A Derivative of the Gerasimov-Drell-Hearn Sum Rule
Vladimir Pascalutsa; Barry Holstein; Marc Vanderhaeghen
2004-08-01
We derive a sum rule which establishes a linear relation between a particle's anomalous magnetic moment and a quantity connected to the photoabsorption cross-section. This quantity cannot be measured directly. However, it can be computed within a given theory. As an example, we demonstrate validity of the sum rule in QED at tree level---the renowned Schwinger's correction to the anomalous magnetic moment is readily reproduced. In the case of the strong interactions, we also consider the calculation of the nucleon magnetic moment within chiral theories.
A derivative of the Gerasimov Drell Hearn sum rule
Pascalutsa, Vladimir; Holstein, Barry R.; Vanderhaeghen, Marc
2004-10-01
We derive a sum rule which establishes a linear relation between a particle's anomalous magnetic moment and a quantity connected to the photoabsorption cross section. This quantity cannot be measured directly. However, it can be computed within a given theory. As an example, we demonstrate validity of the sum rule in QED at tree level-the renowned Schwinger's correction to the anomalous magnetic moment is readily reproduced. In the case of the strong interactions, we also consider the calculation of the nucleon magnetic moment within chiral theories.
A derivative of the Gerasimov-Drell-Hearn sum rule
Pascalutsa, Vladimir [Theory Group, JLab, 12000 Jefferson Ave, Newport News, VA 23606 (United States) and Department of Physics, College of William and Mary, Williamsburg, VA 23188 (United States)]. E-mail: vlad@jlab.org; Holstein, Barry R. [Theory Group, JLab, 12000 Jefferson Ave, Newport News, VA 23606 (United States) and Department of Physics-LGRT, University of Massachusetts, Amherst, MA 01003 (United States)]. E-mail: holstein@physics.umas.edu; Vanderhaeghen, Marc [Theory Group, JLab, 12000 Jefferson Ave, Newport News, VA 23606 (United States) and Department of Physics, College of William and Mary, Williamsburg, VA 23188 (United States)]. E-mail: marcvdh@jlab.org
2004-10-28
We derive a sum rule which establishes a linear relation between a particle's anomalous magnetic moment and a quantity connected to the photoabsorption cross section. This quantity cannot be measured directly. However, it can be computed within a given theory. As an example, we demonstrate validity of the sum rule in QED at tree level-the renowned Schwinger's correction to the anomalous magnetic moment is readily reproduced. In the case of the strong interactions, we also consider the calculation of the nucleon magnetic moment within chiral theories.
Gerasimov-Drell-Hearn Sum Rule and the Discrepancy between the New CLAS and SAPHIR Data
Mart, T
2008-01-01
Contribution of the K^+\\Lambda channel to the Gerasimov-Drell-Hearn (GDH) sum rule has been calculated by using the models that fit the recent SAPHIR or CLAS differential cross section data. It is shown that the two data sets yield quite different contributions. Contribution of this channel to the forward spin polarizability of the proton has been also calculated. It is also shown that the inclusion of the recent CLAS C_x and C_z data in the fitting data base does not significantly change the result of the present calculation. Results of the fit, however, reveal the role of the S_{11}(1650), P_{11}(1710), P_{13}(1720), and P_{13}(1900) resonances for the description of the C_x and C_z data. A brief discussion on the importance of these resonances is given. Measurements of the polarized total cross section \\sigma_{TT'} by the CLAS, LEPS, and MAMI collaborations are expected to verify this finding.
Lvov, A I; Drechsel, D; Scherer, S
1998-01-01
Photoproduction of $e^+e^-$ pairs at small angles is investigated as a tool to determine the functions $f_1$ and $f_2$ entering the real-photon forward Compton scattering amplitude. The method is based on an interference of the Bethe-Heitler and the virtual Compton scattering mechanisms, generating an azimuthal asymmetry in the $e^+$ versus $e^-$ yield. The general case of a circularly polarized beam and a longitudinally polarized target allows one to determine both the real and imaginary parts of $f_1$ as well as $f_2$. The imaginary part of $f_2$ requires target polarization only. We calculate cross sections and asymmetries of the reaction $p(\\gamma,e^+e^-)p$, estimate corrections and backgrounds, and propose suitable kinematical regions to perform the experiment. Our investigation shows that photoproduction of $e^+e^-$-pairs off the proton and light nuclei may serve as a rather sensitive test of the validity of the Gerasimov-Drell-Hearn sum rule.
Kominis, Ioannis
2001-01-31
This thesis presents the results of E-94010, an experiment at Thomas Jefferson National Accelerator Facility (TJNAF) designed to study the spin structure of the neutron at low momentum transfer, and to test the “extended” Gerasimov-Drell-Hearn (GDH) sum rule. The first experiment of its kind, it was performed in experimental Hall-A of TJNAF using a new polarized 3He facility. It has recently been shown that the GDH sum rule and the Bjorken sum rule are both special examples of a more general sum rule that applies to polarized electron scattering off nucleons. This generalized sum rule, due to Ji and Osborne, reduces to the GDH sum rule at Q2 = 0 and to the Bjorken sum rule at Q2 >> 1 GeV2. By studying the Q2 evolution of the extended GDH sum, one learns about the transition from quark-like behavior to hadronic-like behavior. We measured inclusive polarized cross sections by scattering high energy polarized electrons off the new TJNAF polarized 3He target with both longitudinal and transverse target orientations. The high density 3He target, based on optical pumping and spin exchange, was used as an effective neutron target. The target maintained a polarization of about 35% at beam currents as high as 151tA. We describe the precision 3He polarimetry leading to a systematic uncertainty of the target polarization of 4% (relative). A strained GaAs photocathode was utilized in the polarized electron gun, which provided an electron beam with a polarization of about 70%, known to 3% (relative). By using six different beam energies (between 0.86 and 5.06 GeV) and a fixed scattering angle of 15.5°, a wide kinematic coverage was achieved, with 0.02 GeV2< Q2 <1 GcV2 and 0.5 GeV< W < 2.5 GeV for the squared momentum transfer and invariant mass, respectively. From the measured cross sections we extract the 3He spin structure functions He and g1e Finally, we determine the extended GDH sum for the range 0.1 GeV2< Q2 <1 GeV2 for 3He and the neutron.
Djawotho, Pibero [College of William and Mary, Williamsburg, VA (United States)
2002-12-01
This dissertation presents results of experiment E94-010 performed at Jefferson Laboratory (simply known as JLab) in Hall A. The experiment aimed to measure the low Q^{2} evolution of the Gerasimov-Drell-Hearn (GDH) integral from Q^{2} = 0.1 to 0.9 GeV^{2}. The GDH sum rule at the real photon point provides an important test of Quantum Chromodynamics (QCD). The low Q^{2} evolution of the GDH integral contests various resonance models, Chiral Perturbation Theory ({chi} PT) and lattice QCD calculations, but more importantly, it helps us understand the transition between partonic and hadronic degrees of freedom. At high Q^{2}, beyond 1 GeV^{2}, the difference of the GDH integrals for the proton and the neutron is related to the Bjorken sum rule, another fundamental test of QCD. In addition, results of the measurements for the spin structure functions g_{1} and g_{2}, cross sections, and asymmetries are presented. E94-010 was the first experiment of its kind at JLab. It used a high-pressure, polarized ^{3}He target with a gas pressure of 10 atm and average target polarization of 35%. For the first time, the polarized electron source delivered an average beam polarization of 70% with a beam current of 15 micro A. The limit on the beam current was only imposed by the target. The experiment required six different beam energies from 0.86 to 5.1 GeV. This was the first time the accelerator ever reached 5.1 GeV. Both High-Resolution Spectrometers of Hall A, used in singles mode, were positioned at 15.5 ° each.
Deur, A
2000-10-01
This thesis presents an experimental study of the neutron (and {sup 3}He) spin structure with a particular emphasis in the resonance domain (experiment E94010 that took place in 1997 at Jefferson Lab (TJNAF or formerly CEBAF) in Virginia). A polarized {sup 3}He target was built in order to achieve this study since polarized {sup 3}He nuclei can be seen as polarized neutrons. This target allowed the measurement of the polarized absolute cross sections {sigma}{sub 1/2}(Q{sup 2}, {nu}) and {sigma}{sub 3/2}(Q{sup 2}, {nu}) from the inclusive reaction {sup {sup {yields}}{sup 3}He}({sup {yields}}e, e')X for incident beam energies ranging from 0.86 GeV to 5.07 GeV at a scattering angle of 15.5 deg. The Q{sup 2} evolution of the generalized Gerasimov-Drell-Hearn (GDH) integral on {sup 3}He and on neutron was measured from 0.1 GeV{sup 2} to 1.0 GeV{sup 2} in order to understand the transition between perturbative QCD and non-perturbative QCD. The integration domain in {nu} (the energy loss of the scattered electron) is from the pion threshold to about 2.5 GeV which covers both the resonance region and the Deep Inelastic Scattering. The high precision of our data constrains the models giving the Q{sup 2} evolution of the generalized GDH integral. The polarized quasi-elastic scattering was also measured. The cross section {sigma}{sup TT}(Q{sup 2}, {nu}) on {sup 3}He and the spin structure functions g{sub 1}{sup {sup 3}He}(Q{sup 2}, {nu}) and g{sub 2}{sup {sup 3}He}(Q{sup 2}, {nu}) are presented. These data are an indication that the higher-twists are small in our kinematics domain and that the Bloom-Gilman duality seems to hold for the polarized spin structure functions. (author)
The $Q^{2}$-dependence of the Generalised Gerasimov-Drell-Hearn Integral for the Proton
Airapetian, A; Akushevich, I V; Amarian, M; Arrington, J; Aschenauer, E C; Avakian, H; Avakian, R; Avetisian, A; Avetissian, E; Bailey, P; Bains, B; Baumgarten, C; Beckmann, M; Belostotskii, S; Bernreuther, S; Bianchi, N; Böttcher, Helmut B; Borisov, A; Bouwhuis, M; Brack, J; Brauksiepe, S; Brauniu, B; Brückner, W; Brüll, A; Budz, P; Bulten, H J; Capitani, G P; Carter, P; Chumney, P; Cisbani, E; Court, G R; Dalpiaz, P F; De Leo, R; De Nardo, L; De Sanctis, E; De Schepper, D; Devitsin, E G; De Witt-Huberts, P K A; Di Nezza, P; Dzhordzhadze, V; Düren, M; Dvoredsky, A P; Elbakian, G M; Ely, J; Fantoni, A; Feshchenko, A; Ferro-Luzziwad, M; Fiedler, K; Filippone, B W; Fischer, H; Fox, B; Franzl, J; Frullani, S; Gärber, Y; Garibaldi, F; Garutti, E; Gavrilov, G E; Karibian, V; Golendukhin, A; Graw, G; Grebenyuk, O; Green, P W; Greeniaus, L G; Gute, A; Haeberli, W; Hartig, M; Hasch, D; Heesbeen, D; Heinsius, F H; Henoch, M; Hertenberger, R; Hesselink, W H A; Hoffmann-Rothe, P; Hofman, G J; Holler, Y; Holto, R J; Hommez, B; Iarygin, G; Iodice, M; Izotov, A A; Jackson, H E; Jgoun, A; Jung, P; Kaiser, R; Kanesakaac, J; Kinney, E R; Kiselev, A; Kitching, P; Kobayashi, H; Koch, N; Königsmann, K C; Kolster, H; Korotkov, V A; Kotik, E; Kozlov, V; Krivokhizhin, V G; Kyle, G S; Lagamba, L; Laziev, A; Lenisa, P; Lindemann, T; Lorenzon, W; Makins, N C R; Martin, J W; Marukyan, H O; Masoli, F; McAndrew, M; McIlhany, K; McKeown, R D; Menden, F; Metzu, A; Meyners, N; Miklukho, O; Miller, C A; Milner, R; Mitsyn, V; Muccifora, V; Mussa, R; Nagaitsev, A P; Nappi, E; Naryshkin, Yu; Nass, A; Negodaeva, K; Nowak, Wolf-Dieter; O'Neill, T G; Openshaw, R; Ouyang, J; Owen, B R; Pate, S F; Potashov, S Yu; Potterveld, D H; Rakness, G; Rappoport, V; Redwine, R P; Reggiani, D; Reolon, A R; Ristinen, R; Rith, K; Robinson, D; Ruh, M; Ryckbosch, D; Sakemi, Y; Savin, I A; Scarlett, C; Schäfer, A; Schill, C; Schmidt, F; Schnell, G; Schulerf, K P; Schwind, A; Seibert, J; Seitz, B; Shibata, T A; Shin, T; Shutov, V B; Simani, C; Simon, A; Sinram, K; Steffens, E; Steijger, J J M; Stewart, J; Stösslein, U; Suetsugu, K; Sutter, M F; Tallini, H A; Taroian, S P; Terkulov, A R; Tessarin, S; Thomas, E; Tipton, B; Tytgat, M; Urciuoli, G M; Van den Brand, J F J; van der Steenhoven, G; Van de Vyver, R; Van Hunen, J J; Vetterli, Martin C; Vikhrov, V V; Vincter, M G; Visser, J; Volk, E; Weiskopf, C; Wendland, J; Wilbert, J; Wiseq, T; Yen, S; Yoneyama, S; Zohrabyan, H G
2000-01-01
The dependence on Q^2 (the negative square of the 4-momentum of the exchanged virtual photon) of the generalised Gerasimov-Drell-Hearn integral for the proton has been measured in the range 1.2 GeV^2 3 GeV^2, while both contributions are important at low Q^2. The total integral shows no significant deviation from a 1/Q^2 behaviour in the measured Q^2 range, and thus no sign of large effects due to either nucleon-resonance excitations or non-leading twist.
Spin Sum Rules and the Strong Coupling Constant at large distance.
Alexandre Deur
2009-07-01
We present recent results on the Bjorken and the generalized forward spin polarizability sum rules from Jefferson Lab Hall A and CLAS experiments, focusing on the low $Q^2$ part of the measurements. We then discuss the comparison of these results with Chiral Perturbation theory calculations. In the second part of this paper, we show how the Bjorken sum rule with its connection to the Gerasimov-Drell-Hearn sum, allows us to conveniently define an effective coupling for the strong force at all distances.
Hinchliffe, Ian; Hinchliffe, Ian; Kwiatkowski, Axel
1996-01-01
This review article discusses the experimental and theoretical status of various Parton Model sum rules. The basis of the sum rules in perturbative QCD is discussed. Their use in extracting the value of the strong coupling constant is evaluated and the failure of the naive version of some of these rules is assessed.
T. Frandsen, Mads; Masina, Isabella; Sannino, Francesco
2011-01-01
We introduce new sum rules allowing to determine universal properties of the unknown component of the cosmic rays and show how it can be used to predict the positron fraction at energies not yet explored by current experiments and to constrain specific models.......We introduce new sum rules allowing to determine universal properties of the unknown component of the cosmic rays and show how it can be used to predict the positron fraction at energies not yet explored by current experiments and to constrain specific models....
Adler, Stephen L
2009-01-01
The Adler sum rule states that the integral over energy of a difference of neutrino-nucleon and antineutrino-nucleon structure functions is a constant, independent of the four-momentum transfer squared. This constancy is a consequence of the local commutation relations of the time components of the hadronic weak current, which follow from the underlying quark structure of the standard model.
Fluctuations in classical sum rules.
Elton, John R; Lakshminarayan, Arul; Tomsovic, Steven
2010-10-01
Classical sum rules arise in a wide variety of physical contexts. Asymptotic expressions have been derived for many of these sum rules in the limit of long orbital period (or large action). Although sum-rule convergence may well be exponentially rapid for chaotic systems in a global phase-space sense with time, individual contributions to the sums may fluctuate with a width which diverges in time. Our interest is in the global convergence of sum rules as well as their local fluctuations. It turns out that a simple version of a lazy baker map gives an ideal system in which classical sum rules, their corrections, and their fluctuations can be worked out analytically. This is worked out in detail for the Hannay-Ozorio sum rule. In this particular case the rate of convergence of the sum rule is found to be governed by the Pollicott-Ruelle resonances, and both local and global boundaries for which the sum rule may converge are given. In addition, the width of the fluctuations is considered and worked out analytically, and it is shown to have an interesting dependence on the location of the region over which the sum rule is applied. It is also found that as the region of application is decreased in size the fluctuations grow. This suggests a way of controlling the length scale of the fluctuations by considering a time dependent phase-space volume, which for the lazy baker map decreases exponentially rapidly with time.
Dominguez, C. A.
2013-08-01
A general, and very basic introduction to QCD sum rules is presented, with emphasis on recent issues to be described at length in other papers in this issue. Collectively, these papers constitute the proceedings of the International Workshop on Determination of the Fundamental Parameters of QCD, Singapore, March 2013.
Sulkosky, Vincent [College of William and Mary, Williamsburg, VA (United States)
2007-08-01
Since the 1980's, the study of nucleon (proton or neutron) spin structure has been an active field both experimentally and theoretically. One of the primary goals of this work is to test our understanding of Quantum Chromodynamics (QCD), the fundamental theory of the strong interaction. In the high energy region of asymptotically free quarks, QCD has been verified. However, verifiable predictions in the low energy region are harder to obtain due to the complex interactions between the nucleon's constituents: quarks and gluons. In the non-pertubative regime, low-energy effective field theories such as chiral perturbation theory provide predictions for the spin structure functions in the form of sum rules. Spin-dependent sum rules such as the Gerasimov-Drell-Hearn (GDH) sum rule are important tools available to study nucleon spin structure. Originally derived for real photon absorption, the Gerasimov-Drell-Hearn (GDH) sum rule was first extended for virtual photon absorption in 1989. The extension of the sum rule provides a unique relation, valid at any momentum transfer ($Q^{2}$), that can be used to study the nucleon spin structure and make comparisons between theoretical predictions and experimental data. Experiment E97-110 was performed at the Thomas Jefferson National Accelerator Facility (Jefferson Lab) to examine the spin structure of the neutron and $^{3}$He. The Jefferson Lab longitudinally-polarized electron beam with incident energies between 1.1 and 4.4 GeV was scattered from a longitudinally or transversely polarized $^{3}$He gas target in the Hall A end station. Asymmetries and polarized cross-section differences were measured in the quasielastic and resonance regions to extract the spin structure functions $g_{1}(x,Q^{2})$ and $g_{2}(x,Q^{2})$ at low momentum transfers (0.02 $< Q^{2} <$ 0.3 GeV$^{2}$). The goal of the experiment was to perform a precise measurement of the $Q^{2}$ dependence of the extended GDH integral and of the moments of
The Orbital Angular Momentum Sum Rule
Aslan, Fatma; Burkardt, Matthias
2015-10-01
As an alternative to the Ji sum rule for the quark angular momentum, a sum rule for the quark orbital angular momentum, based on a twist-3 generalized parton distribution, has been suggested. We study the validity of this sum rule in the context of scalar Yukawa interactions as well as in QED for an electron.
Aspects of QCD current algebra on a null plane
Beane, S. R.; Hobbs, T. J.
2016-09-01
Consequences of QCD current algebra formulated on a light-like hyperplane are derived for the forward scattering of vector and axial-vector currents on an arbitrary hadronic target. It is shown that current algebra gives rise to a special class of sum rules that are direct consequences of the independent chiral symmetry that exists at every point on the two-dimensional transverse plane orthogonal to the lightlike direction. These sum rules are obtained by exploiting the closed, infinite-dimensional algebra satisfied by the transverse moments of null-plane axial-vector and vector charge distributions. In the special case of a nucleon target, this procedure leads to the Adler-Weisberger, Gerasimov-Drell-Hearn, Cabibbo-Radicati and Fubini-Furlan-Rossetti sum rules. Matching to the dispersion-theoretic language which is usually invoked in deriving these sum rules, the moment sum rules are shown to be equivalent to algebraic constraints on forward S-matrix elements in the Regge limit.
Gryniuk, Oleksii; Hagelstein, Franziska; Pascalutsa, Vladimir
2016-08-01
The forward Compton scattering off the proton is determined by substituting the empirical total photoabsorption cross sections into dispersive sum rules. In addition to the spin-independent amplitude evaluated previously [Phys. Rev. D 92, 074031 (2015)], we obtain the spin-dependent amplitude over a broad energy range. The two amplitudes contain all the information about the forward CS process and we hence can reconstruct the observables. The results are compared with predictions of chiral perturbation theory where available. The low-energy expansion of the spin-dependent Compton scattering amplitude yields the Gerasimov-Drell-Hearn (GDH) sum rule and relations for the forward spin polarizabilities (FSPs) of the proton. Our evaluation provides an empirical verification of the GDH sum rule for the proton and yields empirical values of the proton FSPs. For the GDH integral, we obtain 204.5 (21.4 ) μ b , in agreement with the sum rule prediction: 204.784481 (4 ) μ b . For the FSPs, we obtain γ0=-92.9 (10.5 )×10-6 fm4 and γ0¯=48.4 (8.2 )×10-6 fm6, improving on the accuracy of previous evaluations.
