

    Xiu-hong Hao; Hong-fei Zhang; Ji-de Men

    2016-01-01

    This study proposes a new type of magnetic gear, namely, the electromechanical integrated magnetic gear, that integrates the traditional field-modulated magnetic gear, drive, and control. The topology and operating principle of the electromechanical integrated magnetic gear are described in detail in this article, and the constraints of parameter design and speed ratio of electromechanical integrated magnetic gear are presented. Moreover, magnetic field distribution is analyzed with the finit...

  15. Parametric Differentiation and Integration

    Science.gov (United States)

    Chen, Hongwei

    2009-01-01

    Parametric differentiation and integration under the integral sign constitutes a powerful technique for calculating integrals. However, this topic is generally not included in the undergraduate mathematics curriculum. In this note, we give a comprehensive review of this approach, and show how it can be systematically used to evaluate most of the…

  16. Parametric Differentiation and Integration

    Science.gov (United States)

    Chen, Hongwei

    2009-01-01

    Parametric differentiation and integration under the integral sign constitutes a powerful technique for calculating integrals. However, this topic is generally not included in the undergraduate mathematics curriculum. In this note, we give a comprehensive review of this approach, and show how it can be systematically used to evaluate most of the…

  17. Integrated nursery pest management

    Science.gov (United States)

    R. Kasten Dumroese

    2012-01-01

    What is integrated pest management? Take a look at the definition of each word to better understand the concept. Two of the words (integrated and management) are relatively straightforward. Integrated means to blend pieces or concepts into a unified whole, and management is the wise use of techniques to successfully accomplish a desired outcome. A pest is any biotic (...

  18. Sesquilinear uniform vector integral

    Indian Academy of Sciences (India)

    Ion Chiţescu; Loredana Ioana; Radu Miculescu; Lucian Niţă

    2015-05-01

    We introduce and study an integral of Hilbert valued functions with respect to Hilbert valued measures. The integral is sesquilinear (bilinear in the real case) and takes scalar values. Basic properties of this integral are studied and some examples are introduced.

  19. Foundations for Psychotherapy Integration

    Directory of Open Access Journals (Sweden)

    António Branco Vasco

    2014-10-01

    Full Text Available The movement for integration in psychotheray is clearly one of the main trends that can be observed in the field. The author stresses three main reasons for this state of affairs and as a way of justifying the importance of integration: historical and psychosocial, empirical and philosophical. A specific way of thinking in integrative terms is also outlined - "paradigmatic complementarity."

  20. Ramjets: Airframe integration

    NARCIS (Netherlands)

    Moerel, J.L.; Halswijk, W.

    2010-01-01

    These notes deal with the integration of a (sc)ramjet engine in either an axisymmetric or a waverider type of cruise missile configuration. The integration aspects relate to the integration of the external and internal flow paths in geometrical configurations that are being considered worldwide. Int

  1. Integrated Auto-Tuning PID Control of Continuous Casting Process

    Institute of Scientific and Technical Information of China (English)

    2000-01-01

    PID controllers were used for the hydraulic servo system of sliding gate and the tundish weight control system in continuous caster. These two loops were synthesized in mould level controller based on model reduction and internal model control strategy. Satisfactory control performance of this synthetic mould level controller was demonstrated by simulations and on-line experiments.

  2. Photonic Integrated Circuits

    Science.gov (United States)

    Krainak, Michael; Merritt, Scott

    2016-01-01

    Integrated photonics generally is the integration of multiple lithographically defined photonic and electronic components and devices (e.g. lasers, detectors, waveguides passive structures, modulators, electronic control and optical interconnects) on a single platform with nanometer-scale feature sizes. The development of photonic integrated circuits permits size, weight, power and cost reductions for spacecraft microprocessors, optical communication, processor buses, advanced data processing, and integrated optic science instrument optical systems, subsystems and components. This is particularly critical for small spacecraft platforms. We will give an overview of some NASA applications for integrated photonics.

  3. Transdisciplinary knowledge integration : cases from integrated assessment and vulnerability assessment

    NARCIS (Netherlands)

    Hinkel, J.

    2008-01-01

    Keywords: climate change, integrated assessment, knowledge integration, transdisciplinary research, vulnerability, vulnerability assessment. This thesis explores how transdisciplinary knowledge integration can be facilitated in the context of integrated assessments and vulnerability assessments of

  4. Immigrant Integration: Acculturation and Social Integration

    Directory of Open Access Journals (Sweden)

    Astrid HAMBERGER

    2009-11-01

    Full Text Available This article tackles the concept of “immigrant integration” as it is analyzed by different authors in the international migration field. In this article, I will use the terms “refugee” and “immigrant” as equivalent to each other due to the interchangeable character of these concepts throughout the integration literature. First, the article brings into discussion the definitional and conceptual battle around the concept of immigrant “integration”, and second, it will describe and analyze cultural and social integration with their presupposing processes.

  5. Integrated management systems

    CERN Document Server

    Bugdol, Marek

    2015-01-01

    Examining the challenges of integrated management, this book explores the importance and potential benefits of using an integrated approach as a cross-functional concept of management. It covers not only standardized management systems (e.g. International Organization for Standardization), but also models of self-assessment, as well as different types of integration. Furthermore, it demonstrates how processes and systems can be integrated, and how management efficiency can be increased. The major part of this book focuses on management concepts which use integration as a key tool of management processes (e.g. the systematic approach, supply chain management, virtual and network organizations, processes management and total quality management). Case studies, illustrations, and tables are also provided to exemplify and illuminate the content, as well as examples of successful and failed integrations. Providing a particularly useful resource to managers and specialists involved in the improvement of organization...

  6. Dimensionally regulated pentagon integrals

    CERN Document Server

    Bern, Z; Kosower, D A

    1994-01-01

    We present methods for evaluating the Feynman parameter integrals associated with the pentagon diagram in 4-2 epsilon dimensions, along with explicit results for the integrals with all masses vanishing or with one non-vanishing external mass. The scalar pentagon integral can be expressed as a linear combination of box integrals, up to O(epsilon) corrections, a result which is the dimensionally-regulated version of a D=4 result of Melrose, and of van Neerven and Vermaseren. We obtain and solve differential equations for various dimensionally-regulated box integrals with massless internal lines, which appear in one-loop n-point calculations in QCD. We give a procedure for constructing the tensor pentagon integrals needed in gauge theory, again through O(epsilon^0).

  7. Integration of reusable systems

    CERN Document Server

    Rubin, Stuart

    2014-01-01

    Software reuse and integration has been described as the process of creating software systems from existing software rather than building software systems from scratch. Whereas reuse solely deals with the artifacts creation, integration focuses on how reusable artifacts interact with the already existing parts of the specified transformation. Currently, most reuse research focuses on creating and integrating adaptable components at development or at compile time. However, with the emergence of ubiquitous computing, reuse technologies that can support adaptation and reconfiguration of architectures and components at runtime are in demand. This edited book includes 15 high quality research papers written by experts in information reuse and integration to cover the most recent advances in the field. These papers are extended versions of the best papers which were presented at IEEE International Conference on Information Reuse and Integration and IEEE International Workshop on Formal Methods Integration, which wa...

  8. Four integration patterns

    DEFF Research Database (Denmark)

    Bygstad, Bendik; Nielsen, Peter Axel; Munkvold, Bjørn Erik

    2010-01-01

    . Expanding the perspective of traditional project management research, we draw extensively on central insights from IS research. Building on socio-technical IS research and Software Engineering research we suggest four generic patterns of integration: Big Bang, Stakeholder Integration, Technical Integration...... and Socio-Technical Integration. We analyze and describe the advantages and disadvantages of each pattern. The four patterns are ideal types. To explore the forces and challenges in these patterns three longitudinal case studies were conducted. In particular we investigate the management challenges for each...... pattern. We find that the patterns are context sensitive, and describe the different contexts where the patterns are applicable. For IS project management the four integration patterns is a contribution to the management of integration risks, extending the vocabulary for assessing and mitigating...