Magnetic Dipole Sum Rules for Odd Nuclei
Ginocchio, J N
1997-01-01
Sum rules for the total- and scissors-mode M1 strength in odd-A nuclei are derived within the single-j interacting boson-fermion model. We discuss the physical content and geometric interpretation of these sum rules and apply them to ^{167}Er and ^{161}Dy. We find consistency with the former measurements but not with the latter.
Dai, Y B; Dai, Yuan-Ben; Zhu, Shi-Lin
2006-01-01
We derive a new QCD sum rule for $D(0^+)$ which has only the $D\\pi$ continuum with a resonance in the hadron side, using the assumption similar to that has been successfully used in our previous work to the mass of $D_s(0^+)(2317)$. For the value of the pole mass $M_c=1.38 $ GeV as used in the $D_s(0^+)$ case we find that the mass of $D(0^+)$ derived from this sum rule is significantly lower than that derived from the sum rule with the pole approximation. Our result is in agreement with the experimental dada from Belle.
Generalized Thomas-Reiche-Kuhn sum rule
Zhou, Bing-Lu; Zhu, Jiong-Ming; Yan, Zong-Chao
2006-01-01
The generalized Thomas-Reiche-Kuhn sum rule is established for any Coulombic system with arbitrary masses and charges of its constituent particles. Numerical examples are given for the hydrogen molecular ions.
Sum rules in the oscillator radiation processes
Casana, R. [Instituto de Fisica Teorica-IFT/UNESP, Rua Pamplona 145, 01405-900 Sao Paulo, SP (Brazil)]. E-mail: casana@ift.unesp.br; Flores-Hidalgo, G. [Instituto de Fisica Teorica-IFT/UNESP, Rua Pamplona 145, 01405-900 Sao Paulo, SP (Brazil)]. E-mail: gflores@ift.unesp.br; Pimentel, B.M. [Instituto de Fisica Teorica-IFT/UNESP, Rua Pamplona 145, 01405-900 Sao Paulo, SP (Brazil)]. E-mail: pimentel@ift.unesp.br
2005-03-28
We consider the problem of a harmonic oscillator coupled to a scalar field in the framework of recently introduced dressed coordinates. We compute all the probabilities associated with the decay process of an excited level of the oscillator. Instead of doing direct quantum mechanical calculations we establish some sum rules from which we infer the probabilities associated to the different decay processes of the oscillator. Thus, the sum rules allows to show that the transition probabilities between excited levels follow a binomial distribution.
Sum rules in the oscillator radiation processes
Casana, R.; Flores-Hidalgo, G.; Pimentel, B. M.
2005-03-01
We consider the problem of a harmonic oscillator coupled to a scalar field in the framework of recently introduced dressed coordinates. We compute all the probabilities associated with the decay process of an excited level of the oscillator. Instead of doing direct quantum mechanical calculations we establish some sum rules from which we infer the probabilities associated to the different decay processes of the oscillator. Thus, the sum rules allows to show that the transition probabilities between excited levels follow a binomial distribution.
Systematics of strength function sum rules
Johnson, Calvin W.
2015-11-01
Sum rules provide useful insights into transition strength functions and are often expressed as expectation values of an operator. In this letter I demonstrate that non-energy-weighted transition sum rules have strong secular dependences on the energy of the initial state. Such non-trivial systematics have consequences: the simplification suggested by the generalized Brink-Axel hypothesis, for example, does not hold for most cases, though it weakly holds in at least some cases for electric dipole transitions. Furthermore, I show the systematics can be understood through spectral distribution theory, calculated via traces of operators and of products of operators. Seen through this lens, violation of the generalized Brink-Axel hypothesis is unsurprising: one expects sum rules to evolve with excitation energy. Furthermore, to lowest order the slope of the secular evolution can be traced to a component of the Hamiltonian being positive (repulsive) or negative (attractive).
Systematics of strength function sum rules
Johnson, Calvin W., E-mail: cjohnson@mail.sdsu.edu
2015-11-12
Sum rules provide useful insights into transition strength functions and are often expressed as expectation values of an operator. In this letter I demonstrate that non-energy-weighted transition sum rules have strong secular dependences on the energy of the initial state. Such non-trivial systematics have consequences: the simplification suggested by the generalized Brink–Axel hypothesis, for example, does not hold for most cases, though it weakly holds in at least some cases for electric dipole transitions. Furthermore, I show the systematics can be understood through spectral distribution theory, calculated via traces of operators and of products of operators. Seen through this lens, violation of the generalized Brink–Axel hypothesis is unsurprising: one expects sum rules to evolve with excitation energy. Furthermore, to lowest order the slope of the secular evolution can be traced to a component of the Hamiltonian being positive (repulsive) or negative (attractive).
Finite Temperature QCD Sum Rules: A Review
Alejandro Ayala
2017-01-01
Full Text Available The method of QCD sum rules at finite temperature is reviewed, with emphasis on recent results. These include predictions for the survival of charmonium and bottonium states, at and beyond the critical temperature for deconfinement, as later confirmed by lattice QCD simulations. Also included are determinations in the light-quark vector and axial-vector channels, allowing analysing the Weinberg sum rules and predicting the dimuon spectrum in heavy-ion collisions in the region of the rho-meson. Also, in this sector, the determination of the temperature behaviour of the up-down quark mass, together with the pion decay constant, will be described. Finally, an extension of the QCD sum rule method to incorporate finite baryon chemical potential is reviewed.
Systematics of strength function sum rules
Calvin W. Johnson
2015-11-01
Full Text Available Sum rules provide useful insights into transition strength functions and are often expressed as expectation values of an operator. In this letter I demonstrate that non-energy-weighted transition sum rules have strong secular dependences on the energy of the initial state. Such non-trivial systematics have consequences: the simplification suggested by the generalized Brink–Axel hypothesis, for example, does not hold for most cases, though it weakly holds in at least some cases for electric dipole transitions. Furthermore, I show the systematics can be understood through spectral distribution theory, calculated via traces of operators and of products of operators. Seen through this lens, violation of the generalized Brink–Axel hypothesis is unsurprising: one expects sum rules to evolve with excitation energy. Furthermore, to lowest order the slope of the secular evolution can be traced to a component of the Hamiltonian being positive (repulsive or negative (attractive.
Sum rule of the correlation function
Maj, R; Maj, Radoslaw; Mrowczynski, Stanislaw
2004-01-01
We discuss a sum rule satisfied by the correlation function of two particles with small relative momenta. The sum rule, which results from the completeness condition of the quantum states of the two particles, is first derived and then we check how it works in practice. The sum rule is shown to be trivially satisfied by free particle pair, and then there are considered three different systems of interacting particles. We discuss a pair of neutron and proton in the s-wave approximation and the case of the so-called hard spheres with the phase shifts taken into account up to l=4. Finally, the Coulomb system of two charged particles is analyzed.
Generalized Weinberg Sum Rules in Deconstructed QCD
Sekhar-Chivukula, R; Tanabashi, Masaharu; Kurachi, Masafumi; Tanabashi, Masaharu
2004-01-01
Recently, Son and Stephanov have considered an "open moose" as a possible dual model of a QCD-like theory of chiral symmetry breaking. In this note we demonstrate that although the Weinberg sum rules are satisfied in any such model, the relevant sums converge very slowly and in a manner unlike QCD. Further, we show that such a model satisfies a set of generalized sum rules. These sum rules can be understood by looking at the operator product expansion for the correlation function of chiral currents, and correspond to the absence of low-dimension gauge-invariant chiral symmetry breaking condensates. These results imply that, regardless of the couplings and F-constants chosen, the open moose is not the dual of any QCD-like theory of chiral symmetry breaking. We also show that the generalized sum rules lead to a compact expression for the difference of vector- and axial-current correlation functions. This expression allows for a simple formula for the S parameter (L_10), which implies that S is always positive a...
Moments of the Spin Structure Functions g_1^p and g_1^d for 0.05 < Q^2 < 3.0 GeV^2
Prok, Y; Burkert, V D; Deur, A; Dharmawardane, K V; Dodge, G E; Griffioen, K A; Kuhn, S E; Minehart, R; Adams, G; Amaryan, M J; Anghinolfi, M; Asryan, G; Audit, G; Avakian, H; Bagdasaryan, H; Baillie, N; Ball, J P; Baltzell, N A; Barrow, S; Battaglieri, M; Beard, K; Bedlinskiy, I; Bektasoglu, M; Bellis, M; Benmouna, N; Berman, B L; Biselli, A S; Blaszczyk, L; Boiarinov, S; Bonner, B E; Bouchigny, S; Bradford, R; Branford, D; Briscoe, W J; Brooks, W K; Bültmann, S; Butuceanu, C; Calarco, J R; Careccia, S L; Carman, D S; Casey, L; Cazes, A; Chen, S; Cheng, L; Cole, P L; Collins, P; Coltharp, P; Cords, D; Corvisiero, P; Crabb, D; Credé, V; Cummings, J P; Dale, D; Dashyan, N; De Masi, R; De Vita, R; De Sanctis, E; Degtyarenko, P V; Denizli, H; Dennis, L; Dhuga, K S; Dickson, R; Djalali, C; Doughty, D; Dugger, M; Dytman, S; Dzyubak, O P; Egiyan, H; Egiyan, K S; El Fassi, L; Elouadrhiri, L; Eugenio, P; Fatemi, R; Fedotov, G; Feldman, G; Fersh, R G; Feuerbach, R J; Forest, T A; Fradi, A; Funsten, H; Garçon, M; Gavalian, G; Gevorgyan, N; Gilfoyle, G P; Giovanetti, K L; Girod, F X; Goetz, J T; Golovatch, E; Gothe, R W; Guidal, M; Guillo, M; Guler, N; Guo, L; Gyurjyan, V; Hadjidakis, C; Hafidi, K; Hakobyan, H; Hanretty, C; Hardie, J; Hassall, N; Heddle, D; Hersman, F W; Hicks, K; Hleiqawi, I; Holtrop, M; Huertas, M; Hyde-Wright, C E; Ilieva, Y; Ireland, D G; Ishkhanov, B S; Isupov, E L; Ito, M M; Jenkins, D; Jo, H S; Johnstone, J R; Joo, K; Jüngst, H G; Kalantarians, N; Keith, C D; Kellie, J D; Khandaker, M; Kim, K Y; Kim, K; Kim, W; Klein, A; Klein, F J; Klusman, M; Kossov, M; Krahn, Z; Kramer, L H; Kubarovski, V; Kühn, J; Kuleshov, S V; Kuznetsov, V; Lachniet, J; Laget, J M; Langheinrich, J; Lawrence, D; Ji Li; Lima, A C S; Livingston, K; Lu, H Y; Lukashin, K; MacCormick, M; Marchand, C; Markov, N; Mattione, P; McAleer, S; McKinnon, B; McNabb, J W C; Mecking, B A; Mestayer, M D; Meyer, C A; Mibe, T; Mikhailov, K; Mirazita, M; Miskimen, R; Mokeev, V; Morand, L; Moreno, B; Moriya, K; Morrow, S A; Moteabbed, M; Müller, J; Munevar, E; Mutchler, G S; Nadel-Turonski, P; Nasseripour, R; Niccolai, S; Niculescu, G; Niculescu, I; Niczyporuk, B B; Niroula, M R; Niyazov, R A; Nozar, M; O'Rielly, G V; Osipenko, M; Ostrovidov, A I; Park, K; Pasyuk, E; Paterson, C; Anefalos Pereira, S; Philips, S A; Pierce, J; Pivnyuk, N; Pocanic, D; Pogorelko, O; Popa, I; Pozdniakov, S; Preedom, B M; Price, J W; Procureur, S; Protopopescu, D; Qin, L M; Raue, B A; Riccardi, G; Ricco, G; Ripani, M; Ritchie, B G; Rosner, G; Rossi, P; Rowntree, D; Rubin, P D; Sabati, F; Salamanca, J; Salgado, C; Santoro, e J P; Sapunenko, V; Schumacher, R A; Seely, M L; Serov, V S; Sharabyan, Yu G; Sharov, D; Shaw, J; Shvedunov, N V; Skabelin, A V; Smith, E S; Smith, L C; Sober, D I; Sokhan, D; Stavinsky, A; Stepanyan, S S; Stepanyan, S; Stokes, B E; Stoler, P; Strakovsky, I I; Strauch, S; Suleiman, R; Taiuti, M; Tedeschi, D J; Tkabladze, A; Tkachenko, S; Todor, L; Ungaro, M; Vineyard, M F; Vlassov, A V; Watts, D P; Weinstein, L B; Weygand, D P; Williams, M; Wolin, E; Wood, M H; Yegneswaran, A; Yun, J; Zana, L; Zhang, J; Zhao, B; Zhao, Z W
2008-01-01
The spin structure functions g_1 for the proton and the deuteron have been measured over a wide kinematic range in x and Q2 using 1.6 and 5.7 GeV longitudinally polarized electrons incident upon polarized NH_3 and ND_3 targets at Jefferson Lab. Scattered electrons were detected in the CEBAF Large Acceptance Spectrometer, for 0.05 < Q^2 < 5 GeV^2 and W < 3 GeV. The first moments of g_1 for the proton and deuteron are presented -- both have a negative slope at low Q2, as predicted by the extended Gerasimov-Drell-Hearn sum rule. The first result for the generalized forward spin polarizability of the proton gamma_0^p is also reported, and shows evidence of scaling above Q^2 = 1.5 GeV^2. Although the first moments of g_1 are consistent with Chiral Perturbation Theory (ChPT) calculations up to approximately Q^2 = 0.06 GeV^2, a significant discrepancy is observed between the \\gamma_0^p data and ChPT for gamma_0^p,even at the lowest Q2.
Measurement of inclusive spin structure functions of the deuteron
Yun, J.; Kuhn, S. E.; Dodge, G. E.; Forest, T. A.; Taiuti, M.; Adams, G. S.; Amaryan, M. J.; Anciant, E.; Anghinolfi, M.; Asavapibhop, B.; Asryan, G.; Audit, G.; Auger, T.; Avakian, H.; Barrow, S.; Battaglieri, M.; Beard, K.; Bektasoglu, M.; Bertozzi, W.; Bianchi, N.; Biselli, A. S.; Boiarinov, S.; Bosted, P.; Bouchigny, S.; Bradford, R.; Branford, D.; Brooks, W. K.; Bueltmann, S.; Burkert, V. D.; Butuceanu, C.; Calarco, J. R.; Carman, D. S.; Carnahan, B.; Cetina, C.; Ciciani, L.; Cole, P. L.; Coleman, A.; Connelly, J.; Cords, D.; Corvisiero, P.; Crabb, D.; Crannell, H.; Cummings, J.; Sanctis, E. De; Vita, R. De; Degtyarenko, P. V.; Demirchyan, R. A.; Denizli, H.; Dennis, L. C.; Dharmawardane, K. V.; Djalali, C.; Domingo, J.; Doughty, D.; Dragovitsch, P.; Dugger, M.; Dytman, S.; Eckhause, M.; Efremenko, Y. V.; Egiyan, H.; Egiyan, K. S.; Elouadrhiri, L.; Empl, A.; Farhi, L.; Fatemi, R.; Feuerbach, R. J.; Ficenec, J.; Fissum, K.; Freyberger, A.; Frolov, V.; Funsten, H.; Gaff, S. J.; Gai, M.; Gavalian, G.; Gavrilov, V. B.; Gilad, S.; Gilfoyle, G. P.; Giovanetti, K. L.; Girard, P.; Golovatch, E.; Gordon, C. I.; Griffioen, K. A.; Guidal, M.; Guillo, M.; Guo, L.; Gyurjyan, V.; Hadjidakis, C.; Hancock, D.; Hardie, J.; Heddle, D.; Heimberg, P.; Hersman, F. W.; Hicks, K.; Hicks, R. S.; Holtrop, M.; Hu, J.; Hyde-Wright, C. E.; Ito, M. M.; Jenkins, D.; Joo, K.; Keith, C.; Kelley, J. H.; Khandaker, M.; Kim, K. Y.; Kim, K.; Kim, W.; Klein, A.; Klein, F. J.; Klimenko, A. V.; Klusman, M.; Kossov, M.; Kramer, L. H.; Kuang, Y.; Kuhn, J.; Lachniet, J.; Laget, J. M.; Lawrence, D.; Leksin, G. A.; Loukachine, K.; Major, R. W.; Manak, J. J.; Marchand, C.; McAleer, S.; McNabb, J. W.; McCarthy, J.; Mecking, B. A.; Mestayer, M. D.; Meyer, C. A.; Minehart, R.; Mirazita, M.; Miskimen, R.; Mokeev, V.; Morrow, S.; Muccifora, V.; Mueller, J.; Murphy, L. Y.; Mutchler, G. S.; Napolitano, J.; Nelson, S. O.; Niccolai, S.; Niculescu, G.; Niczyporuk, B.; Niyazov, R. A.; Nozar, M.; O'Rielly, G. V.; Ohandjanyan, M. S.; Opper, A.; Ossipenko, M.; Park, K.; Patois, Y.; Peterson, G. A.; Philips, S.; Pivnyuk, N.; Pocanic, D.; Pogorelko, O.; Polli, E.; Preedom, B. M.; Price, J. W.; Protopopescu, D.; Qin, L. M.; Raue, B. A.; Riccardi, G.; Ricco, G.; Ripani, M.; Ritchie, B. G.; Rock, S.; Ronchetti, F.; Rossi, P.; Rowntree, D.; Rubin, P. D.; Sabourov, K.; Salgado, C. W.; Sapunenko, V.; Sargsyan, M.; Schumacher, R. A.; Serov, V. S.; Sharabian, Y. G.; Shaw, J.; Shuvalov, S. M.; Simionatto, S.; Skabelin, A.; Smith, E. S.; Smith, L. C.; Smith, T.; Sober, D. I.; Sorrell, L.; Spraker, M.; Stepanyan, S.; Stoler, P.; Taylor, S.; Tedeschi, D.; Thoma, U.; Thompson, R.; Todor, L.; Tung, T. Y.; Tur, C.; Vineyard, M. F.; Vlassov, A.; Wang, K.; Weinstein, L. B.; Weller, H.; Welsh, R.; Weygand, D. P.; Whisnant, S.; Witkowski, M.; Wolin, E.; Wood, M. H.; Yegneswaran, A.; Zhang, B.; Zhao, J.; Zhou, Z.
2003-05-01
We report the results of a new measurement of spin structure functions of the deuteron in the region of moderate momentum transfer [Q2=0.27 1.3 (GeV/c)2] and final hadronic state mass in the nucleon resonance region (W=1.08 2.0 GeV). We scattered a 2.5 GeV polarized continuous electron beam at Jefferson Lab off a dynamically polarized cryogenic solid state target (15ND3) and detected the scattered electrons with the CEBAF large acceptance spectrometer. From our data, we extract the longitudinal double spin asymmetry A|| and the spin structure function gd1. Our data are generally in reasonable agreement with existing data from SLAC where they overlap, and they represent a substantial improvement in statistical precision. We compare our results with expectations for resonance asymmetries and extrapolated deep inelastic scaling results. Finally, we evaluate the first moment of the structure function gd1 and study its approach to both the deep inelastic limit at large Q2 and to the Gerasimov-Drell-Hearn sum rule at the real photon limit (Q2→0). We find that the first moment varies rapidly in the Q2 range of our experiment and crosses zero at Q2 between 0.5 and 0.8 (GeV/c)2, indicating the importance of the Δ resonance at these momentum transfers.
Moments of the Spin Structure Functions g1p and g1d for 0.05 < Q2 < 3.0 GeV2
Prok, Yelena; Bosted, Peter; Burkert, Volker; Deur, Alexandre; Dharmawardane, Kahanawita; Dodge, Gail; Griffioen, Keith; Kuhn, Sebastian; Minehart, Ralph; Adams, Gary; Amaryan, Moscov; Amaryan, Moskov; Anghinolfi, Marco; Asryan, G.; Audit, Gerard; Avagyan, Harutyun; Baghdasaryan, Hovhannes; Baillie, Nathan; Ball, J.P.; Ball, Jacques; Baltzell, Nathan; Barrow, Steve; Battaglieri, Marco; Beard, Kevin; Bedlinskiy, Ivan; Bektasoglu, Mehmet; Bellis, Matthew; Benmouna, Nawal; Berman, Barry; Biselli, Angela; Blaszczyk, Lukasz; Boyarinov, Sergey; Bonner, Billy; Bouchigny, Sylvain; Bradford, Robert; Branford, Derek; Briscoe, William; Brooks, William; Bultmann, S.; Bueltmann, Stephen; Butuceanu, Cornel; Calarco, John; Careccia, Sharon; Carman, Daniel; Casey, Liam; Cazes, Antoine; Chen, Shifeng; Cheng, Lu; Cole, Philip; Collins, Patrick; Coltharp, Philip; Cords, Dieter; Corvisiero, Pietro; Crabb, Donald; Crede, Volker; Cummings, John; Dale, Daniel; Dashyan, Natalya; De Masi, Rita; De Vita, Raffaella; De Sanctis, Enzo; Degtiarenko, Pavel; Denizli, Haluk; Dennis, Lawrence; Dhuga, Kalvir; Dickson, Richard; Djalali, Chaden; Doughty, David; Dugger, Michael; Dytman, Steven; Dzyubak, Oleksandr; Egiyan, Hovanes; Egiyan, Kim; Elfassi, Lamiaa; Elouadrhiri, Latifa; Eugenio, Paul; Fatemi, Renee; Fedotov, Gleb; Feldman, Gerald; Fersch, Robert; Feuerbach, Robert; Forest, Tony; Fradi, Ahmed; Funsten, Herbert; Garcon, Michel; Gavalian, Gagik; Gevorgyan, Nerses; Gilfoyle, Gerard; Giovanetti, Kevin; Girod, Francois-Xavier; Goetz, John; Golovach, Evgeny; Gothe, Ralf; Guidal, Michel; Guillo, Matthieu; Guler, Nevzat; Guo, Lei; Gyurjyan, Vardan; Hadjidakis, Cynthia; Hafidi, Kawtar; Hakobyan, Hayk; Hanretty, Charles; Hardie, John; Hassall, Neil; Heddle, David; Hersman, F.; Hicks, Kenneth; Hleiqawi, Ishaq; Holtrop, Maurik; Huertas, Marco; Hyde, Charles; Ilieva, Yordanka; Ireland, David; Ishkhanov, Boris; Isupov, Evgeny; Ito, Mark; Jenkins, David; Jo, Hyon-Suk; Johnstone, John; Joo, Kyungseon; Juengst, Henry; Kalantarians, Narbe; Keith, Christopher; Kellie, James; Khandaker, Mahbubul; Kim, Kui; Kim, Kyungmo; Kim, Wooyoung; Klein, Andreas; Klein, Franz; Klusman, Mike; Kossov, Mikhail; Krahn, Zebulun; Kramer, Laird; Kubarovsky, Valery; Kuhn, Joachim; Kuleshov, Sergey; Kuznetsov, Viacheslav; Lachniet, Jeff; Laget, Jean; Langheinrich, Jorn; Lawrence, Dave; Lima, Ana; Livingston, Kenneth; Lu, Haiyun; Lukashin, K.; MacCormick, Marion; Marchand, Claude; Markov, Nikolai; Mattione, Paul; McAleer, Simeon; McKinnon, Bryan; McNabb, John; Mecking, Bernhard; Mestayer, Mac; Meyer, Curtis; Mibe, Tsutomu; Mikhaylov, Konstantin; Mirazita, Marco; Miskimen, Rory; Mokeev, Viktor; Morand, Ludyvine; Moreno, Brahim; Moriya, Kei; Morrow, Steven; Moteabbed, Maryam; Mueller, James; Munevar Espitia, Edwin; Mutchler, Gordon; Nadel-Turonski, Pawel; Nasseripour, Rakhsha; Niccolai, Silvia; Niculescu, Gabriel; Niculescu, Maria-Ioana; Niczyporuk, Bogdan; Niroula, Megh; Niyazov, Rustam; Nozar, Mina; O' Rielly, Grant; Osipenko, Mikhail; Ostrovidov, Alexander; Park, Kijun; Pasyuk, Evgueni; Paterson, Craig; Anefalos Pereira, S.; Philips, Sasha; Pierce, J.; Pivnyuk, Nikolay; Pocanic, Dinko; Pogorelko, Oleg; Popa, Iulian; Pozdnyakov, Sergey; Preedom, Barry; Price, John; Procureur, Sebastien; Protopopescu, Dan; Qin, Liming; Raue, Brian; Riccardi, Gregory; Ricco, Giovanni; Ripani, Marco; Ritchie, Barry; Rosner, Guenther; Rossi, Patrizia; Rowntree, David; Rubin, Philip; Sabatie, Franck; Salamanca, Julian; Salgado, Carlos; Santoro, Joseph; Sapunenko, Vladimir; Schumacher, Reinhard; Seely, Mikell; Serov, Vladimir; Sharabian, Youri; Sharov, Dmitri; Shaw, Jeffrey; Shvedunov, Nikolay; Skabelin, Alexander; Smith, Elton; Smith, Lee; Sober, Daniel; Sokhan, Daria; Stavinskiy, Aleksey; Stepanyan, Samuel; Stepanyan, Stepan; Stokes, Burnham; Stoler, Paul; Strakovski, Igor; Strauch, Steffen; Suleiman, Riad; Taiuti, Mauro; Tedeschi, David; Tkabladze, Avtandil; Tkachenko, Svyatoslav; Todor, Luminita; Ungaro, Maurizio; V
2009-02-01
The spin structure functions $g_1$ for the proton and the deuteron have been measured over a wide kinematic range in $x$ and \\Q2 using 1.6 and 5.7 GeV longitudinally polarized electrons incident upon polarized NH$_3$ and ND$_3$ targets at Jefferson Lab. Scattered electrons were detected in the CEBAF Large Acceptance Spectrometer, for $0.05 < Q^2 < 5 $\\ GeV$^2$ and $W < 3$ GeV. The first moments of $g_1$ for the proton and deuteron are presented -- both have a negative slope at low \\Q2, as predicted by the extended Gerasimov-Drell-Hearn sum rule. The first result for the generalized forward spin polarizability of the proton $\\gamma_0^p$ is also reported, and shows evidence of scaling above $Q^2$ = 1.5 GeV$^2$. Although the first moments of $g_1$ are consistent with Chiral Perturbation Theory (\\ChPT) calculations up to approximately $Q^2 = 0.06$ GeV$^2$, a significant discrepancy is observed between the $\\gamma_0^p$ data and \\ChPT\\ for $\\gamma_0^p$,even at the lowest \\Q2.
Integrals of Lagrange functions and sum rules
Baye, Daniel, E-mail: dbaye@ulb.ac.be [Physique Quantique, CP 165/82, Universite Libre de Bruxelles, B 1050 Bruxelles (Belgium); Physique Nucleaire Theorique et Physique Mathematique, CP 229, Universite Libre de Bruxelles, B 1050 Bruxelles (Belgium)
2011-09-30
Exact values are derived for some matrix elements of Lagrange functions, i.e. orthonormal cardinal functions, constructed from orthogonal polynomials. They are obtained with exact Gauss quadratures supplemented by corrections. In the particular case of Lagrange-Laguerre and shifted Lagrange-Jacobi functions, sum rules provide exact values for matrix elements of 1/x and 1/x{sup 2} as well as for the kinetic energy. From these expressions, new sum rules involving Laguerre and shifted Jacobi zeros and weights are derived. (paper)
Optical Thomas-Reiche-Kuhn Sum Rules
Barnett, Stephen M.; Loudon, Rodney
2012-01-01
The Thomas-Reiche-Kuhn sum rule is a fundamental consequence of the position-momentum commutation relation for an atomic electron and it provides an important constraint on the transition matrix elements for an atom. Analogously, the commutation relations for the electromagnetic field operators in a magnetodielectric medium constrain the properties of the dispersion relations for the medium through four sum rules for the allowed phase and group velocities for polaritons propagating through the medium. These rules apply to all bulk media including the metamaterials designed to provide negative refractive indices. An immediate consequence of this is that it is not possible to construct a medium in which all the polariton modes for a given wavelength lie in the negative-index region.
New QCD sum rules based on canonical commutation relations
Hayata, Tomoya
2012-04-01
New derivation of QCD sum rules by canonical commutators is developed. It is the simple and straightforward generalization of Thomas-Reiche-Kuhn sum rule on the basis of Kugo-Ojima operator formalism of a non-abelian gauge theory and a suitable subtraction of UV divergences. By applying the method to the vector and axial vector current in QCD, the exact Weinberg’s sum rules are examined. Vector current sum rules and new fractional power sum rules are also discussed.
Advances in QCD sum rule calculations
Melikhov, Dmitri
2016-01-01
We review the recent progress in the applications of QCD sum rules to hadron properties with the emphasis on the following selected problems: (i) development of new algorithms for the extraction of ground-state parameters from two-point correlators; (ii) form factors at large momentum transfers from three-point vacuum correlation functions; (iii) properties of exotic tetraquark hadrons from correlation functions of four-quark currents.
Advances in QCD sum-rule calculations
Melikhov, Dmitri [Institute for High Energy Physics, Austrian Academy of Sciences, Nikolsdorfergasse 18, A-1050 Vienna, Austria D. V. Skobeltsyn Institute of Nuclear Physics, M. V. Lomonosov Moscow State University, Moscow (Russian Federation)
2016-01-22
We review the recent progress in the applications of QCD sum rules to hadron properties with the emphasis on the following selected problems: (i) development of new algorithms for the extraction of ground-state parameters from two-point correlators; (ii) form factors at large momentum transfers from three-point vacuum correlation functions: (iii) properties of exotic tetraquark hadrons from correlation functions of four-quark currents.
Heavy Baryons and QCD Sum Rules
Yakovlev, O I
1996-01-01
We discuss an application of QCD sum rules to the heavy baryons $\\Lambda_Q$ and $\\Sigma_Q$. The predictions for the masses of heavy baryons, residues and Isgur-Wise function are presented. The new results on two loop anomalous dimensions of baryonic currents and QCD radiative corrections (two- and three- loop contributions) to the first two Wilson coefficients in OPE are explicitly presented.
Light four-quark states and QCD sum rule
ZHANG Ai-Lin
2009-01-01
The relations among four-quark states, diquarks and QCD sum rules are discussed. The situation of the existing, but incomplete studies of four-quark states with QCD sum rules is analyzed. Masses of some diquark clusters were attempted to be determined by QCD sum rules, and masses of some light tetraquark states were obtained in terms of the diquarks.
Scalar Glueballs A Gaussian Sum-rules Analysis
Harnett, D
2002-01-01
Although marginally more complicated than the traditional laplace sum-rules, gaussian sum-rules have the advantage of being able to probe excited and ground hadronic states with similar sensitivity. Gaussian sum-rule analysis techniques are applied to the problematic scalar glueball channel to determine masses, widths, and relative resonance strengths of low-lying scalar glueball states contributing to the hadronic spectral function. An important feature of our analysis is the inclusion of instanton contributions to the scalar gluonic correlation function. Compared with the next-to-leading gaussian sum- rule, the analysis of the lowest weighted sum-rule (which contains a large scale independent contribution from the low energy theorem) is shown to be unreliable because of instability under QCD uncertainties. However, the presence of instanton effects leads to approximately consistent mass scales in the lowest weighted and next- lowest weighted sum-rules. The analysis of the next-to- leading sum-rule demonstra...
Nonlocal Condensate Model for QCD Sum Rules
Hsieh, Ron-Chou
2009-01-01
We include effects of nonlocal quark condensates into QCD sum rules (QSR) via the K$\\ddot{\\mathrm{a}}$ll$\\acute{\\mathrm{e}}$n-Lehmann representation for a dressed fermion propagator, in which a negative spectral density function manifests their nonperturbative nature. Applying our formalism to the pion form factor as an example, QSR results are in good agreement with data for momentum transfer squared up to $Q^2 \\approx 10 $ GeV$^2$. It is observed that the nonlocal quark-condensate contribution descends like $1/Q^4$, different from the exponential decrease in $Q^2$ obtained in the literature, and contrary to the linear rise in the local-condensate approximation.
QCD Sum Rules Study of X(4350)
Mo, Zeng; Cui, Chun-Yu; Liu, Yong-Lu; Huang, Ming-Qiu
2014-04-01
The QCD sum rule approach is used to analyze the nature of the recently observed new resonance X(4350), which is assumed to be a diquark-antidiquark state [cs][bar cbar s] with JPC = 1-+. The interpolating current representing this state is proposed. In the calculation, contributions of operators up to dimension six are included in the operator product expansion (OPE), as well as terms which are linear in the strange quark mass ms. We find m1-+ = (4.82 ± 0.19) GeV, which is not compatible with the X(4350) structure as a 1-+ tetraquark state. Finally, we also discuss the difference of a four-quark state's mass whether the state's interpolating current has a definite charge conjugation.
Gaussian Sum-Rules, Scalar Gluonium, and Instantons
Steele, T G; Orlandini, G
2002-01-01
Gaussian sum-rules relate a QCD prediction to a two-parameter Gaussian-weighted integral of a hadronic spectral function, providing a clear conceptual connection to quark-hadron duality. In contrast to Laplace sum-rules, the Gaussian sum-rules exhibit enhanced sensitivity to excited states of the hadronic spectral function. The formulation of Gaussian sum-rules and associated analysis techniques for extracting hadronic properties from the sum-rules are reviewed and applied to scalar gluonium. With the inclusion of instanton effects, the Gaussian sum-rule analysis results in a consistent scenario where the gluonic resonance strength is spread over a broad energy range below 1.6 GeV, and indicates the presence of gluonium content in more than one hadronic state.
Sum Rule for a Schiff-Like Dipole Moment
Raduta, A. A.; Budaca, R.
The energy-weighted sum rule for an electric dipole transition operator of a Schiff type differs from the Thomas-Reiche-Kuhn (TRK) sum rule by several corrective terms which depend on the number of system components, N. For illustration the formalism was applied to the case of Na clusters. One concludes that the random phase approximation (RPA) results for Na clusters obey the modified TRK sum rule.
Nuclear pions and the Gottfried and Bjorken sum rules
Epele, L.N. (Lab. de Fisica Teorica, Dept. de Fisica, Univ. Nacional de La Plata (Argentina)); Fanchiotti, H. (Lab. de Fisica Teorica, Dept. de Fisica, Univ. Nacional de La Plata (Argentina)); Garcia Canal, C.A. (Lab. de Fisica Teorica, Dept. de Fisica, Univ. Nacional de La Plata (Argentina)); Leader, E. (Birkbeck Coll., Univ. of London (United Kingdom)); Sassot, R. (Lab. de Fisica Teorica, Dept. de Fisica, Univ. Nacional de La Plata (Argentina))
1994-10-01
An extremely simple but instructive, ''toy'' model is presented which shows that a small excess of pions in the nucleus can produce a significant change in the values expected for the Gottfried sum rule. The general question of the convergence of the sum rule and of the convergence of the experimental integral is also discussed. It is demonstrated that conclusions about the sum rule, based on deuterium data, are surprisingly model dependent. In contrast, it is stressed, that the Bjorken sum rule can be tested significantly using deuterium data. (orig.)
Tuning sum rules with window functions for optical constant evaluation
Rodríguez-de Marcos, Luis V.; Méndez, José A.; Larruquert, Juan I.
2016-07-01
Sum rules are a useful tool to evaluate the global consistency of a set of optical constants. We present a procedure to spectrally tune sum rules to evaluate the local consistency of optical constants. It enables enhancing the weight of a desired spectral range within the sum-rule integral. The procedure consists in multiplying the complex refractive index with an adapted function, which is named window function. Window functions are constructed through integration of Lorentz oscillators. The asymptotic decay of these window functions enables the derivation of a multiplicity of sum rules akin to the inertial sum rule, along with one modified version of f-sum rule. This multiplicity of sum rules combined with the free selection of the photon energy range provides a double way to tune the spectral contribution within the sum rule. Window functions were applied to reported data of SrF2 and of Al films in order to check data consistency over the spectrum. The use of window functions shows that the optical constants of SrF2 are consistent in a broad spectrum. Regarding Al, some spectral ranges are seen to present a lower consistency, even though the standard sum rules with no window function did not detect inconsistencies. Hence window functions are expected to be a helpful tool to evaluate the local consistency of optical constants.
Octet magnetic Moments and their sum rules in statistical model
Batra, M
2013-01-01
The statistical model is implemented to find the magnetic moments of all octet baryons. The well-known sum rules like GMO and CG sum rules has been checked in order to check the consistency of our approach. The small discrepancy between the results suggests the importance of breaking in SU(3) symmetry.
Radiative Corrections to the Sum Rule of Lepton Flavor Mixing
Zhang, Jue
2016-01-01
The simple correlation among three lepton flavor mixing angles $(\\theta^{}_{12}, \\theta^{}_{13}, \\theta^{}_{23})$ and the leptonic Dirac CP-violating phase $\\delta$ is conventionally called a sum rule of lepton flavor mixing, which may be derived from a class of neutrino mass models with flavor symmetries. In this paper, we consider the sum rule $\\theta^{}_{12} \\approx \\theta^{\
Conservation Rules of Direct Sum Decomposition of Groups
Nakasho Kazuhisa
2016-03-01
Full Text Available In this article, conservation rules of the direct sum decomposition of groups are mainly discussed. In the first section, we prepare miscellaneous definitions and theorems for further formalization in Mizar [5]. In the next three sections, we formalized the fact that the property of direct sum decomposition is preserved against the substitutions of the subscript set, flattening of direct sum, and layering of direct sum, respectively. We referred to [14], [13] [6] and [11] in the formalization.
Neutrino mass sum rules and symmetries of the mass matrix
Gehrlein, Julia [Karlsruhe Institute of Technology, Institut fuer Theoretische Teilchenphysik, Karlsruhe (Germany); Universidad Autonoma de Madrid, Departamento de Fisica Teorica, Madrid (Spain); Instituto de Fisica Teorica UAM/CSIC, Madrid (Spain); Spinrath, Martin [Karlsruhe Institute of Technology, Institut fuer Theoretische Teilchenphysik, Karlsruhe (Germany); National Center for Theoretical Sciences, Physics Division, Hsinchu (China)
2017-05-15
Neutrino mass sum rules have recently gained again more attention as a powerful tool to discriminate and test various flavour models in the near future. A related question which has not yet been discussed fully satisfactorily was the origin of these sum rules and if they are related to any residual or accidental symmetry. We will address this open issue here systematically and find previous statements confirmed. Namely, the sum rules are not related to any enhanced symmetry of the Lagrangian after family symmetry breaking but they are simply the result of a reduction of free parameters due to skillful model building. (orig.)
Compton scattering from nuclei and photo-absorption sum rules
Gorchtein, Mikhail; Hobbs, Timothy; Londergan, J. Timothy; Szczepaniak, Adam P.
2011-12-01
We revisit the photo-absorption sum rule for real Compton scattering from the proton and from nuclear targets. In analogy with the Thomas-Reiche-Kuhn sum rule appropriate at low energies, we propose a new “constituent quark model” sum rule that relates the integrated strength of hadronic resonances to the scattering amplitude on constituent quarks. We study the constituent quark model sum rule for several nuclear targets. In addition, we extract the α=0 pole contribution for both proton and nuclei. Using the modern high-energy proton data, we find that the α=0 pole contribution differs significantly from the Thomson term, in contrast with the original findings by Damashek and Gilman.
Compton Scattering and Photo-absorption Sum Rules on Nuclei
Gorshteyn, Mikhail; Hobbs, Timothy; Londergan, J. Timothy; Szczepaniak, Adam P.
2012-03-01
We revisit the photo-absorption sum rule for real Compton scattering from the proton and from nuclear targets. In analogy with the Thomas-Reiche-Kuhn sum rule appropriate at low energies, we propose a new ``constituent quark model'' sum rule that relates the integrated strength of hadronic resonances to the scattering amplitude on constituent quarks. We study the constituent quark model sum rule for several nuclear targets. In addition we extract the J=0 pole contribution for both proton and nuclei. Using the modern high energy proton data we find that the J=0 pole contribution differs significantly from the Thomson term, in contrast with the original findings by Damashek and Gilman. We discuss phenomenological implications of this new result.
Structure Function Sum rules for Systems with Large Scattering Lengths
Goldberger, Walter D
2010-01-01
We use a dispersion relation in conjunction with the operator product expansion (OPE) to derive model independent sum rules for the dynamic structure functions of systems with large scattering lengths. We present an explicit sum rule for the structure functions that control the density and spin response of the many-body ground state. Our methods are general, and apply to either fermions or bosons which interact through two-body contact interactions with large scattering lengths. By employing a Borel transform of the OPE, the relevant integrals are weighted towards infrared frequencies, thus allowing for greater overlap low energy data. Similar sum rules can be derived for other response functions. The sum rules can be used to extract the contact parameter introduced by Tan, including universality violating corrections at finite scattering lengths.
Faraday effect revisited: sum rules and convergence issues
Cornean, Horia; Nenciu, Gheorghe
2010-01-01
This is the third paper of a series revisiting the Faraday effect. The question of the absolute convergence of the sums over the band indices entering the Verdet constant is considered. In general, sum rules and traces per unit volume play an important role in solid-state physics, and they give...