  9. What constitutes information integrity?

    Directory of Open Access Journals (Sweden)

    S. Flowerday

    2007-12-01

    Full Text Available This research focused on what constitutes information integrity as this is a problem facing companies today. Moreover, information integrity is a pillar of information security and is required in order to have a sound security management programme. However, it is acknowledged that 100% information integrity is not currently achievable due to various limitations and therefore the auditing concept of reasonable assurance is adopted. This is in line with the concept that 100% information security is not achievable and the notion that adequate security is the goal, using appropriate countermeasures. The main contribution of this article is to illustrate the importance of and provide a macro view of what constitutes information integrity. The findings are in harmony with Samuel Johnson's words (1751: 'Integrity without knowledge is weak and useless, and knowledge without integrity is dangerous and dreadful.'

  10. What constitutes information integrity?

    Directory of Open Access Journals (Sweden)

    S. Flowerday

    2008-01-01

    Full Text Available This research focused on what constitutes information integrity as this is a problem facing companies today. Moreover, information integrity is a pillar of information security and is required in order to have a sound security management programme. However, it is acknowledged that 100% information integrity is not currently achievable due to various limitations and therefore the auditing concept of reasonable assurance is adopted. This is in line with the concept that 100% information security is not achievable and the notion that adequate security is the goal, using appropriate countermeasures. The main contribution of this article is to illustrate the importance of and provide a macro view of what constitutes information integrity. The findings are in harmony with Samuel Johnson's words (1751: 'Integrity without knowledge is weak and useless, and knowledge without integrity is dangerous and dreadful.'

  11. Classical Mechanics and Symplectic Integration

    DEFF Research Database (Denmark)

    Nordkvist, Nikolaj; Hjorth, Poul G.

    2005-01-01

    Content: Classical mechanics: Calculus of variations, Lagrange’s equations, Symmetries and Noether’s theorem, Hamilton’s equations, cannonical transformations, integrable systems, pertubation theory. Symplectic integration: Numerical integrators, symplectic integrators, main theorem on symplectic...

  12. Introduction to Feynman Integrals

    CERN Document Server

    Weinzierl, Stefan

    2010-01-01

    In these lectures I will give an introduction to Feynman integrals. In the first part of the course I review the basics of the perturbative expansion in quantum field theories. In the second part of the course I will discuss more advanced topics: Mathematical aspects of loop integrals related to periods, shuffle algebras and multiple polylogarithms are covered as well as practical algorithms for evaluating Feynman integrals.

  13. Integrated Sensitivity Analysis Workflow

    Energy Technology Data Exchange (ETDEWEB)

    Friedman-Hill, Ernest J. [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Hoffman, Edward L. [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Gibson, Marcus J. [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Clay, Robert L. [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)

    2014-08-01

    Sensitivity analysis is a crucial element of rigorous engineering analysis, but performing such an analysis on a complex model is difficult and time consuming. The mission of the DART Workbench team at Sandia National Laboratories is to lower the barriers to adoption of advanced analysis tools through software integration. The integrated environment guides the engineer in the use of these integrated tools and greatly reduces the cycle time for engineering analysis.

  14. Integrated ELM modelling

    Energy Technology Data Exchange (ETDEWEB)

    Loennroth, J.S.; Kiviniemi, T. [Association EURATOM-Tekes, Helsinki University of Technology, P. O. Box 4100, 02015 TKK (Finland); Bateman, G.; Kritz, A. [Lehigh University, Bethlehem, PA (United States); Becoulet, M.; Figarella, C.; Garbet, X.; Huysmans, G. [Association Euratom-CEA, CEA Cadarache (France); Beyer, P. [University of Marseille (France); Corrigan, G.; Fundamenski, W. [UKAEA Fusion Association, Culham Science Centre (United Kingdom); Garcia, O.E.; Naulin, V. [Association Euratom-Risoe National Laboratory, Roskilde (Denmark); Janeschitz, G. [Forschungszentrum Karlsruhe (Germany); Johnson, T. [Association Euratom-VR, Royal Institute of Technology, Stockholm (Sweden); Kuhn, S. [Association Euratom-OeAW, University of Innsbruck (Austria); Loarte, A. [EFDA Close Support Unit, Garching (Germany); Nave, F. [Association Euratom-IST, Centro de Fusao Nuclear, Lisbon (Portugal); Onjun, T. [Sirindhorn International Institute of Technology (Thailand); Pacher, G.W. [Hydro Quebec (Canada); Pacher, H.D.; Pankin, A.; Parail, V.; Pitts, R.; Saibene, G.; Snyder, P.; Spence, J.; Tskhakaya, D.; Wilson, H.

    2006-09-15

    This paper presents a short overview of current trends and progress in integrated ELM modelling. First, the concept of integrated ELM modelling is introduced, various interpretations of it are given and the need for it is discussed. Then follows an overview of different techniques and methods used in integrated ELM modelling presented roughly according to physics approached in use and in order of increasing complexity. The paper concludes with a short discussion of open issues and future modelling requirements within the field of integrated ELM modelling. (copyright 2006 WILEY-VCH Verlag GmbH and Co. KGaA, Weinheim) (orig.)

  15. Factorization of Behavioral Integrity

    DEFF Research Database (Denmark)

    Li, Ximeng; Nielson, Flemming; Nielson, Hanne Riis

    2015-01-01

    We develop a bisimulation-based nonintereference property that describes the allowed dependencies between communication behaviors of different integrity levels. The property is able to capture all possible combinations of integrity levels for the “presence” and “content” of actual communications....... Channels of low presence integrity and high content integrity can be used to model the effect of Message Authentication Codes or the consequence of Denial of Service Attacks. In case the distinction between “presence” and “content” is deliberately blurred, the noninterference property specialises...

  16. Path Integrals and Hamiltonians

    Science.gov (United States)

    Baaquie, Belal E.

    2014-03-01

    1. Synopsis; Part I. Fundamental Principles: 2. The mathematical structure of quantum mechanics; 3. Operators; 4. The Feynman path integral; 5. Hamiltonian mechanics; 6. Path integral quantization; Part II. Stochastic Processes: 7. Stochastic systems; Part III. Discrete Degrees of Freedom: 8. Ising model; 9. Ising model: magnetic field; 10. Fermions; Part IV. Quadratic Path Integrals: 11. Simple harmonic oscillators; 12. Gaussian path integrals; Part V. Action with Acceleration: 13. Acceleration Lagrangian; 14. Pseudo-Hermitian Euclidean Hamiltonian; 15. Non-Hermitian Hamiltonian: Jordan blocks; 16. The quartic potential: instantons; 17. Compact degrees of freedom; Index.

  17. Acquisition IT Integration

    DEFF Research Database (Denmark)

    Henningsson, Stefan; Øhrgaard, Christian

    2015-01-01

    The IT integration of acquisitions consists an important challenge for the many acquiring organizations. Complementing existing research, this paper searches for explanation to differences in acquirers’ abilities for acquisition IT integration in the external of the acquirer, by a study of the use...... of temporary agency workers. Following an analytic induction approach, theoretically grounded in the re-source-based view of the firm, we identify the complimentary and supplementary roles consultants can assume in acquisition IT integration. Through case studies of three acquirers, we investigate how...... of the acquisition IT integration team should consider the balance of these, in practice, commonly mutually excluding needs....

  18. Building integrated photovoltaic; Photovaltaique integre aux batiments

    Energy Technology Data Exchange (ETDEWEB)

    NONE

    2004-01-01

    Durable, modular and flexible in use, as demonstrated by the different case studies in this publication, photovoltaic can replace diverse building elements, from glass facades to weather proof roofs. This leaflet towards architects describes aesthetic, technical, economic and environmental interest of building integrated photovoltaic. (author)

  19. Feynman integrals and hyperlogarithms

    Energy Technology Data Exchange (ETDEWEB)

    Panzer, Erik

    2015-02-05

    We study Feynman integrals in the representation with Schwinger parameters and derive recursive integral formulas for massless 3- and 4-point functions. Properties of analytic (including dimensional) regularization are summarized and we prove that in the Euclidean region, each Feynman integral can be written as a linear combination of convergent Feynman integrals. This means that one can choose a basis of convergent master integrals and need not evaluate any divergent Feynman graph directly. Secondly we give a self-contained account of hyperlogarithms and explain in detail the algorithms needed for their application to the evaluation of multivariate integrals. We define a new method to track singularities of such integrals and present a computer program that implements the integration method. As our main result, we prove the existence of infinite families of massless 3- and 4-point graphs (including the ladder box graphs with arbitrary loop number and their minors) whose Feynman integrals can be expressed in terms of multiple polylogarithms, to all orders in the ε-expansion. These integrals can be computed effectively with the presented program. We include interesting examples of explicit results for Feynman integrals with up to 6 loops. In particular we present the first exactly computed counterterm in massless φ{sup 4} theory which is not a multiple zeta value, but a linear combination of multiple polylogarithms at primitive sixth roots of unity (and divided by the √(3)). To this end we derive a parity result on the reducibility of the real- and imaginary parts of such numbers into products and terms of lower depth.