Lattice energy sum rules and the trace anomaly
Rothe, Heinz J.
1995-01-01
We show that the additional contribution to the Michael lattice energy sum rule for the static quark-antiquark potential, pointed out recently, can be identified with the contribution to the field energy arising from the trace anomaly of the energy momentum tensor. We also exlicitely exhibit the anomalous contribution to the field energy in the sum rule for the glueball mass obtained recently by Michael.
Magnetic Dipole Sum Rules for Odd-Mass Nuclei
Ginocchio, J.N.; Leviatan, A. [Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545 (United States); Leviatan, A. [Racah Institute of Physics, The Hebrew University, Jerusalem 91904 (Israel); Ginocchio, J.N.; Leviatan, A. [European Centre for Theoretical Studies in Nuclear Physics and Related Areas (ECT), I-38050 Villazano, Trento (Italy)
1997-08-01
Sum rules for the total- and scissors-mode M1 strength in odd-A nuclei are derived within the single-j interacting boson-fermion model. We discuss the physical content and geometric interpretation of these sum rules and apply them to {sup 167}Er and {sup 161}Dy. We find consistency with the former measurements but not with the latter. {copyright} {ital 1997 } {ital The American Physical Society}
QCD Sum Rules and Models for Generalized Parton Distributions
Anatoly Radyushkin
2004-10-01
I use QCD sum rule ideas to construct models for generalized parton distributions. To this end, the perturbative parts of QCD sum rules for the pion and nucleon electromagnetic form factors are interpreted in terms of GPDs and two models are discussed. One of them takes the double Borel transform at adjusted value of the Borel parameter as a model for nonforward parton densities, and another is based on the local duality relation. Possible ways of improving these Ansaetze are briefly discussed.
Nuclear effects in deuteron and the Gottfried sum rule
Epele, L.N.; Sassot, R. (Lab. de Fisica Teorica, Univ. Nacional de La Plata (Argentina)); Fanchiotti, H. (Theory Div., CERN, Geneva (Switzerland)); Carcia Canal, C.A. (Lab. de Fisica Teorica, Univ. Nacional de La Plata (Argentina) Theory Div., CERN, Geneva (Switzerland))
1992-01-23
Recent NMC data on the ratio of the deep inelastic structure functions F{sub 2} per nucleon for deuterium relative to hydrogen are analysed in the context of the Gottfried sum rule. It is shown that the discrepancy between the Gottfried sum rule prediction and NMC data analysis may be interpreted as a nuclear effect in deuterium as it is suggested by several models. This fact, applied to nuclear-deuterium measured ratios, modifies the standard picture of nuclear effects. (orig.).
Chiral corrections to the Adler-Weisberger sum rule
Beane, Silas R.; Klco, Natalie
2016-12-01
The Adler-Weisberger sum rule for the nucleon axial-vector charge, gA , offers a unique signature of chiral symmetry and its breaking in QCD. Its derivation relies on both algebraic aspects of chiral symmetry, which guarantee the convergence of the sum rule, and dynamical aspects of chiral symmetry breaking—as exploited using chiral perturbation theory—which allow the rigorous inclusion of explicit chiral symmetry breaking effects due to light-quark masses. The original derivations obtained the sum rule in the chiral limit and, without the benefit of chiral perturbation theory, made various attempts at extrapolating to nonvanishing pion masses. In this paper, the leading, universal, chiral corrections to the chiral-limit sum rule are obtained. Using PDG data, a recent parametrization of the pion-nucleon total cross sections in the resonance region given by the SAID group, as well as recent Roy-Steiner equation determinations of subthreshold amplitudes, threshold parameters, and correlated low-energy constants, the Adler-Weisberger sum rule is confronted with experimental data. With uncertainty estimates associated with the cross-section parametrization, the Goldberger-Treimann discrepancy, and the truncation of the sum rule at O (Mπ4) in the chiral expansion, this work finds gA=1.248 ±0.010 ±0.007 ±0.013 .
Spin Structure Functions of the Deuteron Measured with CLAS in and above the Resonance Region
Dharmawardane, Kahanawita [Old Dominion Univ., Norfolk, VA (United States)
2004-05-01
Spin structure functions of the nucleon in the region of large x and small to moderate Q^{2} continue to be of high current interest. The first moment of the spin structure function g_{1}, γ_{1}, goes through a rapid transition from the photon point (Q^{2}=0), where it is constrained by the Gerasimov-Drell-Hearn sum rule, to the deep inelastic limit where it is sensitive to the nucleon spin fraction carried by quarks. The interesting behavior in the transition region is dominated by baryon resonance excitations. We concluded an experiment to measure these observables for deuterium as part of the ''EG1'' run group in Jefferson Lab's Hall B. We used a highly polarized electron beam with energies from 1.6 GeV to 5.7 GeV and a cryogenic polarized ND_{3} target together with the CEBAF Large Acceptance Spectrometer (CLAS) to accumulate over 11 billion events. In this thesis, we present results for the spin structure function g$d\\atop{1}$ (x,Q^{2}), as well as its first moment, γ$d\\atop{1}$(Q^{2}) in and above the resonance region over a Q^{2} range from 0.05 to 5 Gev^{2}, based on the data taken with beam energies of 1.6 and 5.7 GeV. We also extract the behavior of A$d\\atop{1}$(x) at large x. Our data are consistent with the Hyperfine-perturbed quark model calculation which predicts that A$d\\atop{1}$ (x → 1) → 1. We also see evidence for duality in g$d\\atop{1}$ (x, Q^{2}) at Q^{2} > GeV^{2}.
First doubly polarised photoproduction on {sup 3}He at the photon beam of MAMI
Aguar Bartolome, Patricia
2010-11-15
A first experiment with a polarised {sup 3}He target was carried out in July 2009 at the MAMI accelerator in Mainz in a photon energy range between 200 MeV and 800 MeV. The aim of this measurement was to investigate the Gerasimov-Drell-Hearn sum rule on the neutron. The use of the data obtained with the polarised {sup 3}He target, compared to existing data on the deuteron, gives a complementary and more direct access to the neutron, due to the spin structure of the {sup 3}He. The measurement of the helicity dependence of the inclusive total photoabsorption cross section required a beam of tagged circularly polarised photons incident on the longitudinally polarised {sup 3}He target. The data were taken using the 4{pi} Crystal Ball photon spectrometer in combination with TAPS as a forward wall and complemented by a threshold Cherenkov detector used to on-line suppress the background from electromagnetic events. The development and preparation of the different components of the {sup 3}He experimental setup was an important part of this work and are described in detail in this thesis. The detector system and the analysis method were tested by the measurement of the unpolarised total inclusive photoabsorption cross section on liquid hydrogen. The results obtained are in good agreement with previous published data. Preliminary results of the unpolarised total photoabsorption cross section, as well as the helicity dependent photoabsorption cross section difference on {sup 3}He compared with several theoretical models will also be presented. (orig.)
A critique of the angular momentum sum rules and a new angular momentum sum rule
Bakker, B L G; Trueman, T L
2004-01-01
We show that the expressions in the literature for the tensorial structure of the hadronic matrix elements of the angular momentum operators J are incorrect. Given this disagreement with the published results, we have taken pains to derive the correct expressions in three different ways, two involving explicit physical wave packets and the third, totally independent, based upon the rotational properties of the state vectors. Surprisingly it turns out that the results are very sensitive to the type of relativistic spin state used to describe the motion of the particle i.e. whether a canonical (i.e. boost) state or a helicity state is utilized. We present results for the matrix elements of the angular momentum operators, valid in an arbitrary Lorentz frame, both for helicity states and canonical states. These results are relevant for the construction of angular momentum sum rules, relating the angular momentum of a nucleon to the spin and orbital angular momentum of its constituents. Moreover, we show that it i...
The Black Hole Interior and a Curious Sum Rule
Giveon, Amit; Troost, Jan
2013-01-01
We analyze the Euclidean geometry near non-extremal NS5-branes in string theory, including regions beyond the horizon and beyond the singularity of the black brane. The various regions have an exact description in string theory, in terms of cigar, trumpet and negative level minimal model conformal field theories. We study the worldsheet elliptic genera of these three superconformal theories, and show that their sum vanishes. We speculate on the significance of this curious sum rule for black hole physics.
The black hole interior and a curious sum rule
Giveon, Amit [Racah Institute of Physics, The Hebrew University,Jerusalem, 91904 (Israel); Itzhaki, Nissan [Physics Department, Tel-Aviv University,Ramat-Aviv, 69978 (Israel); Troost, Jan [Laboratoire de Physique Théorique,Unité Mixte du CRNS et de l’École Normale Supérieure,associée à l’Université Pierre et Marie Curie 6,UMR 8549 École Normale Supérieure,24 Rue Lhomond Paris 75005 (France)
2014-03-12
We analyze the Euclidean geometry near non-extremal NS5-branes in string theory, including regions beyond the horizon and beyond the singularity of the black brane. The various regions have an exact description in string theory, in terms of cigar, trumpet and negative level minimal model conformal field theories. We study the worldsheet elliptic genera of these three superconformal theories, and show that their sum vanishes. We speculate on the significance of this curious sum rule for black hole physics.
An efficient method for evaluating energy-dependent sum rules
Dinur, Nir Nevo; Bacca, Sonia; Barnea, Nir
2014-01-01
Energy-dependent sum rules are useful tools in many fields of physics. In nuclear physics, they typically involve an integration of the response function over the nuclear spectrum with a weight function composed of integer powers of the energy. More complicated weight functions are also encountered, e.g., in nuclear polarization corrections of atomic spectra. Using the Lorentz integral transform method and the Lanczos algorithm, we derive a computationally efficient technique for evaluating such sum rules that avoids the explicit calculation of both the continuum states and the response function itself. Our numerical results for electric dipole sum rules of the Helium-4 nucleus with various energy-dependent weights show rapid convergence with respect to the number of Lanczos steps. This demonstrates the usefulness of the method in a variety of electroweak reactions.
The lowest hidden charmed tetraquark state from QCD sum rules
Wang, Zhi-Gang
2015-01-01
In this article, we study the $S\\bar{S}$ type scalar tetraquark state $cq\\bar{c}\\bar{q}$ in details with the QCD sum rules by calculating the contributions of the vacuum condensates up to dimension-10 in the operator product expansion, and obtain the value $M_{Z_c}=\\left(3.82^{+0.08}_{-0.08}\\right)\\,\\rm{GeV}$, which is the lowest mass for the hidden charmed tetraquark states from the QCD sum rules. Furthermore, we calculate the hadronic coupling constants $G_{Z_c\\eta_c\\pi}$ and $G_{Z_cDD}$ with the three-point QCD sum rules, then study the strong decays $ Z_c\\to \\eta_c\\pi\\, ,\\, DD$, and observe that the total width $\\Gamma_{Z_c}\\approx 21\\,\\rm{MeV}$. The present predictions can be confronted with the experimental data in the futures at the BESIII, LHCb and Belle-II.
QCD Sum Rules at Finite Temperature: a Review
Ayala, Alejandro; Loewe, M
2016-01-01
The method of QCD sum rules at finite temperature is reviewed, with emphasis on recent results. These include predictions for the survival of charmonium and bottonium states, at and beyond the critical temperature for de-confinement, as later confirmed by lattice QCD simulations. Also included are determinations in the light-quark vector and axial-vector channels, allowing to analyse the Weinberg sum rules, and predict the dimuon spectrum in heavy ion collisions in the region of the rho-meson. Also in this sector, the determination of the temperature behaviour of the up-down quark mass, together with the pion decay constant, will be described. Finally, an extension of the QCD sum rule method to incorporate finite baryon chemical potential is reviewed.
Heavy hybrid mesons in the QCD sum rule
Huang, Peng-Zhi
2011-01-01
We study the spectra of the hybrid mesons containing one heavy quark ($q\\bar{Q}g$) within the framework of QCD sum rules in the heavy quark limit. The derived sum rules are stable with the variation of the Borel parameter within their corresponding working ranges. The extracted binding energy for the heavy hybrid doublets $H(S)$ and $M(T)$ is almost degenerate. We also calculate the pionic couplings between these heavy hybrid and the conventional heavy meson doublets using the light-cone QCD sum rule method. The extracted coupling constants are rather small as a whole. With these couplings we make a rough estimate of the partial widths of these pionic decay channels.
On the Predictivity of Neutrino Mass Sum Rules
Gehrlein, Julia; Spinrath, Martin
2016-01-01
Correlations between light neutrino observables are arguably the strongest predictions of lepton flavour models based on (discrete) symmetries, except for the very few cases which unambiguously predict the full set of leptonic mixing angles. A subclass of these correlations are neutrino mass sum rules, which connect the three (complex) light neutrino mass eigenvalues among each other. This connection constrains both the light neutrino mass scale and the Majorana phases, so that mass sum rules generically lead to a non-zero value of the lightest neutrino mass and to distinct predictions for the effective mass probed in neutrinoless double beta decay. However, in nearly all cases known, the neutrino mass sum rules are not exact and receive corrections from various sources. We introduce a formalism to handle these corrections perturbatively in a model-independent manner, which overcomes issues present in earlier approaches. Our ansatz allows us to quantify the modification of the predictions derived from neutrin...
Broadening of dielectric response and sum rule conservation
Franta, Daniel, E-mail: franta@physics.muni.cz [Department of Physical Electronics, Faculty of Science, Masaryk University, Kotlářká 2, 611 37 Brno (Czech Republic); CEITEC —Central European Institute of Technology, Masaryk University, Kamenice 5, 625 00 Brno (Czech Republic); Nečas, David; Zajíčková, Lenka [Department of Physical Electronics, Faculty of Science, Masaryk University, Kotlářká 2, 611 37 Brno (Czech Republic); CEITEC —Central European Institute of Technology, Masaryk University, Kamenice 5, 625 00 Brno (Czech Republic); Ohlídal, Ivan [Department of Physical Electronics, Faculty of Science, Masaryk University, Kotlářká 2, 611 37 Brno (Czech Republic)
2014-11-28
Different types of broadening of the dielectric response are studied with respect to the preservation of the Thomas–Reiche–Kuhn sum rule. It is found that only the broadening of the dielectric function and transition strength function conserve this sum rule, whereas the broadening of the transition probability function (joint density of states) increases or decreases the sum. The effect of different kinds of broadening is demonstrated for interband and intraband direct electronic transitions using simplified rectangular models. It is shown that the broadening of the dielectric function is more suitable for interband transitions while broadening of the transition strength function is more suitable for intraband transitions. - Highlights: • Preservation of the sum rule by different types of dielectric response broadening • Only broadening of dielectric function and transition strength function preserves it. • Broadening of joint density of states does not preserve the sum rule. • Broadening of dielectric function is better for direct interband transitions. • Broadening of transition strength is better for indirect interband transitions.
Charm quark mass determined from a pair of sum rules
Erler, Jens; Spiesberger, Hubert
2016-01-01
In this paper, we present preliminary results of the determination of the charm quark mass $\\hat{m}_c$ from QCD sum rules of moments of the vector current correlator calculated in perturbative QCD at ${\\cal O} (\\hat \\alpha_s^3)$. Self-consistency between two different sum rules allow to determine the continuum contribution to the moments without requiring experimental input, except for the charm resonances below the continuum threshold. The existing experimental data from the continuum region is used, then, to confront the theoretical determination and reassess the theoretic uncertainty.
A new neutrino mass sum rule from inverse seesaw
Dorame, L; Peinado, E; Rojas, Alma D; Valle, J W F
2012-01-01
A class of discrete flavor-symmetry-based models predicts constrained neutrino mass matrix schemes that lead to specific neutrino mass sum-rules (MSR). One of these implies in a lower bound on the effective neutrinoless double beta mass parameter, even for normal hierarchy neutrinos. Here we propose a new model based on the S4 flavor symmetry that leads to the new neutrino mass sum-rule and discuss how to generate a nonzero value for the reactor mixing angle indicated by recent experiments, and the resulting correlation with the solar mixing angle.
Testing solar lepton mixing sum rules in neutrino oscillation experiments
Ballett, Peter; Luhn, Christoph; Pascoli, Silvia; Schmidt, Michael A
2014-01-01
Small discrete family symmetries such as S4, A4 or A5 may lead to simple leading-order predictions for the neutrino mixing matrix such as the bimaximal, tribimaximal or golden ratio mixing patterns, which may be brought into agreement with experimental data with the help of corrections from the charged-lepton sector. Such scenarios generally lead to relations among the parameters of the physical leptonic mixing matrix known as solar lepton mixing sum rules. In this article, we present a simple derivation of such solar sum rules, valid for arbitrary neutrino and charged lepton mixing angles and phases, assuming only {\\theta}13^{\
Impact of Duality Violations on Spectral Sum Rule Analyses
Cata, O
2007-01-01
Recent sum rule analyses on the two-point correlator have led to significant discrepancies in the values found for the OPE condensates, most dramatically in the dimension eight condensate and to a lesser extent in the dimension six one. Precise knowledge of these condensates is of relevance in kaon decays and therefore it seems mandatory to assess the actual impact of what is commonly neglected in spectral sum rules, most prominently the issue of duality violations. We will explicitly compute them in a toy model and show that they are a priori non-negligible.
Decay Constants of Beauty Mesons from QCD Sum Rules
Lucha, Wolfgang; Simula, Silvano
2014-01-01
Our recently completed analysis of the decay constants of both pseudoscalar and vector beauty mesons reveals that in the bottom-quark sector two specific features of the sum-rule predictions show up: (i) For the input value of the bottom-quark mass in the $\\overline{\\rm MS}$ scheme $\\overline{m}_b(\\overline{m}_b)\\approx4.18\\;\\mbox{GeV},$ the sum-rule result $f_B\\approx210$-$220\\;\\mbox{MeV}$ for the $B$ meson decay constant is substantially larger than the recent lattice-QCD finding $f_B\\approx190\\;\\mbox{MeV}.$ Requiring QCD sum rules to reproduce the lattice-QCD value of $f_B$ yields a significantly larger $b$-quark mass: $\\overline{m}_b(\\overline{m}_b)=4.247\\;\\mbox{GeV}.$ (ii) Whereas QCD sum-rule predictions for the charmed-meson decay constants $f_D,$ $f_{D_s},$ $f_{D^*}$ and $f_{D_s^*}$ are practically independent of the choice of renormalization scale, in the beauty sector the results for the decay constants - and especially for the ratio $f_{B^*}/f_B$ - prove to be very sensitive to the specific scale s...
Decay Constants of Beauty Mesons from QCD Sum Rules
Lucha Wolfgang
2014-01-01
Full Text Available Our recently completed analysis of the decay constants of both pseudoscalar and vector beauty mesons reveals that in the bottom-quark sector two specific features of the sum-rule predictions show up: (i For the input value of the bottom-quark mass in the M̅S̅ scheme m̅b(m̅b ≈ 4:18 GeV; the sum-rule result fB ≈ 210–220 MeV for the B meson decay constant is substantially larger than the recent lattice-QCD finding fB ≈ 190 MeV: Requiring QCD sum rules to reproduce the lattice-QCD value of fB yields a significantly larger b-quark mass: m̅b(m̅b = 4:247 GeV: (ii Whereas QCD sum-rule predictions for the charmed-meson decay constants fD; fDs, fD* and fDs* are practically independent of the choice of renormalization scale, in the beauty sector the results for the decay constants—and especially for the ratio fB* / fB—prove to be very sensitive to the specific scale setting.
Beauty Vector Meson Decay Constants from QCD Sum Rules
Lucha, Wolfgang; Simula, Silvano
2016-01-01
We present the outcomes of a very recent investigation of the decay constants of nonstrange and strange heavy-light beauty vector mesons, with special emphasis on the ratio of any such decay constant to the decay constant of the corresponding pseudoscalar meson, by means of Borel-transformed QCD sum rules. Our results suggest that both these ratios are below unity.
QCD sum rule studies at finite density and temperature
Kwon, Youngshin
2010-01-21
In-medium modifications of hadronic properties have a strong connection to the restoration of chiral symmetry in hot and/or dense medium. The in-medium spectral functions for vector and axial-vector mesons are of particular interest in this context, considering the experimental dilepton production data which signal the in-medium meson properties. In this thesis, finite energy sum rules are employed to set constraints for the in-medium spectral functions of vector and axial-vector mesons. Finite energy sum rules for the first two moments of the spectral functions are investigated with emphasis on the role of a scale parameter related to the spontaneous chiral symmetry breaking in QCD. It is demonstrated that these lowest moments of vector current spectral functions do permit an accurate sum rule analysis with controlled inputs, such as the QCD condensates of lowest dimensions. In contrast, the higher moments contain uncertainties from the higher dimensional condensates. It turns out that the factorization approximation for the four-quark condensate is not applicable in any of the cases studied in this work. The accurate sum rules for the lowest two moments of the spectral functions are used to clarify and classify the properties of vector meson spectral functions in a nuclear medium. Possible connections with the Brown-Rho scaling hypothesis are also discussed. (orig.)