  20. Implicit Regularisation Technique Calculation of the Two-loop $\\phi_{4}^{4}$-theory $\\beta$-function

    CERN Document Server

    Brizola, A; Battistel, O A; Nemes, M C; Sampaio, Marcos

    1999-01-01

    A new 4-D regularisation scheme is proposed. The main advantage is that no explicit use of a specific regulator is made and thus we can, in principle, avoid undesirable symmmetry-breakings related to its choice. We illustrate with the calculation of the $QED$ and $\\phi^4_4$-theory

  1. Cancellations Between Two-Loop Contributions to the Electron Electric Dipole Moment with a CP-Violating Higgs Sector.

    Science.gov (United States)

    Bian, Ligong; Liu, Tao; Shu, Jing

    2015-07-10

    We present a class of cancellation conditions for suppressing the total contributions of Barr-Zee diagrams to the electron electric dipole moment (eEDM). Such a cancellation is of particular significance after the new eEDM upper limit was released by the ACME Collaboration, which strongly constrains the allowed magnitude of CP violation in Higgs couplings and hence the feasibility of electroweak baryogenesis (EWBG). Explicitly, if both the CP-odd Higgs-photon-photon (Z boson) and the CP-odd Higgs-electron-positron couplings are turned on, a cancellation may occur either between the contributions of a CP-mixing Higgs boson, with the other Higgs bosons being decoupled, or between the contributions of CP-even and CP-odd Higgs bosons. With a cancellation, large CP violation in the Higgs sector is still allowed, yielding successful EWBG. The reopened parameter regions would be probed by future neutron, mercury EDM measurements, and direct measurements of Higgs CP properties at the Large Hadron Collider Run II and future colliders.

  2. The two-loop effective action and some symmetries of the Riemann tensor and the Kalb-Ramond H field

    CERN Document Server

    Ozkurt, S S

    2003-01-01

    Sometimes ago, it has been proposed in a paper by N.Kaloper and K.A.Meissner (\\PR {\\bf D56} (1997) 7940) that if one makes local redefinitions of fields, it does not change the equations of motion (in the redefined fields); however, this comment has not generally been accepted, namely, the redefined fields satisfy different equations of motion. For this reason, the whole action will be written in terms of the zeroth-order field equations in this paper. In this study, we also observe that N.Kaloper and K.A.Meissner's effective action (\\PR {\\bf D56} (1997) 7940)which has a duality symmetry beyond the first loop, can be written in terms of the zeroth-order field equations if the Riemann tensor and the Kalb-Ramond field have some symmetries. For example, K\\"{a}hler manifolds have these symmetries.

  3. Integral transformational coaching

    NARCIS (Netherlands)

    Keizer, W.A.J.; Nandram, S.S.

    2009-01-01

    In Chap. 12, Keizer and Nandram present the concept of Integral Transformational Coaching based on the concept of Flow and its effects on work performance. Integral Transformational Coaching is a method that prevents and cures unhealthy stress and burnout. They draw on some tried and tested spiritua

  4. Integration i flere variable

    DEFF Research Database (Denmark)

    Markvorsen, Steen

    2010-01-01

    -integralerne. Undervejs introduceres \\texttt{Integrator8}. Det er en pakke med Maple procedurer, som er udviklet specielt med henblik på eksempelbaseret visuel læring af de indledende integrationsbegreber og deres mangfoldige anvendelser. Vi giver eksempler på, hvordan integration i flere variable anvendes til beregning...

  5. The discrete Feynman integral

    NARCIS (Netherlands)

    Dorlas, T. C.; Thomas, E. G. F.

    2008-01-01

    We construct a genuine Radon measure with values in B(l(2)(Z(d))) on the set of paths in Z(d) representing Feynman's integral for the discrete Laplacian on l(2)(Z(d)), and we prove the Feynman integral formula for the solutions of the Schrodinger equation with Hamiltonian H=-1/2 Delta+ V, where Delt

  6. An Integrated Teaching Module.

    Science.gov (United States)

    Samuel, Marie R.; Seiferth, Berniece B.

    This integrated teaching module provides elementary and junior high school teachers with a "hands-on" approach to studying the Anasazi Indian. Emphasis is on creative exploration that focuses on integrating art, music, poetry, writing, geography, dance, history, anthropology, sociology, and archaeology. Replicas of artifacts,…

  7. Integrity in Transactional Leadership

    Science.gov (United States)

    Miller, Thomas

    2011-01-01

    This chapter begins with a discussion of the impact of limited resources on the integrity of transactions between students and student affairs administrators. A framework and guiding principles for maintaining integrity are offered, and then some general principles for transactions with students are presented. Next, the chapter involves integrity…

  8. Integrated Marketing Communications

    Science.gov (United States)

    Black, Jim

    2004-01-01

    Integration has become a cliche in enrollment management and student services circles. The term is used to describe everything from integrated marketing to seamless services. Often, it defines organizational structures, processes, student information systems, and even communities. In Robert Sevier's article in this issue of "College and…

  9. Integral transformational coaching

    NARCIS (Netherlands)

    Keizer, W.A.J.; Nandram, S.S.

    2009-01-01

    In Chap. 12, Keizer and Nandram present the concept of Integral Transformational Coaching based on the concept of Flow and its effects on work performance. Integral Transformational Coaching is a method that prevents and cures unhealthy stress and burnout. They draw on some tried and tested

  10. On an integral transform

    Directory of Open Access Journals (Sweden)

    D. Naylor

    1986-01-01

    Full Text Available This paper establishes properties of a convolution type integral transform whose kernel is a Macdonald type Bessel function of zero order. An inversion formula is developed and the transform is applied to obtain the solution of some related integral equations.

  11. Integrity in Student Development

    Science.gov (United States)

    Roberts, Dennis C.; Banta, Trudy W.

    2011-01-01

    The quest for integrity in practice and theory has been part of the evolution of student personnel work all the way back to the turn of the 20th century. This chapter seeks to take stock of the question of integrity in relation to one of the core knowledge bases used by those engaged in student affairs work today--student development. The authors…

  12. Integrated Marketing Communications

    Science.gov (United States)

    Black, Jim

    2004-01-01

    Integration has become a cliche in enrollment management and student services circles. The term is used to describe everything from integrated marketing to seamless services. Often, it defines organizational structures, processes, student information systems, and even communities. In Robert Sevier's article in this issue of "College and…

  13. Intelligent test integration system

    Science.gov (United States)

    Sztipanovits, J.; Padalkar, S.; Rodriguez-Moscoso, J.; Kawamura, K.; Purves, B.; Williams, R.; Biglari, H.

    1988-01-01

    A new test technology is described which was developed for space system integration. The ultimate purpose of the system is to support the automatic generation of test systems in real time, distributed computing environments. The Intelligent Test Integration System (ITIS) is a knowledge based layer above the traditional test system components which can generate complex test configurations from the specification of test scenarios.

  14. Religion and cultural integration

    DEFF Research Database (Denmark)

    Borup, Jørn; Ahlin, Lars

    2011-01-01

    The relations and possible causality between religion, ethnicity, and cultural integration is discussed using empirical data from survey on a group people with Vietnamese origin in Denmark......The relations and possible causality between religion, ethnicity, and cultural integration is discussed using empirical data from survey on a group people with Vietnamese origin in Denmark...

  15. System integration report

    Science.gov (United States)

    Badler, N. I.; Korein, J. D.; Meyer, C.; Manoochehri, K.; Rovins, J.; Beale, J.; Barr, B.

    1985-01-01

    Several areas that arise from the system integration issue were examined. Intersystem analysis is discussed as it relates to software development, shared data bases and interfaces between TEMPUS and PLAID, shaded graphics rendering systems, object design (BUILD), the TEMPUS animation system, anthropometric lab integration, ongoing TEMPUS support and maintenance, and the impact of UNIX and local workstations on the OSDS environment.

  16. Hermeneutics of Integrative Knowledge.

    Science.gov (United States)

    Shin, Un-chol

    This paper examines and compares the formation processes and structures of three types of integrative knowledge that in general represent natural sciences, social sciences, and humanities. These three types can be observed, respectively, in the philosophies of Michael Polanyi, Jurgen Habermas, and Paul Ricoeur. These types of integrative knowledge…

  17. Systems Integration (Fact Sheet)

    Energy Technology Data Exchange (ETDEWEB)

    2011-10-01

    The Systems Integration (SI) subprogram works closely with industry, universities, and the national laboratories to overcome technical barriers to the large-scale deployment of solar technologies. To support these goals, the subprogram invests primarily in four areas: grid integration, technology validation, solar resource assessment, and balance of system development.

  18. Systems Integration (Fact Sheet)

    Energy Technology Data Exchange (ETDEWEB)

    DOE Solar Energy Technologies Program

    2011-10-13

    The Systems Integration (SI) subprogram works closely with industry, universities, and the national laboratories to overcome technical barriers to the large-scale deployment of solar technologies. To support these goals, the subprogram invests primarily in four areas: grid integration, technology validation, solar resource assessment, and balance of system development.

  19. Integrated Optics Some Aspects

    Directory of Open Access Journals (Sweden)

    R. Hradaynath

    1990-01-01

    Full Text Available Status of some key individual integrated optics components, their application in the field of telecommunications, integrated optoelectronic circuits, fibre optics sensors, optical interconnects and logic devices are highlighted in this paper. Possibilities of opto-opto processors in the computers field are also outlined.

  20. Generalized Bihari Type Integral Inequalities and the Corresponding Integral Equations

    OpenAIRE

    2009-01-01

    We study some special nonlinear integral inequalities and the corresponding integral equations in measure spaces. They are significant generalizations of Bihari type integral inequalities and Volterra and Fredholm type integral equations. The kernels of the integral operators are determined by concave functions. Explicit upper bounds are given for the solutions of the integral inequalities. The integral equations are investigated with regard to the existence of a minimal and a maximal soluti...

  1. Personal Integrity and Leadership

    Directory of Open Access Journals (Sweden)

    Antonius Gea

    2016-07-01

    Full Text Available Generally, integrity is associated with leadership, especially in the organization or company. Integrity in leadership becomes a growing concern in business and organizations. The aim of this study was to find out the connection that could be shaped between personal integrity and the skill of leadership especially in the performance of work. This study used a library research, a literature study that done by using the available resources and relevant literature, related to the topic being discussed by the author. Books or journal articles related to topics were used as background reading to understand well about the problems of integrity and leadership, especially in the organization or company. This study finds out that the leader integrity is related to follower work role performance and that this effect is fully mediated through follower affective organizational commitment. 

  2. Feynman integral calculus

    CERN Document Server

    Smirnov, Vladimir A

    2006-01-01

    The problem of evaluating Feynman integrals over loop momenta has existed from the early days of perturbative quantum field theory. The goal of the book is to summarize those methods for evaluating Feynman integrals that have been developed over a span of more than fifty years. `Feynman Integral Calculus' characterizes the most powerful methods in a systematic way. It concentrates on the methods that have been employed recently for most sophisticated calculations and illustrates them with numerous examples, starting from very simple ones and progressing to nontrivial examples. It also shows how to choose adequate methods and combine them in a non-trivial way. This is a textbook version of the previous book (Evaluating Feynman integrals, STMP 211) of the author. Problems and solutions have been included, Appendix G has been added, more details have been presented, recent publications on evaluating Feynman integrals have been taken into account and the bibliography has been updated.

  3. Integral Politics as Process

    Directory of Open Access Journals (Sweden)

    Tom Atlee

    2010-03-01

    Full Text Available Using the definition proposed here, integral politics can be a process of integrating diverse perspectives into wholesome guidance for a community or society. Characteristics that follow from this definition have ramifications for understanding what such political processes involve. Politics becomes integral as it transcends partisan battle and nurtures generative conversation toward the common good. Problems, conflicts and crises become opportunities for new (or renewed social coherence. Conversational methodologies abound that can help citizen awareness temporarily expand during policy-making, thus helping raise society’s manifested developmental stage. Convening archetypal stakeholders or randomly selected citizens in conversations designed to engage the broader public enhances democratic legitimacy. With minimal issue- and candidate-advocacy, integral political leaders would develop society’s capacity to use integral conversational tools to improve its health, resilience, and collective intelligence. This both furthers and manifests evolution becoming conscious of itself.

  4. Integrable Cosmological Potentials

    CERN Document Server

    Sokolov, V V

    2016-01-01

    The problem of classification of the Einstein--Friedman cosmological Hamiltonians $H$ with a single scalar inflaton field $\\varphi$ that possess an additional integral of motion polynomial in momenta on the shell of the Friedman constraint $H=0$ is considered. Necessary and sufficient conditions for the existence of first, second, and third degree integrals are derived. These conditions have the form of ODEs for the cosmological potential $V(\\varphi)$. In the case of linear and quadratic integrals we find general solutions of the ODEs and construct the corresponding integrals explicitly. A new wide class of Hamiltonians that possess a cubic integral is derived. The corresponding potentials are represented in a parametric form in terms of the associated Legendre functions. Six families of special elementary solutions are described and sporadic superintegrable cases are discussed.

  5. Integrated silicon optoelectronics

    CERN Document Server

    Zimmermann, Horst

    2000-01-01

    'Integrated Silicon Optoelectronics'assembles optoelectronics and microelectronics The book concentrates on silicon as the major basis of modern semiconductor devices and circuits Starting from the basics of optical emission and absorption and from the device physics of photodetectors, the aspects of the integration of photodetectors in modern bipolar, CMOS, and BiCMOS technologies are discussed Detailed descriptions of fabrication technologies and applications of optoelectronic integrated circuits are included The book, furthermore, contains a review of the state of research on eagerly expected silicon light emitters In order to cover the topic of the book comprehensively, integrated waveguides, gratings, and optoelectronic power devices are included in addition Numerous elaborate illustrations promote an easy comprehension 'Integrated Silicon Optoelectronics'will be of value to engineers, physicists, and scientists in industry and at universities The book is also recommendable for graduate students speciali...

  6. Integrated terahertz optoelectronics

    Science.gov (United States)

    Liang, Guozhen; Wang, Qi Jie

    2016-11-01

    Currently, terahertz (THz) optical systems are based on bulky free-space optics. This is due to the lack of a common platform onto which different THz components, e.g., source, waveguide, modulator and detector, can be monolithically integrated. With the development of THz quantum cascade laser (QCL), it has been realized that the QCL chip may be such a platform for integrated THz photonics. Here, we report our recent works where the THz QCL is integrated with passive or optoelectronic components. They are: 1) integrated graphene modulator with THz QCL achieving 100% modulation depth and fast speed; 2) phase-locked THz QCL with integrated plasmonic waveguide and subwavelength antennas realizing dynamically widely tunable polarizations.