Beauty vector meson decay constants from QCD sum rules
Lucha, Wolfgang [Institute for High Energy Physics, Austrian Academy of Sciences, Nikolsdorfergasse 18, A-1050 Vienna (Austria); Melikhov, Dmitri [Institute for High Energy Physics, Austrian Academy of Sciences, Nikolsdorfergasse 18, A-1050 Vienna (Austria); D. V. Skobeltsyn Institute of Nuclear Physics, M. V. Lomonosov Moscow State University, 119991, Moscow (Russian Federation); Simula, Silvano [Istituto Nazionale di Fisica Nucleare, Sezione di Roma Tre, Via della Vasca Navale 84, I-00146, Roma (Italy)
2016-01-22
We present the outcomes of a very recent investigation of the decay constants of nonstrange and strange heavy-light beauty vector mesons, with special emphasis on the ratio of any such decay constant to the decay constant of the corresponding pseudoscalar meson, by means of Borel-transformed QCD sum rules. Our results suggest that both these ratios are below unity.
Renormalisation Group Corrections to Neutrino Mixing Sum Rules
Gehrlein, J; Spinrath, M; Titov, A V
2016-01-01
Neutrino mixing sum rules are common to a large class of models based on the (discrete) symmetry approach to lepton flavour. In this approach the neutrino mixing matrix $U$ is assumed to have an underlying approximate symmetry form $\\tilde{U}_{\
Dibaryon decay sum rules and other multiquark states
Polanco-Euán, E N; Sánchez-Colón, G; Bambah, B A
2015-01-01
The decays of the antisymmetric dibaryon octet $D(8_F)$ into two baryon octets are considered. Sum rules for these decays in first order broken SU(3) are given. An SU(4) extension of the analysis is commented upon. Possibilities for the experimental observation of multibaryon and anti-multibaryon states is pointed out.
Beauty vector meson decay constants from QCD sum rules
Lucha, Wolfgang; Melikhov, Dmitri; Simula, Silvano
2016-01-01
We present the outcomes of a very recent investigation of the decay constants of nonstrange and strange heavy-light beauty vector mesons, with special emphasis on the ratio of any such decay constant to the decay constant of the corresponding pseudoscalar meson, by means of Borel-transformed QCD sum rules. Our results suggest that both these ratios are below unity.
Perturbative corrections to zero recoil inclusive B decay sum rules
Kapustin, A A; Wise, M B; Grinstein, B; Kapustin, Anton; Ligeti, Zoltan; Wise, Mark B; Grinstein, Benjamin
1996-01-01
Comparing the result of inserting a complete set of physical states in a time ordered product of b decay currents with the operator product expansion gives a class of zero recoil sum rules. They sum over physical states with excitation energies less than \\Delta, where \\Delta is much greater than the QCD scale and much less than the heavy charm and bottom quark masses. These sum rules have been used to derive an upper bound on the zero recoil limit of the B\\to D^* form-factor, and on the matrix element of the kinetic energy operator between B meson states. Perturbative corrections to the sum rules of order \\alpha_s(\\Delta) \\Delta^2/m_{c,b}^2 have previously been computed. We calculate the corrections of order \\alpha_s(\\Delta) and \\alpha_s^2(\\Delta) \\beta_0 keeping all orders in \\Delta/m_{c,b}, and show that these perturbative QCD corrections suppressed by powers of \\Delta/m_{c,b} significantly weaken the upper bound on the zero recoil B\\to D^* form-factor, and also on the kinetic energy operator's matrix eleme...
Improved light quark masses from pseudoscalar sum rules
Stephan Narison
2014-11-01
Full Text Available Using ratios of the inverse Laplace transform sum rules within stability criteria for the subtraction point μ in addition to the ones of the usual τ spectral sum rule variable and continuum threshold tc, we extract the π(1300 and K(1460 decay constants to order αs4 of perturbative QCD by including power corrections up to dimension-six condensates, tachyonic gluon mass for an estimate of large order PT terms, instanton and finite width corrections. Using these inputs with enlarged generous errors, we extract, in a model-independent and conservative ways, the sum of the scale-independent renormalization group invariant (RGI quark masses (mˆu+mˆq:q≡d,s and the corresponding running masses (m¯u+m¯q evaluated at 2 GeV. By giving the value of the ratio mu/md, we deduce the running quark masses m¯u,d,s and condensate 〈u¯u¯〉 and the scale-independent mass ratios: 2ms/(mu+md and ms/md. Using the positivity of the QCD continuum contribution to the spectral function, we also deduce, from the inverse Laplace transform sum rules, for the first time to order αs4, new lower bounds on the RGI masses which are translated into the running masses at 2 GeV and into upper bounds on the running quark condensate 〈u¯u¯〉. Our results summarized in Table 3 and compared with our previous results and with recent lattice averages suggest that precise phenomenological determinations of the sum of light quark masses require improved experimental measurements of the π(1.3 and K(1.46 hadronic widths and/or decay constants which are the dominant sources of errors in the analysis.
Direct instantons, topological charge screening and QCD glueball sum rules
Forkel, H
2003-01-01
Nonperturbative Wilson coefficients of the operator product expansion (OPE) for the spin-0 glueball correlators are derived and analyzed. A systematic treatment of the direct instanton contributions is given, based on realistic instanton size distributions and renormalization at the operator scale. In the pseudoscalar channel, topological charge screening is identified as an additional source of (semi-) hard nonperturbative physics. The screening contributions are shown to be vital for consistency with the anomalous axial Ward identity, and previously encountered pathologies (positivity violations and the disappearance of the 0^{-+} glueball signal) are traced to their neglect. On the basis of the extended OPE, a comprehensive quantitative analysis of eight Borel-moment sum rules in both spin-0 glueball channels is then performed. The nonperturbative OPE coefficients turn out to be indispensable for consistent sum rules and for their reconciliation with the underlying low-energy theorems. The topological shor...
Ds(0±) Meson Spectroscopy in Gaussian Sum Rules
WEN Shui-Guo; LIU Jue-Ping
2009-01-01
Masses of the Ds(0±) mesons are investigated from a view-point of ordinary light-heavy system in the framework of the Gaussian sum rules, which are worked out by means of the Laplacian transformation to the usual Borel sum rules. Using the standard input of QCD non-perturbative parameters, the corresponding mass spectra and couplings of the currents to the Ds(0±) mesons are obtained. Our results are mDs(O-) = 1.968±0.016±0.003 GeV and mDs(0+) = 2.320±0.014v0.003 GeV, which are in good accordance with the experimental data, 1.969 GeV and 2.317 GeV.
Circulation-strain sum rule in stochastic magnetohydrodynamics.
Moriconi, L; Nobre, F A S
2002-03-01
We study probability density functions (PDFs) of the circulation of velocity and magnetic fields in magnetohydrodynamics, computed for a circular contour within inertial range scales. The analysis is based on the instanton method as adapted to the Martin-Siggia-Rose field theory formalism. While in the viscous limit the expected Gaussian behavior of fluctuations is indeed verified, the case of vanishing viscosity is not suitable of a direct saddle-point treatment. To study the latter limit, we take into account fluctuations around quasistatic background fields, which allows us to derive a sum rule relating PDFs of the circulation observables and the rate of the strain tensor. A simple inspection of the sum rule definition leads straightforwardly to the algebraic decay rho(Gamma)-1/Gamma(2) at the circulation PDF tails.
Uraltsev Sum Rule in Bakamjian-Thomas Quark Models addendum
Le Yaouanc, A; Oliver, L; Pène, O; Raynal, J C
2001-01-01
In previous work it has been shown that, either from a sum rule for the subleading Isgur-Wise function $\\xi_3(1)$ or from a combination of Uraltsev and Bjorken SR, one infers for $P$-wave states $|\\tau_{1/2}(1)| \\ll |\\tau_{3/2}(1)|$. This implies, in the heavy quark limit of QCD, a hierarchy for the {\\it production} rates of $P$-states $\\Gamma(\\bar{B}_d \\to D ({1 \\over 2}) \\ell \
Magnetic absorption dichroism and sum rules in itinerant magnets
Strange, Paul
1994-01-01
In this letter we discuss X-ray magnetic dichroism in magnetic materials where an itinerant model of the magnetic behaviour is appropriate. Inspired by progress made in interpreting dichroism spectra in a localized approach, we show that dichroism spectra are an excellent measure of the orbital and spin magnetic moments in itinerant magnets. By performing an energy decomposition of the sum rules we show that the structure found in dichroism spectra reflects the energy dependence of the magnet...
Axial Vector Current Matrix Elements and QCD Sum Rules
Pasupathy, J; Singh, Ritesh K.
2003-01-01
The matrix element of the isoscalar axial vector current, $\\bar{u}\\gamma_\\mu\\gamma_5u + \\bar{d}\\gamma_\\mu\\gamma_5d $, between nucleon states is computed using the external field QCD sum rule method. The external field induced correlator, $$, is calculated from the spectrum of the isoscalar axial vector meson states. Since it is difficult to ascertain, from QCD sum rule for hyperons, the accuracy of validity of flavour SU(3) symmetry in hyperon decays when strange quark mass is taken into account, we rely on the empirical validity of Cabbibo theory to dertermine the matrix element $\\bar{u}\\gamma_{\\mu}\\gamma_5 u + \\bar{d}\\gamma_{\\mu}\\gamma_5 d - 2 \\bar{s}\\gamma_{\\mu}\\gamma_5 s$ between nucleon states. Combining with our calculation of $\\bar{u}\\gamma_{\\mu}\\gamma_5 u + \\bar{d}\\gamma_{\\mu}\\gamma_5 d$ and the well known nucleon $\\beta$-decay constant allows us to determine $$ occuring in the Bjorken sum rule. The result is in reasonable agreement with experiment. We also discuss the role of the anomaly in maintaini...
Evaluating chiral symmetry restoration through the use of sum rules
Rapp Ralf
2012-11-01
Full Text Available We pursue the idea of assessing chiral restoration via in-medium modifications of hadronic spectral functions of chiral partners. The usefulness of sum rules in this endeavor is illustrated, focusing on the vector/axial-vector channel. We first present an update on obtaining quantitative results for pertinent vacuum spectral functions. These serve as a basis upon which the in-medium spectral functions can be constructed. A novel feature of our analysis of the vacuum spectral functions is the need to include excited resonances, dictated by satisfying the Weinberg-type sum rules. This includes excited states in both the vector and axial-vector channels.We also analyze the QCD sum rule for the finite temperature vector spectral function, based on a ρ spectral function tested in dilepton data which develops a shoulder at low energies.We find that the ρ′ peak flattens off which may be a sign of chiral restoration, though a study of the finite temperature axial-vector spectral function remains to be carried out.
Radiative corrections to the solar lepton mixing sum rule
Zhang, Jue; Zhou, Shun
2016-08-01
The simple correlation among three lepton flavor mixing angles ( θ 12, θ 13, θ 23) and the leptonic Dirac CP-violating phase δ is conventionally called a sum rule of lepton flavor mixing, which may be derived from a class of neutrino mass models with flavor symmetries. In this paper, we consider the solar lepton mixing sum rule θ 12 ≈ θ 12 ν + θ 13 cos δ, where θ 12 ν stems from a constant mixing pattern in the neutrino sector and takes the value of θ 12 ν = 45 ° for the bi-maximal mixing (BM), {θ}_{12}^{ν } = { tan}^{-1}(1/√{2}) ≈ 35.3° for the tri-bimaximal mixing (TBM) or {θ}_{12}^{ν } = { tan}^{-1}(1/√{5+1}) ≈ 31.7° for the golden-ratio mixing (GR), and investigate the renormalization-group (RG) running effects on lepton flavor mixing parameters when this sum rule is assumed at a superhigh-energy scale. For illustration, we work within the framework of the minimal supersymmetric standard model (MSSM), and implement the Bayesian approach to explore the posterior distribution of δ at the low-energy scale, which becomes quite broad when the RG running effects are significant. Moreover, we also discuss the compatibility of the above three mixing scenarios with current neutrino oscillation data, and observe that radiative corrections can increase such a compatibility for the BM scenario, resulting in a weaker preference for the TBM and GR ones.
Electric-dipole sum rule in nuclear matter
Fabrocini, A.; Fantoni, S.
1985-03-01
The enhancement factor K in the electric-dipole sum rule for some realistic models of symmetrical nuclear matter is calculated using variational theory. The nuclear-matter wave function used contains central, spin, isospin, tensor and spin-orbit pair correlations. The non-central correlations, particularly the tensor one, give the major contribution to K. At experimental equilibrium density K. turns out to be ≈ 1.8, of which 65% comes from OPEP and 30% from the short-range part of the interaction. The two-pion-exchange three-nucleon interaction contributes ≈ 0.2% and is cancelled, to a large extent, by the contribution due to the intermediate-range two-body potential. The relationship of the summed oscillator strength with the effective mass is also discussed.
Improved light quark masses from pseudoscalar sum rules
Narison, Stephan, E-mail: snarison@yahoo.fr
2014-11-10
Using ratios of the inverse Laplace transform sum rules within stability criteria for the subtraction point μ in addition to the ones of the usual τ spectral sum rule variable and continuum threshold t{sub c}, we extract the π(1300) and K(1460) decay constants to order α{sub s}{sup 4} of perturbative QCD by including power corrections up to dimension-six condensates, tachyonic gluon mass for an estimate of large order PT terms, instanton and finite width corrections. Using these inputs with enlarged generous errors, we extract, in a model-independent and conservative ways, the sum of the scale-independent renormalization group invariant (RGI) quark masses (m{sup ^}{sub u}+m{sup ^}{sub q}):q≡d,s and the corresponding running masses (m{sup ¯}{sub u}+m{sup ¯}{sub q}) evaluated at 2 GeV. By giving the value of the ratio m{sub u}/m{sub d}, we deduce the running quark masses m{sup ¯}{sub u,d,s} and condensate 〈u{sup ¯}u{sup ¯}〉 and the scale-independent mass ratios: 2m{sub s}/(m{sub u}+m{sub d}) and m{sub s}/m{sub d}. Using the positivity of the QCD continuum contribution to the spectral function, we also deduce, from the inverse Laplace transform sum rules, for the first time to order α{sub s}{sup 4}, new lower bounds on the RGI masses which are translated into the running masses at 2 GeV and into upper bounds on the running quark condensate 〈u{sup ¯}u{sup ¯}〉. Our results summarized in Table 3 and compared with our previous results and with recent lattice averages suggest that precise phenomenological determinations of the sum of light quark masses require improved experimental measurements of the π(1.3) and K(1.46) hadronic widths and/or decay constants which are the dominant sources of errors in the analysis.
Analysis of the scalar nonet mesons with QCD sum rules
Wang, Zhi-Gang [North China Electric Power University, Department of Physics, Baoding (China)
2016-08-15
In this article, we assume that the nonet scalar mesons below 1 GeV are the two-quark-tetraquark mixed states and study their masses and pole residues using the QCD sum rules. In the calculation, we take into account the vacuum condensates up to dimension 10 and the O(α{sub s}) corrections to the perturbative terms in the operator product expansion. We determine the mixing angles, which indicate the two-quark components are much larger than 50 %, then we obtain the masses and pole residues of the nonet scalar mesons. (orig.)
Light-cone sum rule approach for Baryon form factors
Offen, Nils
2016-01-01
We present the state-of-the-art of the light-cone sum rule approach to Baryon form factors. The essence of this approach is that soft Feynman contributions are calculated in terms of small transverse distance quantities using dispersion relations and duality. The form factors are thus expressed in terms of nucleon wave functions at small transverse separations, called distribution amplitudes, without any additional parameters. The distribution amplitudes, therefore, can be extracted from the comparison with the experimental data on form factors and compared to the results of lattice QCD simulations.
Light-Cone Sum Rule Approach for Baryon Form Factors
Offen, Nils
2016-10-01
We present the state-of-the-art of the light-cone sum rule approach to Baryon form factors. The essence of this approach is that soft Feynman contributions are calculated in terms of small transverse distance quantities using dispersion relations and duality. The form factors are thus expressed in terms of nucleon wave functions at small transverse separations, called distribution amplitudes, without any additional parameters. The distribution amplitudes, therefore, can be extracted from the comparison with the experimental data on form factors and compared to the results of lattice QCD simulations.
Study of Doubly Heavy Baryon Spectrum via QCD Sum Rules
TANG Liang; YUAN Xu-Hao; QIAO Cong-Feng; LI Xue-Qian
2012-01-01
In this work, we calculate the mass spectrum of doubly heavy baryons with the diquaxk model in terms of the QCD sum rules. The interpolating currents are composed of a heavy diquaxk field and a light quark field. Contributions of the operators up to dimension six are taken into account in the operator product expansion. Within a reasonable error tolerance, our numerical results axe compatible with other theoretical predictions. This indicates that the diquaxk picture reflects the reality and is applicable to the study of doubly heavy baryons.
QCD Sum Rules: Intercrossed Relations for Sigma^0 and Lambda Magnetic Moments
Özpineci, A; Zamiralov, V S
2003-01-01
New relations between QCD Borel sum rules for magnetic moments of Sigma^0 and Lambda hyperons are constructed. It is shown that starting from the sum rule for the Sigma^0 hyperon magnetic moment it is straightforward to obtain the corresponding sum rule for the Lambda hyperon magnetic moment et vice versa.
QCD Sum Rules: Intercrossed Relations for the Sigma^0-Lambda Mass Splitting
Zamiralov, V S
2003-01-01
New relations between QCD Borel sum rules for masses of Sigma^0 and Lambda hyperons are constructed. It is shown that starting from the sum rule for the Sigma^0 hyperon mass it is straightforward to obtain the corresponding sum rule for the Lambda hyperon mass and vice versa.
Connections between chiral Lagrangians and QCD sum-rules
Fariborz, Amir H; Steele, T G
2016-01-01
It is shown how a chiral Lagrangian framework can be used to derive relationships connecting quark-level QCD correlation functions to mesonic-level two-point functions. Crucial ingredients of this connection are scale factor matrices relating each distinct quark-level substructure (e.g., quark-antiquark, four-quark) to its mesonic counterpart. The scale factors and mixing angles are combined into a projection matrix to obtain the physical (hadronic) projection of the QCD correlation function matrix. Such relationships provide a powerful bridge between chiral Lagrangians and QCD sum-rules that are particularly effective in studies of the substructure of light scalar mesons with multiple complicated resonance shapes and substantial underlying mixings. The validity of these connections is demonstrated for the example of the isotriplet $a_0(980)$-$a_0(1450)$ system, resulting in an unambiguous determination of the scale factors from the combined inputs of QCD sum-rules and chiral Lagrangians. These scale factors ...
Bottom mass from nonrelativistic sum rules at NNLL
Stahlhofen, Maximilian
2013-01-15
We report on a recent determination of the bottom quark mass from nonrelativistic (large-n) {Upsilon} sum rules with renormalization group improvement (RGI) at next-to-next-to-leading logarithmic (NNLL) order. The comparison to previous fixed-order analyses shows that the RGI computed in the vNRQCD framework leads to a substantial stabilization of the theoretical sum rule moments with respect to scale variations. A single moment fit (n=10) to the available experimental data yields M{sub b}{sup 1S}=4.755{+-}0.057{sub pert}{+-}0.009{sub {alpha}{sub s}}{+-}0.003{sub exp} GeV for the bottom 1S mass and anti m{sub b}(anti m{sub b})=4.235{+-}0.055{sub pert}{+-}0.003{sub exp} GeV for the bottom MS mass. The quoted uncertainties refer to the perturbative error and the uncertainties associated with the strong coupling and the experimental input.
Spectral sum rules and search for periodicities in DNA sequences
Chechetkin, V.R., E-mail: chechet@biochip.r [Theoretical Department of Division for Perspective Investigations, Troitsk Institute of Innovation and Thermonuclear Investigations (TRINITI), Troitsk, 142190 Moscow Region (Russian Federation)
2011-04-18
Periodic patterns play the important regulatory and structural roles in genomic DNA sequences. Commonly, the underlying periodicities should be understood in a broad statistical sense, since the corresponding periodic patterns have been strongly distorted by the random point mutations and insertions/deletions during molecular evolution. The latent periodicities in DNA sequences can be efficiently displayed by Fourier transform. The criteria of significance for observed periodicities are obtained via the comparison versus the counterpart characteristics of the reference random sequences. We show that the restrictions imposed on the significance criteria by the rigorous spectral sum rules can be rationally described with De Finetti distribution. This distribution provides the convenient intermediate asymptotic form between Rayleigh distribution and exact combinatoric theory. - Highlights: We study the significance criteria for latent periodicities in DNA sequences. The constraints imposed by sum rules can be described with De Finetti distribution. It is intermediate between Rayleigh distribution and exact combinatoric theory. Theory is applicable to the study of correlations between different periodicities. The approach can be generalized to the arbitrary discrete Fourier transform.