  7. Electromechanical integrated magnetic gear

    Directory of Open Access Journals (Sweden)

    Xiu-hong Hao

    2016-06-01

    Full Text Available This study proposes a new type of magnetic gear, namely, the electromechanical integrated magnetic gear, that integrates the traditional field-modulated magnetic gear, drive, and control. The topology and operating principle of the electromechanical integrated magnetic gear are described in detail in this article, and the constraints of parameter design and speed ratio of electromechanical integrated magnetic gear are presented. Moreover, magnetic field distribution is analyzed with the finite element method. Subsequently, the harmonics of the magnetic field and the electromagnetic torque are calculated. The static torques on all the components are exhibited by finite element method and torque test. The effects of the design parameters on the torques and the torque densities are discussed, and the results show that electromechanical integrated magnetic gear has a high speed ratio and can generate a high torque at low speed. The maximum torques are affected by air-gap thickness and other parameters.

  8. Integrable cosmological potentials

    Science.gov (United States)

    Sokolov, V. V.; Sorin, A. S.

    2017-05-01

    The problem of classification of the Einstein-Friedman cosmological Hamiltonians H with a single scalar inflaton field φ, which possess an additional integral of motion polynomial in momenta on the shell of the Friedman constraint H=0 , is considered. Necessary and sufficient conditions for the existence of the first-, second- and third-degree integrals are derived. These conditions have the form of ODEs for the cosmological potential V(φ) . In the case of linear and quadratic integrals we find general solutions of the ODEs and construct the corresponding integrals explicitly. A new wide class of Hamiltonians that possess a cubic integral is derived. The corresponding potentials are represented in parametric form in terms of the associated Legendre functions. Six families of special elementary solutions are described, and sporadic superintegrable cases are discussed.

  9. Conditional generalized analytic Feynman integrals and a generalized integral equation

    OpenAIRE

    Seung Jun Chang; Soon Ja Kang; David Skoug

    2000-01-01

    We use a generalized Brownian motion process to define a generalized Feynman integral and a conditional generalized Feynman integral. We then establish the existence of these integrals for various functionals. Finally we use the conditional generalized Feynman integral to derive a Schrödinger integral equation.

  10. Integrated assessment briefs

    Energy Technology Data Exchange (ETDEWEB)

    NONE

    1995-04-01

    Integrated assessment can be used to evaluate and clarify resource management policy options and outcomes for decision makers. The defining characteristics of integrated assessment are (1) focus on providing information and analysis that can be understood and used by decision makers rather than for merely advancing understanding and (2) its multidisciplinary approach, using methods, styles of study, and considerations from a broader variety of technical areas than would typically characterize studies produced from a single disciplinary standpoint. Integrated assessment may combine scientific, social, economic, health, and environmental data and models. Integrated assessment requires bridging the gap between science and policy considerations. Because not everything can be valued using a single metric, such as a dollar value, the integrated assessment process also involves evaluating trade-offs among dissimilar attributes. Scientists at Oak Ridge National Laboratory (ORNL) recognized the importance and value of multidisciplinary approaches to solving environmental problems early on and have pioneered the development of tools and methods for integrated assessment over the past three decades. Major examples of ORNL`s experience in the development of its capabilities for integrated assessment are given.

  11. SQL Server Integration Services

    CERN Document Server

    Hamilton, Bill

    2007-01-01

    SQL Server 2005 Integration Services (SSIS) lets you build high-performance data integration solutions. SSIS solutions wrap sophisticated workflows around tasks that extract, transform, and load (ETL) data from and to a wide variety of data sources. This Short Cut begins with an overview of key SSIS concepts, capabilities, standard workflow and ETL elements, the development environment, execution, deployment, and migration from Data Transformation Services (DTS). Next, you'll see how to apply the concepts you've learned through hands-on examples of common integration scenarios. Once you've

  12. The Integration Paradox

    Science.gov (United States)

    Verkuyten, Maykel

    2016-01-01

    The integration paradox refers to the phenomenon of the more highly educated and structurally integrated immigrants turning away from the host society, rather than becoming more oriented toward it. This article provides an overview of the empirical evidence documenting this paradox in the Netherlands. In addition, the theoretical arguments and the available findings about the social psychological processes involved in this paradox are considered. The existing evidence for the integration paradox and what might explain it form the basis for making suggestion for future theoretical work and empirical research, and for discussing possible policy implications. PMID:27152028

  13. Integrated microwave photonics

    CERN Document Server

    Marpaung, David; Heideman, Rene; Leinse, Arne; Sales, Salvador; Capmany, Jose

    2012-01-01

    Microwave photonics (MWP) is an emerging field in which radio frequency (RF) signals are generated, distributed, processed and analyzed using the strength of photonic techniques. It is a technology that enables various functionalities which are not feasible to achieve only in the microwave domain. A particular aspect that recently gains significant interests is the use of photonic integrated circuit (PIC) technology in the MWP field for enhanced functionalities and robustness as well as the reduction of size, weight, cost and power consumption. This article reviews the recent advances in this emerging field which is dubbed as integrated microwave photonics. Key integrated MWP technologies are reviewed and the prospective of the field is discussed.

  14. Evaluating Feynman integrals

    CERN Document Server

    Smirnov, Vladimir A

    2004-01-01

    The problem of evaluating Feynman integrals over loop momenta has existed from the early days of perturbative quantum field theory. Although a great variety of methods for evaluating Feynman integrals has been developed over a span of more than fifty years, this book is a first attempt to summarize them. 'Evaluating Feynman Integrals' characterizes the most powerful methods, in particular those used for recent, quite sophisticated calculations, and then illustrates them with numerous examples, starting from very simple ones and progressing to nontrivial examples.

  15. Integrity, Concept of

    DEFF Research Database (Denmark)

    Rendtorff, Jacob Dahl

    2015-01-01

    Integrity can be defined in the following sense: Integrity accounts for the inviolability of the human being. Although originally a virtue of uncorrupted character, expressing uprightness, honesty, and good intentions, it has, like dignity, been universalized as a quality of the person as such. T...... own life and illness. Integrity is the most important principle for the creation of trust between physician and patient, because it demands that the physician listens to the patient telling the story about his or her life and illness....

  16. Integral Method for Gratings

    CERN Document Server

    Maystre, Daniel

    2014-01-01

    The chapter contains a detailed presentation of the surface integral theory for modelling light diffraction by surface-relief diffraction gratings having a one-dimensional periodicity. Several different approaches are presented, leading either to a single integral equation, or to a system of coupled integral equations. Special attention is paid to the singularities of the kernels, and to different techniques to accelerate the convergence of the numerical computations. The theory is applied to gratings having different profiles with or without edges, to real metal and dielectrics, and to perfectly conducting substrates.

  17. Integrals of Bessel functions

    CERN Document Server

    Luke, Yudell L

    2014-01-01

    Integrals of Bessel Functions concerns definite and indefinite integrals, the evaluation of which is necessary to numerous applied problems. A massive compendium of useful information, this volume represents a resource for applied mathematicians in many areas of academia and industry as well as an excellent text for advanced undergraduates and graduate students of mathematics.Starting with an extensive introductory chapter on basic formulas, the treatment advances to indefinite integrals, examining them in terms of Lommel and Bessel functions. Subsequent chapters explore airy functions, incomp

  18. Approximate calculation of integrals

    CERN Document Server

    Krylov, V I

    2006-01-01

    A systematic introduction to the principal ideas and results of the contemporary theory of approximate integration, this volume approaches its subject from the viewpoint of functional analysis. In addition, it offers a useful reference for practical computations. Its primary focus lies in the problem of approximate integration of functions of a single variable, rather than the more difficult problem of approximate integration of functions of more than one variable.The three-part treatment begins with concepts and theorems encountered in the theory of quadrature. The second part is devoted to t

  19. Services for data integration

    Directory of Open Access Journals (Sweden)

    Catharina Riedemann

    2003-02-01

    Full Text Available The fact that many decisions need a combination of information sources makes easy integration of geospatial data an important data usability issue. Our vision is to achieve automated just-in-time integration. As a foundation, we present a system architecture with distributed data and services. Existing and evolving standards and technologies fitting into this architecture are presented along with their scope and shortcomings. A major point is the appropriate definition of data and operation semantics. Further research is needed here to make the automatic formation of service chains for data integration possible.