Thermal Properties of Light Tensor Mesons via QCD Sum Rules
K. Azizi
2015-01-01
Full Text Available The thermal properties of f2(1270, a2(1320, and K2*(1430 light tensor mesons are investigated in the framework of QCD sum rules at finite temperature. In particular, the masses and decay constants of the light tensor mesons are calculated taking into account the new operators appearing at finite temperature. The numerical results show that, at the point at which the temperature-dependent continuum threshold vanishes, the decay constants decrease with amount of (70–85% compared to their vacuum values, while the masses diminish about (60–72% depending on the kinds of the mesons under consideration. The results obtained at zero temperature are in good consistency with the experimental data as well as the existing theoretical predictions.
The $\\omega DD$ vertex in a Sum Rule approach
Holanda, L B; Mihara, A
2007-01-01
The study of charmonium dissociation in heavy ion collisions is generally performed in the framework of effective Lagrangians with meson exchange. Some studies are also developed with the intention of calculate form factors and coupling constants related with charmed and light mesons. These quantities are important in the evaluation of charmonium cross sections. In this paper we present a calculation of the $\\omega DD$ vertex that is a possible interaction vertex in some meson-exchange models spread in the literature. We used the standard method of QCD Sum Rules in order to obtain the vertex form factor as a function of the transferred momentum. Our results are compatible with the value of this vertex form factor (at zero momentum transfer) obtained in the vector-meson dominance model.
QCD phase diagram from finite energy sum rules
Ayala, Alejandro; Dominguez, C A; Gutierrez, Enif; Loewe, M; Raya, Alfredo
2011-01-01
We study the QCD phase diagram at finite temperature and baryon chemical potential by relating the behavior of the light-quark condensate to the threshold energy for the onset of perturbative QCD. These parameters are connected to the chiral symmetry restoration and the deconfinement phase transition, respectively. This relation is obtained in the framework of finite energy QCD sum rules at finite temperature and density, with input from Schwinger-Dyson methods to determine the light-quark condensate. Results indicate that both critical temperatures are basically the same within some 3% accuracy. We also obtain bounds for the position of the critical end point, mu_{B c} >~ 300 MeV and T_c <~ 185 MeV.
Spectral sum rules and search for periodicities in DNA sequences
Chechetkin, V. R.
2011-04-01
Periodic patterns play the important regulatory and structural roles in genomic DNA sequences. Commonly, the underlying periodicities should be understood in a broad statistical sense, since the corresponding periodic patterns have been strongly distorted by the random point mutations and insertions/deletions during molecular evolution. The latent periodicities in DNA sequences can be efficiently displayed by Fourier transform. The criteria of significance for observed periodicities are obtained via the comparison versus the counterpart characteristics of the reference random sequences. We show that the restrictions imposed on the significance criteria by the rigorous spectral sum rules can be rationally described with De Finetti distribution. This distribution provides the convenient intermediate asymptotic form between Rayleigh distribution and exact combinatoric theory.
On properties of the exotic hadrons from QCD sum rules
Lucha Wolfgang
2016-01-01
Full Text Available We discuss the specific features of extracting properties of the exotic polyquark hadrons (tetraquarks, pentaquarks compared to the usual hadrons by the QCD sum-rule approach. In the case of the ordinary hadrons, already the one-loop leading-order O(α0s correlation functions provide the bulk of the hadron observables, e.g., of the form factor; inclusion of radiative corrections O(αs modifies already nonzero one-loop contributions. In the case of an exotic hadron, the situation is qualitatively different: discussing strong decays of an exotic tetraquark meson, which provide the main contribution to its width, we show that the disconnected leading-order diagrams are not related to the tetraquark properties. For a proper description of the tetraquark decay width, it is mandatory to calculate specific radiative corrections which generate the connected diagrams.
Optical sum rule anomalies in high-temperature superconductors
Toschi, Alessandro; Sangiovanni, Giorgio; Held, Karsten [Institut fuer Festkoerperphysik, Technische Universitaet Wien (Austria); Capone, Massimo [Dipartimento di Fisica, Universita ' ' La Sapienza' ' , Roma (Italy); SMC, CNR-INFM, Roma (Italy); Castellani, Claudio [Dipartimento di Fisica, Universita ' ' La Sapienza' ' , Roma (Italy)
2009-07-01
Many unusual features recently observed in the optical spectroscopy experiments in the cuprates can be simply understood as arising from the vicinity to the Mott transition, without invoking more involved and exotic mechanisms. Specifically, we compare calculations based on the Dynamical Mean Field Theory (DMFT) of the Hubbard model with the optical spectral weight W{sub opt} of different cuprates, explaining most of the anomalies found in the optical sum rules with respect to normal metals, including the existence of two different energy scales for the doping- and the T-dependence of W{sub opt}. A further support to this result is provided by the analysis of the optical conductivity in a typical case of the Mott-Hubbard metal-insulator transition, namely the V{sub 2}O{sub 3}.
QCD Sum Rule Studies of Heavy Quarkonium-like States
Kleiv, Robin
2014-01-01
The research presented here uses QCD sum rules (QSR) to study exotic hadrons. There are several themes in this work. First is the use of QSR to predict the masses of exotic hadrons that may exist among the heavy quarkonium-like states. The second theme is the application of sophisticated loop integration methods in order to obtain more complete theoretical results. These in turn can be extended to higher orders in the perturbative expansion in order to predict the properties of exotic hadrons more accurately. The third theme involves developing a renormalization methodology for these higher order calculations. This research has implications for the $Y(3940)$, $X(3872)$, $Z_c^\\pm\\left(3895\\right)$, $Y_b\\left(10890\\right)$, $Z_b^{\\pm}(10610)$ and $Z_b^{\\pm}(10650)$ particles, thereby contributing to the ongoing effort to understand these and other heavy quarkonium-like states.
Holographic RG flows, entanglement entropy and the sum rule
Casini, Horacio; Torroba, Gonzalo
2015-01-01
We calculate the two-point function of the trace of the stress tensor in holographic renormalization group flows between pairs of conformal field theories. We show that the term proportional to the momentum squared in this correlator gives the change of the central charge between fixed points in d=2 and in d>2 it gives the holographic entanglement entropy for a planar region. This can also be seen as a holographic realization of the Adler-Zee formula for the renormalization of Newton's constant. Holographic regularization is found to provide a perfect match of the finite and divergent terms of the sum rule, and it is analogous to the regularization of the entropy in terms of mutual information. Finally, we provide a general proof of reflection positivity in terms of stability of the dual bulk action, and discuss the relation between unitarity constraints, the null energy condition and regularity in the interior of the gravity solution.
The DHG sum rule measured with medium energy photons
Hicks, K.; Ardashev, K. [Ohio Univ., Athens, OH (United States); Babusci, D. [INFN-Lab. Nazionali di Frascati (Italy)] [and others
1997-12-31
The structure of the nucleon has many important features that are yet to be uncovered. Of current interest is the nucleon spin-structure which can be measured by doing double-polarization experiments with photon beams of medium energies (0.1 to 2 GeV). One such experiment uses dispersion relations, applied to the Compton scattering amplitude, to relate measurement of the total reaction cross section integrated over the incident photon energy to the nucleon anomalous magnetic moment. At present, no single facility spans the entire range of photon energies necessary to test this sum rule. The Laser-Electron Gamma Source (LEGS) facility will measure the double-polarization observables at photon energies between 0.15--0.47 MeV. Either the SPring8 facility, the GRAAL facility (France), or Jefferson Laboratory could make similar measurements at higher photon energies. A high-precision measurement of the spin-polarizability and the Drell-Hearn-Gerasimov sum rule is now possible with the advent of high-polarization solid HD targets at medium energy polarized photon facilities such as LEGS, GRAAL and SPring8. Other facilities with lower polarization in either the photon beam or target (or both) are also pursuing these measurements because of the high priority associated with this physics. The Spin-asymmetry (SASY) detector that will be used at LEGS has been briefly outlined in this paper. The detector efficiencies have been explored with simulations studies using the GEANT software, with the result that both charged and uncharged pions can be detected with a reasonable efficiency (> 30%) over a large solid angle. Tracking with a TPC, which will be built at LEGS over the next few years, will improve the capabilities of these measurements.
Spin-1 charmonium-like states in QCD sum rule
Chen, Wei
2012-01-01
We study the possible spin-1 charmonium-like states by using QCD sum rule approach. We calculate the two-point correlation functions for all the local form tetraquark interpolating currents with $J^{PC}=1^{--}, 1^{-+}, 1^{++}$ and $1^{+-}$ and extract the masses of the tetraquark charmonium-like states. The mass of the $1^{--}$ $qc\\bar q\\bar c$ state is $4.6\\sim4.7$ GeV, which implies a possible tetraquark interpretation for Y(4660) meson. The masses for both the $1^{++}$ $qc\\bar q\\bar c$ and $sc\\bar s\\bar c$ states are $4.0\\sim 4.2$ GeV, which is slightly above the mass of X(3872). For the $1^{-+}$ and $1^{+-}$ $qc\\bar q\\bar c$ states, the extracted masses are $4.5\\sim4.7$ GeV and $4.0\\sim 4.2$ GeV respectively.
Spin-1 charmonium-like states in QCD sum rule
Chen Wei
2012-02-01
Full Text Available We study the possible spin-1 charmonium-like states by using QCD sum rule approach.We calculate the two-point correlation functions for all the local form tetraquark interpolating currents with JPC = 1−− 1−+, 1++ and 1+− and extract the masses of these tetraquark charmonium-like states. The mass of the 1−− qc$ar{q}$q¯$ar{c}$c¯ state is 4.6 ~ 4.7 GeV, which implies a possible tetraquark interpretation for Y(4660 meson. The masses for both the 1++ qc$ar{q}$q¯$ar{c}$c¯ and sc$ar{s}$s¯$ar{c}$c¯ states are 4.0 ~ 4.2 GeV, which is slightly above the mass of X(3872. For the 1−+ and 1+− qc$ar{q}$q¯ $ar{c}$c¯ states, the extracted masses are 4.5 ~ 4.7 GeV and 4.0 ~ 4.2 GeV respectively.
The leptonic Dirac CP-violating phase from sum rules
Girardi, I.; Petcov, S. T.; Titov, A. V.
2016-05-01
In the reference 3-neutrino mixing scheme with three light massive neutrinos, CP-violating effects in neutrino oscillations can be caused by the Dirac CP-violating phase δ present in the unitary neutrino mixing matrix U. Using the fact that U = U†eUv , where Ue and Uv are unitary matrices arising from the diagonalisation, respectively, of the charged lepton and neutrino mass matrices, we consider in a systematic way forms of Ue and Uv allowing us to express δ as a function of the neutrino mixing angles present in U and the angles contained in Uv. After obtaining sum rules for cos δ, we consider several forms of Uv dictated by, or associated with, symmetries, such as tri-bimaximal, bimaximal, etc., for which the angles in Uv are fixed. For each of these forms and forms of Ue allowing to reproduce the measured values of the neutrino mixing angles, we construct the likelihood function for cos δ, using the prospective uncertainties in the determination of the mixing angles. Our results show that the measurement of δ along with improvement of the precision on the neutrino mixing angles can provide unique information about the possible existence of a new fundamental symmetry in the lepton sector.
QCD sum rule study of hidden-charm pentaquarks
Chen, Hua-Xing; Chen, Wei; Steele, T G; Liu, Xiang; Zhu, Shi-Lin
2016-01-01
We study the mass spectra of hidden-charm pentaquarks having spin $J = {1\\over2},{3\\over2},{5\\over2}$ and quark contents $uud c \\bar c$. We systematically construct all the relevant local hidden-charm pentaquark currents, and select some of them to perform QCD sum rule analyses. We find that the $P_c(4380)$ and $P_c(4450)$ can be identified as hidden-charm pentaquark states composed of an anti-charmed meson and a charmed baryon. We also find the lowest-lying hidden-charm $J^P = 1/2^-$ pentaquark state of mass $4.33^{+0.17}_{-0.13}$ GeV, while the $J^P = 1/2^+$ mass prediction of 4.7--4.9 GeV is significantly higher. Similarly, the lowest-lying hidden-charm $J^P = 3/2^-$ pentaquark state mass is $4.37^{+0.18}_{-0.13}$ GeV, consistent with the $J^P = 3/2^-$ $P_c(4380)$, while the $J^P = 3/2^+$ is also significantly higher with a mass above 4.6 GeV. The hidden-charm $J^P = 5/2^-$ pentaquark state mass is 4.5--4.6 GeV, slightly larger than the $J^P = 5/2^+$ $P_c(4450)$.
Evaluation of the Axial Vector Commutator Sum Rule for Pion-Pion Scattering
Adler, Stephen L
2007-01-01
We consider the sum rule proposed by one of us (SLA), obtained by taking the expectation value of an axial vector commutator in a state with one pion. The sum rule relates the pion decay constant to integrals of pion-pion cross sections, with one pion off the mass shell. We remark that recent data on pion-pion scattering allow a precise evaluation of the sum rule. We also discuss the related Adler--Weisberger sum rule (obtained by taking the expectation value of the same commutator in a state with one nucleon), especially in connection with the problem of extrapolation of the pion momentum off its mass shell.
QCD sum rule study of hidden-charm pentaquarks
Chen, Hua-Xing; Cui, Er-Liang [Beihang University, School of Physics and Beijing Key Laboratory of Advanced Nuclear Materials and Physics, Beijing (China); Chen, Wei; Steele, T.G. [University of Saskatchewan, Department of Physics and Engineering Physics, Saskatoon, Saskatchewan (Canada); Liu, Xiang [Lanzhou University, School of Physical Science and Technology, Lanzhou (China); Lanzhou University and Institute of Modern Physics of CAS, Research Center for Hadron and CSR Physics, Lanzhou (China); Zhu, Shi-Lin [Peking University, School of Physics and State Key Laboratory of Nuclear Physics and Technology, Beijing (China); Collaborative Innovation Center of Quantum Matter, Beijing (China); Peking University, Center of High Energy Physics, Beijing (China)
2016-10-15
We study the mass spectra of hidden-charm pentaquarks having spin J = (1)/(2)/(3)/(2)/(5)/(2) and quark contents uudc anti c. We systematically construct all the relevant local hidden-charm pentaquark currents, and we select some of them to perform QCD sum rule analyses. We find that the P{sub c}(4380) and P{sub c}(4450) can be identified as hidden-charm pentaquark states composed of an anti-charmed meson and a charmed baryon. Besides them, we also find (a) the lowest-lying hidden-charm pentaquark state of J{sup P} = 1/2{sup -} has the mass 4.33{sup +0.17}{sub -0.13} GeV, while the one of J{sup P} = 1/2{sup +} is significantly higher, that is, around 4.7-4.9 GeV; (b) the lowest-lying hidden-charm pentaquark state of J{sup P} = 3/2{sup -} has the mass 4.37{sup +0.18}{sub -0.13} GeV, consistent with the P{sub c}(4380) of J{sup P} = 3/2{sup -}, while the one of J{sup P} = 3/2{sup +} is also significantly higher, that is, above 4.6 GeV; (c) the hidden-charm pentaquark state of J{sup P} = 5/2{sup -} has a mass around 4.5-4.6 GeV, slightly larger than the P{sub c}(4450) of J{sup P} = 5/2{sup +}. (orig.)
Constraints on Airy function zeros from quantum-mechanical sum rules
Belloni, M
2010-01-01
We derive new constraints on the zeros of Airy functions by using the so-called quantum bouncer system to evaluate quantum-mechanical sum rules and perform perturbation theory calculations for the Stark effect. Using commutation and completeness relations, we show how to systematically evaluate sums of the form $S_{p}(n) = \\sum_{k \
The Bethe Sum Rule and Basis Set Selection in the Calculation of Generalized Oscillator Strengths
Cabrera-Trujillo, Remigio; Sabin, John R.; Oddershede, Jens;
1999-01-01
Fulfillment of the Bethe sum rule may be construed as a measure of basis set quality for atomic and molecular properties involving the generalized oscillator strength distribution. It is first shown that, in the case of a complete basis, the Bethe sum rule is fulfilled exactly in the random phase...
Sum rules and moments for lepton-pair production. [Cross sections, Drell--Yan formula
Hwa, R.C.
1978-01-01
Sum rules on lepton-pair production cross sections are derived on the bases of the Drell--Yan formula and the known sum rules in leptoproduction. Also exact relations are obtained between the average transverse momenta squared of the valence quarks and moments of the dilepton cross sections. 12 references.
Continuum contributions to dipole oscillator-strength sum rules for hydrogen in finite basis sets
Oddershede, Jens; Ogilvie, John F.; Sauer, Stephan P. A.;
2017-01-01
Calculations of the continuum contributions to dipole oscillator sum rules for hydrogen are performed using both exact and basis-set representations of the stick spectra of the continuum wave function. We show that the same results are obtained for the sum rules in both cases, but that the conver...
Lindhard's polarization parameter and atomic sum rules in the local plasma approximation
Cabrera-Trujillo, R.; Apell, P.; Oddershede, J.
2017-01-01
In this work, we analyze the effects of Lindhard polarization parameter, χ, on the sum rule, Sp, within the local plasma approximation (LPA) as well as on the logarithmic sum rule Lp = dSp/dp, in both cases for the system in an initial excited state. We show results for a hydrogenic atom with nuc...
Kuzyk, Mark G
2014-01-01
The Thomas Kuhn Reich sum rules and the sum-over-states (SOS) expression for the hyperpolarizabilities are truncated when calculating the fundamental limits of nonlinear susceptibilities. Truncation of the SOS expression can lead to an accurate approximation of the first and second hyperpolarizabilities due to energy denominators, which can make the truncated series converge to within 10% of the full series after only a few excited states are included in the sum. The terms in the sum rule series, however, are weighted by the state energies, so convergence of the series requires that the position matrix elements scale at most in inverse proportion to the square root of the energy. Even if the convergence condition is met, serious pathologies arise, including self inconsistent sum rules and equations that contradict reality. As a result, using the truncated sum rules alone leads to pathologies that make any rigorous calculations impossible, let alone yielding even good approximations. This paper discusses condi...
Gubler, Philipp; Satow, Daisuke
2016-11-01
We derive three exact sum rules for the spectral function of the electromagnetic current with zero spatial momentum at finite temperature. Two of them are derived in this paper for the first time. We explicitly check that these sum rules are satisfied in the weak coupling regime and examine which sum rule is sensitive to the transport peak in the spectral function at low energy or the continuum at high energy. Possible applications of the three sum rules to lattice computations of the spectral function and transport coefficients are also discussed: we propose an Ansatz for the spectral function that can be applied to all three sum rules and fit it to available lattice data of the Euclidean vector correlator above the critical temperature. As a result, we obtain estimates for both the electrical conductivity σ and the second-order transport coefficient τJ .
Exact vector channel sum rules at finite temperature and their applications to lattice QCD
Gubler, Philipp
2016-01-01
We derive three exact sum rules for the spectral function of the electromagnetic current with zero spatial momentum at finite temperature. Two of them are derived in this paper for the first time. We explicitly check that these sum rules are satisfied in the weak coupling regime and examine which sum rule is sensitive to the transport peak in the spectral function at low energy or the continuum at high energy. Possible applications of the three sum rules to lattice computations of the spectral function and transport coefficients are also discussed: We propose an ansatz for the spectral function that can be applied to all three sum rules and fit it to available lattice data of the Euclidean vector correlator above the critical temperature. As a result, we obtain estimates for both the electrical conductivity $\\sigma$ and the second order transport coefficient $\\tau_J$.
Renormalization group summation of Laplace QCD sum rules for scalar gluon currents
Farrukh Chishtie
2016-03-01
Full Text Available We employ renormalization group (RG summation techniques to obtain portions of Laplace QCD sum rules for scalar gluon currents beyond the order to which they have been explicitly calculated. The first two of these sum rules are considered in some detail, and it is shown that they have significantly less dependence on the renormalization scale parameter μ2 once the RG summation is used to extend the perturbative results. Using the sum rules, we then compute the bound on the scalar glueball mass and demonstrate that the 3 and 4-Loop perturbative results form lower and upper bounds to their RG summed counterparts. We further demonstrate improved convergence of the RG summed expressions with respect to perturbative results.
QCD sum rules for quark-gluon three-body components in the B meson
Nishikawa, Tetsuo
2011-01-01
We discuss the QCD sum rule calculation of the heavy-quark effective theory parameters, $\\lambda_E$ and $\\lambda_H$, which correspond to matrix elements representing quark-gluon three-body components in the $B$-meson wavefunction. We derive the sum rules for $\\lambda_{E,H}$ calculating the new higher-order QCD corrections, i.e., the order $\\alpha_s$ radiative corrections to the Wilson coefficients associated with the dimension-5 quark-gluon mixed condensates, and the power corrections due to the dimension-6 vacuum condensates. We find that the new radiative corrections significantly improve the stability of the corresponding Borel sum rules and lead to the reduction of the values of $\\lambda_{E,H}$. We also discuss the renormalization-group improvement for the sum rules and present update on the values of $\\lambda_{E,H}$.
Analytic structure of ϕ{sup 4} theory using light-by-light sum rules
Pauk, V. [PRISMA Cluster of Excellence, Johannes Gutenberg-Universität, Mainz (Germany); Institut für Kernphysik, Johannes Gutenberg-Universität, Mainz (Germany); Department of Physics, Taras Shevchenko National University of Kyiv (Ukraine); Pascalutsa, V. [PRISMA Cluster of Excellence, Johannes Gutenberg-Universität, Mainz (Germany); Institut für Kernphysik, Johannes Gutenberg-Universität, Mainz (Germany); Vanderhaeghen, M., E-mail: marcvdh@kph.uni-mainz.de [PRISMA Cluster of Excellence, Johannes Gutenberg-Universität, Mainz (Germany); Institut für Kernphysik, Johannes Gutenberg-Universität, Mainz (Germany)
2013-10-01
We apply a sum rule for the forward light-by-light scattering process within the context of the ϕ{sup 4} quantum field theory. As a consequence of the sum rule a stringent causality criterion is presented and the resulting constraints are studied within a particular resummation of graphs. Such resummation is demonstrated to be consistent with the sum rule to all orders of perturbation theory. We furthermore show the appearance of particular non-perturbative solutions within such approximation to be a necessary requirement of the sum rule. For a range of values of the coupling constant, these solutions manifest themselves as a physical bound state and a K-matrix pole. For another domain however, they appear as tachyon solutions, showing the inconsistency of the approximation in this region.
Is the Coulomb sum rule violated in nuclei?
Morgenstern, J
2001-01-01
Guided by the experimental confirmation of the validity of the Effective Momentum Approximation (EMA) in quasi-elastic scattering off nuclei, we have re-examined the extraction of the longitudinal and transverse response functions in medium-weight and heavy nuclei. In the EMA we have performed a Rosenbluth separation of the available world data on $^{40}$Ca, $^{48}$Ca, $^{56}$Fe, $^{197}$Au, $^{208}$Pb and $^{238}$U. We find that the longitudinal response function for these nuclei is "quenched" and that the Coulomb sum is not saturated, at odds with claims in the literature.
Sum Rules of Charm CP Asymmetries beyond the SU(3)$_F$ Limit
Müller, Sarah; Schacht, Stefan
2015-01-01
We find new sum rules between direct CP asymmetries in $D$ meson decays with coefficients that can be determined from a global fit to branching ratio data. Our sum rules eliminate the penguin topologies $P$ and $PA$, which cannot be determined from branching ratios. In this way we can make predictions about direct CP asymmetries in the Standard Model without ad-hoc assumptions on the sizes of penguin diagrams. We consistently include first-order SU(3)$_F$ breaking in the topological amplitudes extracted from the branching ratios. By confronting our sum rules with future precise data from LHCb and Belle II one will identify or constrain new-physics contributions to $P$ or $PA$. The first sum rule correlates the CP asymmetries $a_{CP}^{\\mathrm{dir}}$ in $D^0\\to K^+K^-$, $D^0\\to \\pi^+\\pi^-$, and $D^0\\to \\pi^0\\pi^0$. We study the region of the $a_{CP}^{\\mathrm{dir}}(D^0\\to \\pi^+\\pi^-)$--$a_{CP}^{\\mathrm{dir}} (D^0\\to \\pi^0\\pi^0)$ plane allowed by current data and find that our sum rule excludes more than half of ...
Spectral Density Functions and Their Sum Rules in an Effective Chiral Field Theory
Klevansky, S P
1997-01-01
The validity of Weinberg's two sum rules for massless QCD, as well as the six additional sum rules introduced into chiral perturbation theory by Gasser and Leutwyler, are investigated for the extended Nambu-Jona-Lasinio chiral model that includes vector and axial vector degrees of freedom. A detailed analysis of the vector, axial vector and coupled pion plus longitudinal axial vector modes is given. We show that, under Pauli-Villars regularization of the meson polarization amplitudes that determine the spectral density functions, all of the sum rules involving inverse moments higher than zero are automatically obeyed by the model spectral densities. By contrast, the zero moment sum rules acquire a non-vanishing right hand side that is proportional to the quark condensate density of the non-perturbative groundstate. We use selected sum rules in conjunction with other calculations to obtain explicit expressions for the scale-independent coupling constants $\\bar l_i$ of chiral perturbation theory in the combinat...
The hidden sterile neutrino and the (2+2) sum rule
Päs, H; Weiler, Thomas J
2003-01-01
We discuss oscillations of atmospheric and solar neutrinos into sterile neutrinos in the 2+2 scheme. A zeroth order sum rule requires equal probabilities for oscillation into nu_s and nu_tau in the solar+atmospheric data sample. Data does not favor this claim. Here we use scatter plots to assess corrections of the zeroth order sum rule when (i) the 4 x 4 neutrino mixing matrix assumes its full range of allowed values, and (ii) matter effects are included. We also introduce a related "product rule". We find that the sum rule is significantly relaxed, due to both the inclusion of the small mixing angles (which provide a short-baseline contribution) and to matter effects. The product rule is also dramatically altered. The observed relaxation of the sum rule weakens the case against the 2+2 model and the sterile neutrino. To invalidate the 2+2 model, a global fit to data with the small mixing angles included seems to be required.
Constraints on Airy function zeros from quantum-mechanical sum rules
Belloni, M.; Robinett, R. W.
2009-02-01
We derive new constraints on the zeros of Airy functions by using the so-called quantum bouncer system to evaluate quantum-mechanical sum rules and perform perturbation theory calculations for the Stark effect. Using commutation and completeness relations, we show how to systematically evaluate sums of the form Sp(n) = ∑k≠n1/(ζk - ζn)p, for natural p > 1, where -ζn is the nth zero of Ai(ζ).
Extended M1 sum rule for excited symmetric and mixed-symmetry states in nuclei
Smirnova, N A; Leviatan, A; Ginocchio, J N; Fransen, C
2002-01-01
A generalized M1 sum rule for orbital magnetic dipole strength from excited symmetric states to mixed-symmetry states is considered within the proton-neutron interacting boson model of even-even nuclei. Analytic expressions for the dominant terms in the B(M1) transition rates from the first and second $2^+$ states are derived in the U(5) and SO(6) dynamic symmetry limits of the model, and the applicability of a sum rule approach is examined at and in-between these limits. Lastly, the sum rule is applied to the new data on mixed-symmetry states of 94Mo and a quadrupole d-boson ratio $nd(0^+_1)/nd(2^+_2) \\approx 0.6$ is obtained in a largely parameter-independent way
Chiral sum rules and vacuum condensates from tau-lepton decay data
Dominguez, C.A.; Hernandez, L.A. [Centre for Theoretical and Mathematical Physics, and Department of Physics,University of Cape Town, Rondebosch 7700 (South Africa); National Institute of Theoretical Physics,Private Bag X1, Matieland 7602 (South Africa); Schilcher, K.; Spiesberger, H. [Centre for Theoretical and Mathematical Physics, and Department of Physics,University of Cape Town, Rondebosch 7700 (South Africa); National Institute of Theoretical Physics,Private Bag X1, Matieland 7602 (South Africa); PRISMA Cluster of Excellence, Institut für Physik,Johannes Gutenberg-Universität, D-55099 Mainz (Germany)
2015-03-10
QCD finite energy sum rules, together with the latest updated ALEPH data on hadronic decays of the tau-lepton are used in order to determine the vacuum condensates of dimension d=2 and d=4. These data are also used to check the validity of the Weinberg sum rules, and to determine the chiral condensates of dimension d=6 and d=8, as well as the chiral correlator at zero momentum, proportional to the counter term of the O(p{sup 4}) Lagrangian of chiral perturbation theory, L-bar{sub 10}. Suitable (pinched) integration kernels are introduced in the sum rules in order to suppress potential quark-hadron duality violations. We find no compelling indications of duality violations in the kinematic region above s≃2.2 GeV{sup 2} after using pinched integration kernels.
Nuclear magnetic polarizability and the slope of the Thomas-Reiche-Kuhn-Levinger-Bethe sum rule
Gorchtein, Mikhail
2015-01-01
Thomas-Reiche-Kuhn-Levinger-Bethe sum rule that relates the strength of the photoexcitation of the giant dipole resonance in a nucleus to the number of elementary scatterers-protons within that nucleus by means of a subtracted forward dispersion relation. I extend this dispersion relation consideration to the case of virtual photons and show that the size of the magnetic polarizability of a nucleus, under the assumption of a separation between the nuclear and hadronic scales, may be related to the slope of the transverse virtual photoabsorption cross section integrated over the energy. I check this approximate sum rule for the deuteron where necessary data is available, discuss possible applications and connection with other sum rules postulated in the literature.
Bjorken unpolarized and polarized sum rules comparative analysis of large-N_F expansions
Broadhurst, D J
2002-01-01
Analytical all-orders results are presented for the one-renormalon-chain contributions to the Bjorken unpolarized sum rule for the F_1 structure function of nu N deep-inelastic scattering in the large-N_F limit. The feasibility of estimating higher order perturbative QCD corrections, by the process of naive nonabelianization (NNA), is studied, in anticipation of measurement of this sum rule at a Neutrino Factory. A comparison is made with similar estimates obtained for the Bjorken polarized sum rule. Application of the NNA procedure to correlators of quark vector and scalar currents, in the euclidean region, is compared with recent analytical results for the O(alpha_s^4 N_F^2) terms.
Charmonium spectrum at finite temperature from a Bayesian analysis of QCD sum rules
Morita Kenji
2012-02-01
Full Text Available Making use of a recently developed method of analyzing QCD sum rules, we investigate charmonium spectral functions at finite temperature. This method employs the Maximum Entropy Method, which makes it possible to directly obtain the spectral function from the sum rules, without having to introduce any strong assumption about its functional form. Finite temperature effects are incorporated into the sum rules by the change of the various gluonic condensates that appear in the operator product expansion. These changes depend on the energy density and pressure at finite temperature, which are extracted from lattice QCD. As a result, J/ψ and ηc dissolve into the continuum already at temperatures around 1.0 ~ 1.1 Tc.
B{yields}D{sup (*)} form factors from QCD light-cone sum rules
Faller, S. [Universitaet Siegen, Theoretische Physik 1, Fachbereich Physik, Siegen (Germany); CERN, Theory Division, Department of Physics, Geneva 23 (Switzerland); Khodjamirian, A.; Klein, C.; Mannel, T. [Universitaet Siegen, Theoretische Physik 1, Fachbereich Physik, Siegen (Germany)
2009-04-15
We derive new QCD sum rules for B{yields}D and B{yields}D{sup *} form factors. The underlying correlation functions are expanded near the light-cone in terms of B-meson distribution amplitudes defined in HQET, whereas the c-quark mass is kept finite. The leading-order contributions of two- and three-particle distribution amplitudes are taken into account. From the resulting light-cone sum rules we calculate all B{yields}D{sup (*)} form factors in the region of small momentum transfer (maximal recoil). In the infinite heavy-quark mass limit the sum rules reduce to a single expression for the Isgur-Wise function. We compare our predictions with the form factors extracted from experimental B{yields}D{sup (*)}l{nu} {sub l} decay rates fitted to dispersive parameterizations. (orig.)
B→ D (*) form factors from QCD light-cone sum rules
Faller, S.; Khodjamirian, A.; Klein, Ch.; Mannel, Th.
2009-04-01
We derive new QCD sum rules for B→ D and B→ D * form factors. The underlying correlation functions are expanded near the light-cone in terms of B-meson distribution amplitudes defined in HQET, whereas the c-quark mass is kept finite. The leading-order contributions of two- and three-particle distribution amplitudes are taken into account. From the resulting light-cone sum rules we calculate all B→ D (*) form factors in the region of small momentum transfer (maximal recoil). In the infinite heavy-quark mass limit the sum rules reduce to a single expression for the Isgur-Wise function. We compare our predictions with the form factors extracted from experimental B→(*) l ν l decay rates fitted to dispersive parameterizations.
$B \\to D^{(*)}$ Form Factors from QCD Light-Cone Sum Rules
Faller, S; Klein, Ch; Mannel, T
2009-01-01
We derive new QCD sum rules for $B\\to D$ and $B\\to D^*$ form factors. The underlying correlation functions are expanded near the light-cone in terms of $B$-meson distribution amplitudes defined in HQET, whereas the $c$-quark mass is kept finite. The leading-order contributions of two- and three-particle distribution amplitudes are taken into account. From the resulting light-cone sum rules we calculate all $B\\to \\Dst $ form factors in the region of small momentum transfer (maximal recoil). In the infinite heavy-quark mass limit the sum rules reduce to a single expression for the Isgur-Wise function. We compare our predictions with the form factors extracted from experimental $B\\to \\Dst l \
Factorization, resummation and sum rules for heavy-to-light form factors
Wang, Yu-Ming
2016-01-01
Precision calculations of heavy-to-light form factors are essential to sharpen our understanding towards the strong interaction dynamics of the heavy-quark system and to shed light on a coherent solution of flavor anomalies. We briefly review factorization properties of heavy-to-light form factors in the framework of QCD factorization in the heavy quark limit and discuss the recent progress on the QCD calculation of $B \\to \\pi$ form factors from the light-cone sum rules with the $B$-meson distribution amplitudes. Demonstration of QCD factorization for the vacuum-to-$B$-meson correlation function used in the sum-rule construction and resummation of large logarithms in the short-distance functions entering the factorization theorem are presented in detail. Phenomenological implications of the newly derived sum rules for $B \\to \\pi$ form factors are further addressed with a particular attention to the extraction of the CKM matrix element $|V_{ub}|$.
Gaussian Sum-Rule Analysis of Scalar Gluonium and Quark Mesons
Steele, T G; Orlandini, G
2003-01-01
Gaussian sum-rules, which are related to a two-parameter Gaussian-weighted integral of a hadronic spectral function, are able to examine the possibility that more than one resonance makes a significant contribution to the spectral function. The Gaussian sum-rules, including instanton effects, for scalar gluonic and non-strange scalar quark currents clearly indicate a distribution of the resonance strength in their respective spectral functions. Furthermore, analysis of a two narrow resonance model leads to excellent agreement between theory and phenomenology in both channels. The scalar quark and gluonic sum-rules are remarkably consistent in their prediction of masses of approximately 1.0 GeV and 1.4 GeV within this model. Such a similarity would be expected from hadronic states which are mixtures of gluonium and quark mesons.
Strength function sum rules and the generalized Brink-Axel hypothesis
Johnson, Calvin W
2015-01-01
Sum rules provide useful insights into transition strength functions and are often expressed as expectation values of an operator. In this letter I demonstrate that non-energy-weighted transition sum rules have strong secular dependences on the energy of the initial state. Such non-trivial systematics have consequences: the simplification suggested by the generalized Brink-Axel hypothesis, for example, does not hold for most cases. Furthermore, I show the systematics can be understood through spectral distribution theory, calculated via traces of operators and of products of operators.
Light Cone Sum Rules for gamma*N ->Delta Transition Form Factors
V.M. Braun; A. Lenz; G. Peters; A. Radyushkin
2006-02-01
A theoretical framework is suggested for the calculation of {gamma}* N {yields} {Delta} transition form factors using the light-cone sum rule approach. Leading-order sum rules are derived and compared with the existing experimental data. We find that the transition form factors in a several GeV region are dominated by the ''soft'' contributions that can be thought of as overlap integrals of the valence components of the hadron wave functions. The ''minus'' components of the quark fields contribute significantly to the result, which can be reinterpreted as large contributions of the quark orbital angular momentum.
Strong coupling constant of negative parity nucleon with $\\pi$ meson in light cone QCD sum rules
Aliev, T M; Savcı, M
2016-01-01
We estimate strong coupling constant between the negative parity nucleons with $\\pi$ meson within the light cone QCD sum rules. A method for eliminating the unwanted contributions coming from the nucleon--nucleon and nucleon--negative parity nucleon transition is presented. It is observed that the value strong coupling constant of the negative parity nucleon $N^\\ast N^\\ast \\pi$ transition is considerably different from the one predicted by the 3--point QCD sum rules, but is quite close to the coupling constant of the positive parity $N N \\pi$ transition.
The sigma meson from QCD sum rules for large-$N_c$ Regge spectra
Afonin, S S
2016-01-01
The QCD sum rules in the large-$N_c$ limit for the light non-strange vector, axial-vector and scalar mesons are considered assuming a string-like linear spectrum for the radially excited states. We propose a improved method for a combined analysis of these channels that gives a reasonable description of the observed spectrum. Fixing the universal slope of radial trajectories and the quark condensate from the vector channels, we argue that, in contrast to a common belief, the prediction of a light quark-antiquark scalar state compatible with $f_0(500)$ can be quite natural within the planar QCD sum rules.
$B \\to A$ transitions in the light-cone QCD sum rules with the chiral current
Yan-Jun, Sun; Tao, Huang
2011-01-01
In this article, we calculate the form-factors of the transitions $B \\to a_1(1260)$, $b_1(1235) $ in the leading-order approximation using the light-cone QCD sum rules. In calculations, we choose the chiral current to interpolate the $B$-meson, which has outstanding advantage that the twist-3 light-cone distribution amplitudes of the axial-vector mesons have no contributions, and the resulting sum rules for the form-factors suffer from much less uncertainties. Then we study the semi-leptonic decays $B \\to a_1(1260) l\\bar{\
Exact duality and Bjorken sum rule in heavy quark models à la Bakamjian-Thomas
Le Yaouanc, A; Pène, O; Raynal, J C
1996-01-01
The heavy mass limit of quark models based on the Bakamjian-Thomas cons\\-truction reveals remarkable features. In addition to previously demonstrated properties of covariance and Isgur-Wise scaling, exact duality, leading to the Bjorken-Isgur-Wise sum rule, is proven, for the first time to our knowledge in relativistic quark models. Inelastic as well as elastic contributions to the sum rule are then discussed in terms of ground state averages of a few number of operators corresponding to the nonrelativistic dipole operator and various relativistic corrections.
Form Factors and Strong Couplings of Heavy Baryons from QCD Light-Cone Sum Rules
Khodjamirian, A; Mannel, Th; Wang, Y -M
2011-01-01
We derive QCD light-cone sum rules for the hadronic matrix elements of the heavy baryon transitions to nucleon. In the correlation functions the $\\Lambda_c,\\Sigma_c$ and $\\Lambda_b$ -baryons are interpolated by three-quark currents and the nucleon distribution amplitudes are used. To eliminate the contributions of negative parity heavy baryons, we combine the sum rules obtained from different kinematical structures. The results are then less sensitive to the choice of the interpolating current. We predict the $\\Lambda_{b}\\to p$ form factor and calculate the widths of the $\\Lambda_{b}\\to p\\ell\
Analysis of the tensor-tensor type scalar tetraquark states with QCD sum rules
Wang, Zhi-Gang
2016-01-01
In this article, we study the ground states and the first radial excited states of the tensor-tensor type scalar hidden-charm tetraquark states with the QCD sum rules. We separate the ground state contributions from the first radial excited state contributions unambiguously, and obtain the QCD sum rules for the ground states and the first radial excited states, respectively. Then we search for the Borel parameters and continuum threshold parameters according to four criteria and obtain the masses of the tensor-tensor type scalar hidden-charm tetraquark states, which can be confronted to the experimental data in the future.
Light-by-light scattering sum rules in light of new data
Danilkin, Igor
2016-01-01
We evaluate the light-quark meson contributions to three exact light-by-light scattering sum rules in light of new data by the Belle Collaboration, which recently has extracted the transition form factors of the tensor meson $f_2(1270)$ as well as of the scalar meson $f_0(980)$. We confirm a previous finding that the $\\eta, \\eta^\\prime$ and helicity-2 $f_2(1270)$ contributions saturate one of these sum rules up to photon virtualities up to around 1 GeV$^2$. At larger virtualities, our sum rule analysis shows an important contribution of the $f_2(1565)$ meson and provides a first empirical extraction of its helicity-2 transition form factor. Two further sum rules allow us to predict the helicity-0 and helicity-1 transition form factors of the $f_2(1270)$ meson. Furthermore, our analysis also provides an update for the scalar and tensor meson hadronic light-by-light contributions to the muon's anomalous magnetic moment.