  20. Principles of data integration

    CERN Document Server

    Doan, AnHai; Ives, Zachary

    2012-01-01

    How do you approach answering queries when your data is stored in multiple databases that were designed independently by different people? This is first comprehensive book on data integration and is written by three of the most respected experts in the field. This book provides an extensive introduction to the theory and concepts underlying today's data integration techniques, with detailed, instruction for their application using concrete examples throughout to explain the concepts. Data integration is the problem of answering queries that span multiple data sources (e.g., databases, web

  1. Social integration i arbejdslivet

    DEFF Research Database (Denmark)

    Nielsen, Kjeld; Christensen, Allan

    2002-01-01

    The study reported in this article is based on a combination of methods related to working environment and to organisational culture. The combination is aimed at studying the extent and meaning of the social integration of the employees in an institution for handicapped adults. It is the conclusion...... of the study that social integration depends on working environment conditions as well as cultural conditions. The social integration again is crucial for the way in which employees perceive the daily work situation and indirectly also for the well-being of the clients of the institution....

  2. MOS integrated circuit design

    CERN Document Server

    Wolfendale, E

    2013-01-01

    MOS Integral Circuit Design aims to help in the design of integrated circuits, especially large-scale ones, using MOS Technology through teaching of techniques, practical applications, and examples. The book covers topics such as design equation and process parameters; MOS static and dynamic circuits; logic design techniques, system partitioning, and layout techniques. Also featured are computer aids such as logic simulation and mask layout, as well as examples on simple MOS design. The text is recommended for electrical engineers who would like to know how to use MOS for integral circuit desi

  3. Three dimensional system integration

    CERN Document Server

    Papanikolaou, Antonis; Radojcic, Riko

    2010-01-01

    Three-dimensional (3D) integrated circuit (IC) stacking is the next big step in electronic system integration. It enables packing more functionality, as well as integration of heterogeneous materials, devices, and signals, in the same space (volume). This results in consumer electronics (e.g., mobile, handheld devices) which can run more powerful applications, such as full-length movies and 3D games, with longer battery life. This technology is so promising that it is expected to be a mainstream technology a few years from now, less than 10-15 years from its original conception. To achieve thi

  4. GMRES and integral operators

    Energy Technology Data Exchange (ETDEWEB)

    Kelley, C.T.; Xue, Z.Q. [North Carolina State Univ., Raleigh, NC (United States)

    1994-12-31

    Many discretizations of integral equations and compact fixed point problems are collectively compact and strongly convergent in spaces of continuous functions. These properties not only lead to stable and convergent approximations but also can be used in the construction of fast multilevel algorithms. Recently the GMRES algorithm has become a standard coarse mesh solver. The purpose of this paper is to show how the special properties of integral operators and their approximations are reflected in the performance of the GMRES iteration and how these properties can be used to strengthen the norm in which convergence takes place. The authors illustrate these ideas with composite Gauss rules for integral equations on the unit interval.

  5. PEV Integration with Renewables (Presentation)

    Energy Technology Data Exchange (ETDEWEB)

    Markel, T.

    2014-06-18

    This presentation discusses current research at NREL on integrating plug-in electric vehicles with the grid and using renewable energy to charge the grid. The Electric Vehicle Grid Integration (EVGI) and Integrated Network Testbed for Energy Grid Research and Technology Experimentation (INTEGRATE) are addressing the opportunities and technical requirements for vehicle grid integration that will increase marketability and lead to greater petroleum reduction.

  6. Integrated Health Management Definitions

    Data.gov (United States)

    National Aeronautics and Space Administration — The Joint Army Navy NASA Air Force Modeling and Simulation Subcommittee's Integrated Health Management panel was started about 6 years ago to help foster...

  7. Integrated Reporting Information System -

    Data.gov (United States)

    Department of Transportation — The Integrated Reporting Information System (IRIS) is a flexible and scalable web-based system that supports post operational analysis and evaluation of the National...

  8. Financial Integrity Benchmarks

    Data.gov (United States)

    City of Jackson, Mississippi — This data compiles standard financial integrity benchmarks that allow the City to measure its financial standing. It measure the City's debt ratio and bond ratings....

  9. Wellbore Integrity Network

    Energy Technology Data Exchange (ETDEWEB)

    Carey, James W. [Los Alamos National Laboratory; Bachu, Stefan [Alberta Innovates

    2012-06-21

    In this presentation, we review the current state of knowledge on wellbore integrity as developed in the IEA Greenhouse Gas Programme's Wellbore Integrity Network. Wells are one of the primary risks to the successful implementation of CO{sub 2} storage programs. Experimental studies show that wellbore materials react with CO{sub 2} (carbonation of cement and corrosion of steel) but the impact on zonal isolation is unclear. Field studies of wells in CO{sub 2}-bearing fields show that CO{sub 2} does migrate external to casing. However, rates and amounts of CO{sub 2} have not been quantified. At the decade time scale, wellbore integrity is driven by construction quality and geomechanical processes. Over longer time-scales (> 100 years), chemical processes (cement degradation and corrosion) become more important, but competing geomechanical processes may preserve wellbore integrity.

  10. Integration, measure and probability

    CERN Document Server

    Pitt, H R

    2012-01-01

    Introductory treatment develops the theory of integration in a general context, making it applicable to other branches of analysis. More specialized topics include convergence theorems and random sequences and functions. 1963 edition.

  11. Integrated route analysis

    National Research Council Canada - National Science Library

    1981-01-01

    The integrated route analysis provides a data base for the second phase of the Arctic Pilot Project, the selection of a shipping corridor over which LNG icebreaking carriers will transport liquified...

  12. Integrating Forensic Science.

    Science.gov (United States)

    Funkhouser, John; Deslich, Barbara J.

    2000-01-01

    Explains the implementation of forensic science in an integrated curriculum and discusses the advantages of this approach. Lists the forensic science course syllabi studied in three high schools. Discusses the unit on polymers in detail. (YDS)

  13. State Program Integrity Reviews

    Data.gov (United States)

    U.S. Department of Health & Human Services — State program integrity reviews play a critical role in how CMS provides effective support and assistance to states in their efforts to combat provider fraud and...

  14. Advances in integrated optics

    CERN Document Server

    Chester, A; Bertolotti, M

    1994-01-01

    This volwne contains the Proceedings of a two-week summer conference titled "Advances in Integrated Optics" held June 1-9, 1993, in Erice, Sicily. This was the 18th annual course organized by the International School of Quantum Electronics, under the auspices of the "Ettore Majorana" Centre for Scientific Culture. The term Integrated Optics signifies guided-wave optical circuits consisting of two or more devices on a single substrate. Since its inception in the late 1960's, Integrated Optics has evolved from a specialized research topic into a broad field of work, ranging from basic research through commercial applications. Today many devices are available on market while a big effort is devolved to research on integrated nonlinear optical devices. This conference was organized to provide a comprehensive survey of the frontiers of this technology, including fundamental concepts, nonlinear optical materials, devices both in the linear and nonlinear regimes, and selected applications. These Proceedings update a...

  15. Integrated Biophotonics with CYTOP

    Directory of Open Access Journals (Sweden)

    Björn Agnarsson

    2012-02-01

    Full Text Available We describe how the amorphous fluoropolymer CYTOP can be advantageously used as a waveguide cladding material in integrated optical circuits suitable for applications in integrated biophotonics. The unique refractive index of CYTOP (n = 1.34 enables the cladding material to be well index-matched to an optically probed sample solution. Furthermore, ultra-high index contrast waveguides can be fabricated, using conventional optical polymers as waveguide core materials, offering a route to large-scale integration of optical functions on a single chip. We discuss applications of this platform to evanescent-wave excitation fluorescence microscopy, passive and/or thermo-electrically-controlled on-chip light manipulation, on-chip light generation, and direct integration with microfluidic circuits through low-temperature bonding.

  16. Integrated Disposal Facility

    Data.gov (United States)

    Federal Laboratory Consortium — Located near the center of the 586-square-mile Hanford Site is the Integrated Disposal Facility, also known as the IDF.This facility is a landfill similar in concept...

  17. Integration a functional approach

    CERN Document Server

    Bichteler, Klaus

    1998-01-01

    This book covers Lebesgue integration and its generalizations from Daniell's point of view, modified by the use of seminorms. Integrating functions rather than measuring sets is posited as the main purpose of measure theory. From this point of view Lebesgue's integral can be had as a rather straightforward, even simplistic, extension of Riemann's integral; and its aims, definitions, and procedures can be motivated at an elementary level. The notion of measurability, for example, is suggested by Littlewood's observations rather than being conveyed authoritatively through definitions of (sigma)-algebras and good-cut-conditions, the latter of which are hard to justify and thus appear mysterious, even nettlesome, to the beginner. The approach taken provides the additional benefit of cutting the labor in half. The use of seminorms, ubiquitous in modern analysis, speeds things up even further. The book is intended for the reader who has some experience with proofs, a beginning graduate student for example. It might...

  18. Integrated Silicon Optoelectronics

    CERN Document Server

    Zimmermann, Horst K

    2010-01-01

    Integrated Silicon Optoelectronics synthesizes topics from optoelectronics and microelectronics. The book concentrates on silicon as the major base of modern semiconductor devices and circuits. Starting from the basics of optical emission and absorption, as well as from the device physics of photodetectors, the aspects of the integration of photodetectors in modern bipolar, CMOS, and BiCMOS technologies are discussed. Detailed descriptions of fabrication technologies and applications of optoelectronic integrated circuits are included. The book, furthermore, contains a review of the newest state of research on eagerly anticipated silicon light emitters. In order to cover the topics comprehensively, also included are integrated waveguides, gratings, and optoelectronic power devices. Numerous elaborate illustrations facilitate and enhance comprehension. This extended edition will be of value to engineers, physicists, and scientists in industry and at universities. The book is also recommended to graduate student...

  19. Stochastic Lie group integrators

    CERN Document Server

    Malham, Simon J A

    2007-01-01

    We present Lie group integrators for nonlinear stochastic differential equations with non-commutative vector fields whose solution evolves on a smooth finite dimensional manifold. Given a Lie group action that generates transport along the manifold, we pull back the stochastic flow on the manifold to the Lie group via the action, and subsequently pull back the flow to the corresponding Lie algebra via the exponential map. We construct an approximation to the stochastic flow in the Lie algebra via closed operations and then push back to the Lie group and then to the manifold, thus ensuring our approximation lies in the manifold. We call such schemes stochastic Munthe-Kaas methods after their deterministic counterparts. We also present stochastic Lie group integration schemes based on Castell--Gaines methods. These involve using an underlying ordinary differential integrator to approximate the flow generated by a truncated stochastic exponential Lie series. They become stochastic Lie group integrator schemes if...

  20. Integrated library systems.

    Science.gov (United States)

    Goldstein, C M

    1983-07-01

    The development of integrated library systems is discussed. The four major discussion points are (1) initial efforts; (2) network resources; (3) minicomputer-based systems; and (4) beyond library automation. Four existing systems are cited as examples of current systems.

  1. INTEGRATED RENEWAL PROCESS

    Directory of Open Access Journals (Sweden)

    Suyono .

    2012-07-01

    Full Text Available The marginal distribution of integrated renewal process is derived in this paper. Our approach is based on the theory of point processes, especially Poisson point processes. The results are presented in the form of Laplace transforms.

  2. Integrating Forensic Science.

    Science.gov (United States)

    Funkhouser, John; Deslich, Barbara J.

    2000-01-01

    Explains the implementation of forensic science in an integrated curriculum and discusses the advantages of this approach. Lists the forensic science course syllabi studied in three high schools. Discusses the unit on polymers in detail. (YDS)

  3. Integrated Microfluidic Reactors.

    Science.gov (United States)

    Lin, Wei-Yu; Wang, Yanju; Wang, Shutao; Tseng, Hsian-Rong

    2009-12-01

    Microfluidic reactors exhibit intrinsic advantages of reduced chemical consumption, safety, high surface-area-to-volume ratios, and improved control over mass and heat transfer superior to the macroscopic reaction setting. In contract to a continuous-flow microfluidic system composed of only a microchannel network, an integrated microfluidic system represents a scalable integration of a microchannel network with functional microfluidic modules, thus enabling the execution and automation of complicated chemical reactions in a single device. In this review, we summarize recent progresses on the development of integrated microfluidics-based chemical reactors for (i) parallel screening of in situ click chemistry libraries, (ii) multistep synthesis of radiolabeled imaging probes for positron emission tomography (PET), (iii) sequential preparation of individually addressable conducting polymer nanowire (CPNW), and (iv) solid-phase synthesis of DNA oligonucleotides. These proof-of-principle demonstrations validate the feasibility and set a solid foundation for exploring a broad application of the integrated microfluidic system.

  4. Managing for Organizational Integrity.

    Science.gov (United States)

    Paine, Lynn Sharp

    1994-01-01

    Compliance-based ethics programs focus on prevention, detection, and punishment. Companies should adopt an integrity-based approach to ethics management that combines a concern for the law with an emphasis on managerial responsibility for ethical behavior. (JOW)

  5. Complementary and Integrative Medicine

    Science.gov (United States)

    ... medical treatments that are not part of mainstream medicine. When you are using these types of care, it may be called complementary, integrative, or alternative medicine. Complementary medicine is used together with mainstream medical ...

  6. Managing for Organizational Integrity.

    Science.gov (United States)

    Paine, Lynn Sharp

    1994-01-01

    Compliance-based ethics programs focus on prevention, detection, and punishment. Companies should adopt an integrity-based approach to ethics management that combines a concern for the law with an emphasis on managerial responsibility for ethical behavior. (JOW)

  7. Systems Integration Fact Sheet

    Energy Technology Data Exchange (ETDEWEB)

    None

    2016-06-01

    This fact sheet is an overview of the Systems Integration subprogram at the U.S. Department of Energy SunShot Initiative. The Systems Integration subprogram enables the widespread deployment of safe, reliable, and cost-effective solar energy technologies by addressing the associated technical and non-technical challenges. These include timely and cost-effective interconnection procedures, optimal system planning, accurate prediction of solar resources, monitoring and control of solar power, maintaining grid reliability and stability, and many more. To address the challenges associated with interconnecting and integrating hundreds of gigawatts of solar power onto the electricity grid, the Systems Integration program funds research, development, and demonstration projects in four broad, interrelated focus areas: grid performance and reliability, dispatchability, power electronics, and communications.

  8. Integrated inventory information system

    Digital Repository Service at National Institute of Oceanography (India)

    Sarupria, J.S.; Kunte, P.D.

    The nature of oceanographic data and the management of inventory level information are described in Integrated Inventory Information System (IIIS). It is shown how a ROSCOPO (report on observations/samples collected during oceanographic programme...

  9. 2014 SRP Integration Transcript

    Science.gov (United States)

    Steinberg, Susan

    2014-01-01

    HRP's mission is to reduce the risks to human health and performance during long-duration spaceflight. The HRP Integrated Research Plan (IRP) contains the research plans for the 32 risks that require research to characterize and mitigate. From its inception the "integrate" aspect of the IRP has denoted the integrated nature of risks to human health and performance. Even though each risk in the IRP has its own research plan and is tracked separately, the interrelated nature of health and performance requires that they be addressed in an integrative or holistic fashion so that the connectedness of physiological systems within the human body and the integrated response to spaceflight can be addressed. Common characteristics of the spaceflight environment include altered gravity, atmospheres, and light/dark cycles; space radiation; isolation; noise; and periods of high or low workload. Long-term exposure to this unique environment produces a suite of physiological effects such as stress; vision, neurocognitive, and anthropometric changes; circadian misalignment; fluid shifts; cardiovascular deconditioning; immune dysregulation; and altered nutritional requirements. Expanding cross-disciplinary integrative approaches that synthesize concepts or data from two or more disciplines would improve the identification and characterization risk factors, and enable the development of countermeasures relevant to multiple risks. Cross-disciplinary approaches might also help to illuminate problem areas that may arise when a countermeasure adversely impacts risks other than those which it was developed to mitigate, or to identify groupings of physiological changes that are likely to occur that may impact the overall risk posture. In 2014 HRP embarked on a pilot study that combined four SRPs (and 12 HRP risks) - Behavioral Health, Sensorimotor, Cardiovascular, and Bone/Muscle - specifically to discuss cross-disciplinary integration. The points outlined below were suggested to seed the

  10. Function integrated track system

    OpenAIRE

    Hohnecker, Eberhard

    2010-01-01

    The paper discusses a function integrated track system that focuses on the reduction of acoustic emissions from railway lines. It is shown that the combination of an embedded rail system (ERS), a sound absorbing track surface, and an integrated mini sound barrier has significant acoustic advantages compared to a standard ballast superstructure. The acoustic advantages of an embedded rail system are particularly pronounced in the case of railway bridges. Finally, it is shown that a...

  11. Integrating corpora and dictionaries

    DEFF Research Database (Denmark)

    2012-01-01

    In this paper, we will discuss different possibilities for integration of corpus data with dictionary data, mainly seen from a lexicographic point of view and in a sign language context. For about 25 years a text corpus has been considered a useful, if not necessary tool for editing dictionaries ...... interface, and, finally, we briefly outline the future perspectives of integrated sign language corpus-dictionary interfaces....

  12. IDC Integrated Master Plan.

    Energy Technology Data Exchange (ETDEWEB)

    Clifford, David J.; Harris, James M.

    2014-12-01

    This is the IDC Re-Engineering Phase 2 project Integrated Master Plan (IMP). The IMP presents the major accomplishments planned over time to re-engineer the IDC system. The IMP and the associate Integrated Master Schedule (IMS) are used for planning, scheduling, executing, and tracking the project technical work efforts. REVISIONS Version Date Author/Team Revision Description Authorized by V1.0 12/2014 IDC Re- engineering Project Team Initial delivery M. Harris

  13. Holomorphic matrix integrals

    CERN Document Server

    Felder, G; Felder, Giovanni; Riser, Roman

    2004-01-01

    We study a class of holomorphic matrix models. The integrals are taken over middle dimensional cycles in the space of complex square matrices. As the size of the matrices tends to infinity, the distribution of eigenvalues is given by a measure with support on a collection of arcs in the complex planes. We show that the arcs are level sets of the imaginary part of a hyperelliptic integral connecting branch points.

  14. Fakta om integration

    DEFF Research Database (Denmark)

    Frederiksen, Hanne Winther; Nørredam, Marie

    Afsnit i Social- og Integrationsministeriets årlige publikation "Fakta om integration". Bygger på et litteraturreview foretaget i 2012 i samarbejde med Forskningscenter for Migration, Etnicitet og Sundhed (MESU) på opdrag af Social- og Integrationsministeriet.......Afsnit i Social- og Integrationsministeriets årlige publikation "Fakta om integration". Bygger på et litteraturreview foretaget i 2012 i samarbejde med Forskningscenter for Migration, Etnicitet og Sundhed (MESU) på opdrag af Social- og Integrationsministeriet....

  15. The INTEGRAL Universe

    Science.gov (United States)

    Schoenfelder, V.; Lichti, G.; Winkler, C.

    2004-10-01

    The 5th INTEGRAL workshop "The INTEGRAL Universe" was held at the premises of the Bayerische Akademie der Wissenschaften in Munich, Germany, from February 16 - 20, 2004. The workshop was attended by over 230 scientists from all over the world. The aim of the workshop was twofold: to bring the scientists together who are using data from the INTEGRAL mission and to present first results which were obtained by the four INTEGRAL instruments during the first 18 months of operation. It was for the first time after launch that INTEGRAL results were presented and discussed in a broader scientific context and compared with results obtained with other instruments at different wavelengths (especially in the optical, infrared and radio). Naturally the results concentrated mainly on the hard X-ray regime since photons are plentiful and the sensitivity of the INTEGRAL instruments is best there. But also very interesting early results at low-energy gamma-rays, especially on gamma-ray lines, were presented. Because of INTEGRAL?s ability to measure and localize gamma-ray bursts quickly, this topic also drew a lot of attention and stimulating results were presented. The following list emphasizes the scientific importance of the topics which were covered by 6 invited, 1 special and 64 contributed talks as well as about 180 posters: + Nucleosynthesis and gamma-ray line spectroscopy + Pulsars + X-ray binaries (with neutron stars and black holes) + Interstellar continuum emission + AGN (Seyferts and Blazars) + Clusters of galaxies + Cosmic background radiation + Gamma-ray bursts + Unidentified gamma-ray sources + Solar flare gamma-rays + Data analysis (posters only) * Future instruments and missions (posters only)

  16. NPS AUV Integrated Simulator

    Science.gov (United States)

    1992-03-01

    147 3. GRAPHIC OBJECT MODEI’QUSING OBJECTFILE FORMAT (cIF)...................... ........... 149. APPENDIX -C. NPS, AUV SONAR CLASSIFICATION SYSTEM...Monterey Bay .. 15 Figure 2.8 Graphics simulation for NPS AUV sonar visualization .......... 15’ Figure 3.1 Integrated simulator network physical...3.11 Integrated simulation display of AUV minefield searh ........ 39 Figure4.1 NPS AUV sonar beam profiles in the NPS pool .......... 43 Figure 42 NPS

  17. HETEROGENEOUS INTEGRATION TECHNOLOGY

    Science.gov (United States)

    2017-08-24

    in- package integration. It involves the integration of circuits from fully processed wafers using micro- bumps and TSVs. There are 3 basic kinds of... bumping ” and “Cu-to-Cu” categories. The first approach involves the fabrication of micro- bumps on both sides of the thinned wafers with TSVs, and...interfacing wafers with bumps aligned. The application of pressure and heat makes permanent contact between bumps . A thin adhesive layer can be used between

  18. The Integrated Renovation Process

    DEFF Research Database (Denmark)

    Galiotto, Nicolas; Heiselberg, Per; Knudstrup, Mary-Ann

    The Integrated Renovation Process (IRP) is a user customized methodology based on judiciously selected constructivist and interactive multi-criteria decision making methods (Galiotto, Heiselberg, & Knudstrup, 2014 (expected)). When applied for home renovation, the Integrated Renovation Process...... for the quantitative analyses and the generation of the renovation scenarios so they get more time for the cost optimisation and the qualitative analysis of the homeowners’ needs, wishes and behaviours....

  19. Unified description of seagull cancellations and infrared finiteness of gluon propagators

    CERN Document Server

    Aguilar, A C; Figueiredo, C T; Papavassiliou, J

    2016-01-01

    We present a generalized theoretical framework for dealing with the important issue of dynamical mass generation in Yang-Mills theories, and, in particular, with the infrared finiteness of the gluon propagators, observed in a multitude of recent lattice simulations. Our analysis is manifestly gauge-invariant, in the sense that it preserves the transversality of the gluon self-energy, and gauge-independent, given that the conclusions do not depend on the choice of the gauge-fixing parameter within the linear covariant gauges. The central construction relies crucially on the subtle interplay between the Abelian Ward identities satisfied by the nonperturbative vertices and a special integral identity that enforces a vast number of 'seagull cancellations' among the one- and two-loop dressed diagrams of the gluon Schwinger-Dyson equation. The key result of these considerations is that the gluon propagator remains rigorously massless, provided that the vertices do not contain (dynamical) massless poles. When such p...

  20. APPROACHES TO PUBLIC INTEGRITY

    Directory of Open Access Journals (Sweden)

    Simona-Roxana ULMAN

    2015-08-01

    Full Text Available Both concepts, integrity and public integrity, are always asked qualities in the social and economic environment, but they are never well defined. In this context, finding precise definitions and offering an ample explanation of the concepts are desired and useful for both economic theoretical and practical levels and become the aim of the present paper. Without a good understanding of a concept, no one is capable to attain it. In this context, it is impossible to ask for a public sector of integrity if both public actors and the citizens do not know what it really means. Therefore, the public actors first have to understand what integrity really supposes, and, then, to be capable to respect its principles. Taking into consideration the effects of public integrity or, on its opposite, of the divergence from it, especially represented by the phenomenon of corruption, on the economy at the macro, but also, on the micro level, public integrity in itself becomes a real economic problem that is aimed to be extensively analyzed through our interdisciplinary approach.