Comparison principles for viscosity solutions of elliptic equations via fuzzy sum rule
Luo, Yousong; Eberhard, Andrew
2005-07-01
A comparison principle for viscosity sub- and super-solutions of second order elliptic partial differential equations is derived using the "fuzzy sum rule" of non-smooth calculus. This method allows us to weaken the assumptions made on the function F when the equation F(x,u,=u,=2u)=0 is under consideration.
In-medium QCD sum rules for {omega} meson, nucleon and D meson
Thomas, Ronny
2008-07-01
The modifications of hadronic properties caused by an ambient nuclear medium are investigated within the scope of QCD sum rules. This is exemplified for the cases of the {omega} meson, the nucleon and the D meson. By virtue of the sum rules, integrated spectral densities of these hadrons are linked to properties of the QCD ground state, quantified in condensates. For the cases of the {omega} meson and the nucleon it is discussed how the sum rules allow a restriction of the parameter range of poorly known four-quark condensates by a comparison of experimental and theoretical knowledge. The catalog of independent four-quark condensates is covered and relations among these condensates are revealed. The behavior of four-quark condensates under the chiral symmetry group and the relation to order parameters of spontaneous chiral symmetry breaking are outlined. In this respect, also the QCD condensates appearing in differences of sum rules of chiral partners are investigated. Finally, the effects of an ambient nuclear medium on the D meson are discussed and relevant condensates are identified. (orig.)
A comprehensive revisit of the ρ meson with improved Monte-Carlo based QCD sum rules
Wang, Qi-Nan; Zhang, Zhu-Feng; Steele, T. G.; Jin, Hong-Ying; Huang, Zhuo-Ran
2017-07-01
We improve the Monte-Carlo based QCD sum rules by introducing the rigorous Hölder-inequality-determined sum rule window and a Breit-Wigner type parametrization for the phenomenological spectral function. In this improved sum rule analysis methodology, the sum rule analysis window can be determined without any assumptions on OPE convergence or the QCD continuum. Therefore, an unbiased prediction can be obtained for the phenomenological parameters (the hadronic mass and width etc.). We test the new approach in the ρ meson channel with re-examination and inclusion of α s corrections to dimension-4 condensates in the OPE. We obtain results highly consistent with experimental values. We also discuss the possible extension of this method to some other channels. Supported by NSFC (11175153, 11205093, 11347020), Open Foundation of the Most Important Subjects of Zhejiang Province, and K. C. Wong Magna Fund in Ningbo University, TGS is Supported by the Natural Sciences and Engineering Research Council of Canada (NSERC), Z. F. Zhang and Z. R. Huang are Grateful to the University of Saskatchewan for its Warm Hospitality
New Heavy Quark Limit Sum Rules involving Isgur-Wise Functions and Decay Constants
Yaouanc, A L; Pène, O; Raynal, J C
1996-01-01
We consider the dominant $c\\bar{c}$ contribution to $\\Delta \\Gamma$ for the $B_s^0$-$\\bar{B}_s^0$ system in the heavy quark limit for both $b$ and $c$ quarks. In analogy with the Bjorken-Isgur-Wise sum rule in semileptonic heavy hadron decay, we impose duality between the parton model calculation of $\\Delta $m_c/m_b$ and assuming factorization and saturation by narrow resonances $(N_c $f^{(n)}_{1/2}$ ($n$ stands for any radial excitation). Alternatively, we deduce the sum rules with another method free of the factorization hypothesis, from the saturation of the expectation value of a product of two currents by heavy hadrons and by the corresponding free quarks. The sum rules read for all $w$. Moreover, we obtain, in the heavy quark limit, $f^{(n)}_{3/2} = 0$. As a consequence, unlike the BIW sum rule, the slope of the elastic function $\\xi (w)$ is related to radial excitations alone. These are generalizations, rigorous for QCD in the heavy quark limit, of results that have an easy understanding in the non-rel...
Reanalyzing Pentaquark Θ+(1540) in Framework of QCD Sum Rules Approach with Direct Instantons
无
2006-01-01
In this article, we study the pentaquark state Θ+(1540) with a (scalar) diquark-(pseudoscalar) diquarkantiquark type interpolating current in the framework of the QCD sum rules approach by including the contributions from the direct instantons. The numerical results indicate that the contributions from the direct instantons are very small and can be safely neglected.
Analysis of the Triply Heavy Baryon States with QCD Sum Rules
WANG Zhi-Gang
2012-01-01
In this article, we study the (1/2)± and (3/2)± triply heavy baryon states in a systematic way by subtracting the contributions from the corresponding (1/2) and (3/2) triply heavy baryon states with the QCD sum rules, and make reasonable predictions for their masses.
Determination of the $\\Sigma$--$\\Lambda$ mixing angle from QCD sum rules
Aliev, T M; Savcı, M
2015-01-01
The $\\Sigma$--$\\Lambda$ mixing angle is calculated in framework of the QCD sum rules. We find that our prediction for the mixing angle is $(1.00\\pm 0.15)^0$ which is in good agreement with the quark model prediction, and approximately two times larger than the recent lattice QCD calculations.
Sum rule distortions in fluorescence-yield x-ray magnetic circular dichroism
Liu, Boyang; Piamonteze, Cinthia; Delgado-Jaime, Mario Ulises; Wang, Ru-Pan; Heidler, Jakoba; Dreiser, Jan; Chopdekar, Rajesh; Nolting, Frithjof; de Groot, Frank M. F.
2017-08-01
The quantitative analysis of 3 d transition metal L2 ,3 edge x-ray magnetic circular dichroism (XMCD) spectra and the related sum rules are compared for measurements with electron yield and fluorescence yield detection. Multiplet calculations on divalent ions show that fluorescence yield detected sum rule derived expectation values of Lz and Sz show noticeable deviations and detection angle dependence. We show that small deviations of the polarization dependent fluorescent decay values lead to significant deviations in the Lz and Sz sum rule values. Fe and Co experimental XMCD spectra of a supported 10 nm CoFe2O4 thin film are measured simultaneously by both electron and fluorescence yield. The deviations shown in the experimental data are well explained by the calculations and are shown to mainly depend on the polarization dependent total decay. We conclude that fluorescence yield detected x-ray magnetic circular dichroism is unsuitable for quantitative analysis of the Lz and Sz sum rule values.
SUM-RULES FOR MAGNETIC DICHROISM IN RARE-EARTH 4F-PHOTOEMISSION
THOLE, BT; VANDERLAAN, G
1993-01-01
We present new sum rules for magnetic dichroism in spin polarized photoemission from partly filled shells which give the expectation values of the orbital and spin magnetic moments and their correlations in the ground state. We apply this to the 4f photoemission of rare earths, where the
Jakubassa-Amundsen, D H
2016-01-01
Inspired by the work of Pratt and coworkers on a sum rule for the polarization correlations in electron bremsstrahlung when the outgoing electron is not observed, we derive the corresponding sum rule for the elementary process of bremsstrahlung. This sum rule is valid for arbitrary electron wavefunctions provided the electron is emitted in the reaction plane. The numerical evaluation of this sum rule within the Dirac partial-wave theory for bare inert spin-zero nuclei and collision energies in the range of 1-10 MeV reveals violations for high nuclear charge. Such violations serve as a measure of the inaccuracies in the bremsstrahlung calculations.
Constraints on Airy function zeros from quantum-mechanical sum rules
Belloni, M [Physics Department, Davidson College, Davidson, NC 28035 (United States); Robinett, R W [Department of Physics, Pennsylvania State University, University Park, PA 16802 (United States)], E-mail: mabelloni@davidson.edu, E-mail: rick@phys.psu.edu
2009-02-20
We derive new constraints on the zeros of Airy functions by using the so-called quantum bouncer system to evaluate quantum-mechanical sum rules and perform perturbation theory calculations for the Stark effect. Using commutation and completeness relations, we show how to systematically evaluate sums of the form S{sub p}(n) = {sigma}{sub k{ne}}{sub n}1/({zeta}{sub k} - {zeta}{sub n}){sup p}, for natural p > 1, where -{zeta}{sub n} is the nth zero of Ai({zeta})
X-ray-absorption sum rules in jj-coupled operators and ground-state moments of actinide ions
van der Laan, G; Thole, BT
1996-01-01
Sum rules for magnetic x-ray dichroism, relating the signals of the spin-orbit split core level absorption edges to the ground-state spin and orbital operators, are expressed in jj-coupled operators. These sum rules can be used in the region of intermediate coupling by taking into account the cross
Strength function sum rules and the generalized Brink-Axel hypothesis
Johnson, Calvin W.
2015-10-01
Sum rules provide useful insights into transition strength functions and are often expressed as expectation values of an operator. I will show that non-energy-weighted transition sum rules have strong secular dependences on the energy of the initial state. Such non-trivial systematics have consequences: the simplification suggested by the generalized Brink-Axel hypothesis, for example, does not hold for most cases, though it weakly holds for electric dipole transitions. Furthermore, I show the systematics can be understood through spectral distribution theory, calculated via traces of operators and of products of operators; seen through this lens, violation of the generalized Brink-Axel hypothesis is unsurprising. Supported by the U.S. Department of Energy, Office of Science, Office of Nuclear Physics, under Award Number DE-FG02-96ER40985.
Unitarity sum rules, three site moose model, and the ATLAS 2 TeV diboson anomalies
Abe, Tomohiro; Okawa, Shohei; Tanabashi, Masaharu
2015-01-01
We investigate $W'$ interpretations for the ATLAS 2 TeV diboson anomalies. The roles of the unitarity sum rules, which ensure the perturbativity of the longitudinal vector boson scattering amplitudes, are emphasized. We find the unitarity sum rules and the custodial symmetry relations are powerful enough to predict various nontrivial relations among $WWZ'$, $WZW'$, $WWh$, $WW'h$ and $ZZ'h$ coupling strengths in a model independent manner. We also perform surveys in the general parameter space of $W'$ models and find the ATLAS 2 TeV diboson anomalies may be interpreted as a $W'$ particle of the three site moose model, i.e., a Kaluza-Klein like particle in a deconstructed extra dimension model. It is also shown that the non SM-like Higgs boson is favored by the present data to interpret the ATLAS diboson anomalies as the consequences of the $W'$ and $Z'$ bosons.
B→A transitions in the light-cone QCD sum rules with the chiral current
SUN Yan-Jun; WANG Zhi-Gang; HUANG Tao
2012-01-01
In this article,we calculate the form-factors of the transitions B → a1(1260),b1(1235) in the leading-order approximation using the light-cone QCD sum rules.In calculations,we choose the chiral current to interpolate the B-meson,which has the outstanding advantage that the twist-3 light-cone distribution amplitudes of the axial-vector mesons make no contributions,and the resulting sum rules for the form-factors suffer from far fewer uncertainties.Then we study the semi-leptonic decays B → a1(1260)l(v1),b1(1235)l(v1) (l =e,μ,Τ),and make predictions for the differential decay widths and decay widths,which can be compared with the experimental data in the coming future.
Kramers-Kronig relations and sum rules in nonlinear optical spectroscopy.
Peiponen, Kai-Erik; Lucarini, Valerio; Saarinen, Jarkko J; Vartiainen, Erik
2004-05-01
The full potential of the Kramers-Kronig relations and sum rules for nonlinear susceptibilities has unfortunately drawn relatively little attention in nonlinear optical spectra analysis. In this feature article a simple treatment of an anharmonic oscillator model in description of the nonlinear susceptibility of media and holomorphic properties of the nonlinear susceptibility were utilized. Using such concepts, conventional Kramers-Kronig, multiply-subtractive Kramers-Kronig, and generalized Kramers-Kronig dispersion relations can be derived. We demonstrate how in practice the variety of different Kramers-Kronig relations mentioned above, as well as various sum rules, can be applied in nonlinear optical spectra analysis. As an example we treat the third-harmonic wave generation spectrum from a polymer.
Diagonal and transition magnetic moments of negative parity heavy baryons in QCD sum rules
Aliev, T M; Barakat, T; Savcı, M
2015-01-01
Diagonal and transition magnetic moments of the negative parity, spin-1/2 heavy baryons are studied in framework of the light cone QCD sum rules. By constructing the sum rules for different Lorentz structures, the unwanted contributions coming from negative (positive) to positive (negative) parity transitions are removed. It is obtained that the magnetic moments of all baryons, except $\\Lambda_b^0$, $\\Sigma_c^+$ and $\\Xi_c^{\\prime +}$, are quite large. It is also found that the transition magnetic moments between neutral negative parity heavy $\\Xi_Q^{\\prime 0}$ and $\\Xi_Q^0$ baryons are very small. Magnetic moments of the $\\Sigma_Q \\to \\Lambda_Q$ and $ \\Xi_Q^{\\prime \\pm} \\to \\Xi_Q^\\pm$ transitions are quite large and can be measured in further experiments.
Finite-Energy Sum Rules in Eta Photoproduction off the Nucleon
Nys, J; Fernández-Ramírez, C; Blin, A N Hiller; Jackura, A; Mikhasenko, M; Pilloni, A; Szczepaniak, A P; Fox, G; Ryckebusch, J
2016-01-01
The reaction ${\\gamma}N \\to {\\eta}N$ is studied in the high-energy regime (with photon lab energies $E_{\\gamma}^{\\textrm{lab}} > 4$ GeV) using information from the resonance region through the use of finite-energy sum rules (FESR). We illustrate how analyticity allows one to map the t-dependence of the unknown Regge residue functions. We provide predictions for the energy dependence of the beam asymmetry at high energies.
Remarks on sum rules in the heavy quark limit of QCD
Le Yaouanc, A; Pène, O; Raynal, J C; Morénas, V
2001-01-01
We underline a problem existing in the heavy quark limit of QCD concerning the rates of semileptonic B decays into P-wave $D_J(j)$ mesons, where $j = {1 \\over 2}$ (wide states) or $j = {3 \\over 2}$ (narrow states). The leading order sum rules of Bjorken and Uraltsev suggest $\\Gamma [ \\bar{B} \\to D_{0,1} ({1 \\over 2}) \\ell \
Analysis of Vertex DDρ with Light-Cone QCD Sum Rules
WANG Zhi-Gang; WANG Zhi-Bin
2008-01-01
We analyse the vertex DD ρ with the light-cone QCD sum rules.The strong coupling constant Gd*D*ρ is an important parameter in evaluating the charmonium absorption cross sections in searching for the quark-gluon plasmas.Our numerical value for the Gd*D*ρ is consistent with the prediction of the effective SU(4)symmetry and vector meson dominance theory.
QCD Sum Rule Analysis for the $\\Lambda_b\\rightarrow\\Lambda_c$ Semileptonic Decay
Dai, Y; Huang, M; Liu, C; Dai, Yuan-ben; Huang, Chao-shang; Huang, Ming-qiu; Liu, Chun
1996-01-01
The 1/m_c and 1/m_b corrections to the \\Lambda_b to \\Lambda_c semi- leptonic decay are analyzed by QCD sum rules. Within the framework of heavy quark effective theory,the subleading baryonic Isgur-Wise func- tion of \\Lambda_b to Lagrangian insertion are negligibly small. The sizable 1/m_Q effect to the decay lies only in the weak current. The decay spectrum and the branching ratio are given.
Effects of Nuclear Medium on the Sum Rules in Electron and Neutrino Scattering
Zaidi, F; Athar, M Sajjad; Singh, S K; Simo, I Ruiz
2016-01-01
In this work, we study the influence of nuclear medium effects on various parton model sum rules in nuclei and compare the results with the free nucleon case. We have used relativistic nucleon spectral function to take into account Fermi motion, binding and nucleon correlations. The pion and rho meson cloud contributions have been incorporated in a microscopic model. The effect of shadowing has also been considered.
In-medium \\Sigma^0-\\Lambda Mixing in QCD Sum Rules
Yagisawa, N; Hayashigaki, A
2002-01-01
The \\Sigma^0-\\Lambda mixing angle in isospin-asymetric nuclear medium is investigted by using QCD sum rules. From the general consideration of the in-medium baryonic correlations, in-medium baryon mixings are shown to have several Lorentz structures such as the scalar mixing angle \\theta^S and the vector mixing angle \\theta^V. This causes a difference between the particle mixing \\theta (= \\theta^S + \\theta^V) and the anti-particle mixing \\bar{\\theta} (= \\theta^S - \\theat^V). From the finite energy sum rules for the \\Sigma^0-\\Lambda mixing, we find that the in-medium part of the mixing angle has a relation \\theta^S_{Med} \\simeq - \\theta^V_{Med} in the isospin-asymmetric medium. This implies that the medium affects mainly the anti-particle mixing. From the Borel sum rules, we obtain |\\bar{\\theta} - \\theta_0| \\simeq 0.39 |(\\rho_n - \\rho_p)| / \\rho_0 with \\theta_0, \\rho_n, \\rho_p and \\rho_0 being the vacuum mixing angle, the neutron density, the proton density and the normal nuclear matter density respectively.
First nucleation theorem with cluster losses: sum rules and applications to new particle formation
McGraw, R. L.; Malila, J.; Laaksonen, A. J.; Lehtinen, K. E.
2013-12-01
Derivations of the first nucleation theorem for homogeneous nucleation invoke certain idealized conditions that would appear to render questionable any application the theorem to more complex systems such as atmospheric new particle formation (NPF). These include absence of cluster loss due to coagulation with background aerosol (or vessel walls in a laboratory experiment) and competing channels to NPF such as the potential conversion, hence loss, of pre-critical clusters by heterogeneous nucleation. To overcome these restrictions, we extend the kinetic derivation of the first nucleation theorem to include such cluster loss processes and discuss the implications of our findings for atmospheric NPF. The analysis yields a remarkable pair of sum rules that connect the formation and loss rates as a function of cluster size to the corresponding homogeneous nucleation rate. A third, equally remarkable, sum rule connects the observed, apparent critical size that results from naïve application of the first nucleation theorem without correcting for loss to the true critical cluster size from homogeneous nucleation theory, d*. We show that for clusters of true size d>d* (d
A resolution of the inclusive flavor-breaking sum rule $\\tau$ $V_{us}$ puzzle
Maltman, K; Lewis, R; Wolfe, C E; Zanotti, J
2015-01-01
A combination of continuum and lattice methods is used to investigate systematic issues in the finite-energy-sum-rule determination of $V_{us}$ based on flavor-breaking combinations of hadronic $\\tau$ decay data. Results for $V_{us}$ obtained using assumptions for $D>4$ OPE contributions employed in previous conventional implementations of this approach are shown to display significant unphysical dependences on the choice of sum rule weight, $w$, and upper limit, $s_0$, of the relevant experimental spectral integrals. Continuum and lattice results suggest the necessity of a new implementation of the flavor-breaking sum rule approach, in which not only $\\vert V_{us}\\vert$, but also $D>4$ effective condensates are fit to data. Lattice results also provide a means of quantifying the truncation error for the slowly converging $D=2$ OPE series. The new implementation is shown to produce $\\vert V_{us}\\vert$ results free of unphysical $s_0$- and $w$-dependences and typically $\\sim 0.0020$ higher than the (unstable) ...
New identities from quantum-mechanical sum rules of parity-related potentials
Ayorinde, O A; Belloni, M; Robinett, R W
2010-01-01
We apply quantum mechanical sum rules to pairs of one-dimensional systems defined by potential energy functions related by parity. Specifically, we consider symmetric potentials, $V(x) = V(-x)$, and their parity-restricted partners, ones with $V(x)$, but defined only on the positive half-line. We extend recent discussions of sum rules for the quantum bouncer by considering the parity-extended version of this problem, defined by the symmetric linear potential, $V(z) = F|z|$ and find new classes of constraints on the zeros of the Airy function, $Ai(z)$, and its derivative $Ai'(z)$. We also consider the parity-restricted version of the harmonic oscillator and find completely new classes of mathematical relations, unrleated to those of the ordinary oscillator problem. These two soluble quantum-mechanical systems defined by power-law potentials provide examples of how the form of the potential (both parity and continuity properties) affects the convergence of quantum-mechanical sum rules. We also discuss semi-clas...
New identities from quantum-mechanical sum rules of parity-related potentials
Ayorinde, O A; Chisholm, K; Belloni, M [Physics Department, Davidson College, Davidson, NC 28035 (United States); Robinett, R W, E-mail: seayorinde@davidson.ed, E-mail: kechisholm@davidson.ed, E-mail: mabelloni@davidson.ed, E-mail: rick@phys.psu.ed [Department of Physics, Pennsylvania State University, University Park, PA 16802 (United States)
2010-06-11
We apply quantum-mechanical sum rules to pairs of one-dimensional systems defined by potential energy functions related by parity. Specifically, we consider symmetric potentials, V(x) = V(- x), and their parity-restricted partners, ones with V(x) but defined only on the positive half-line. We extend recent discussions of sum rules for the quantum bouncer by considering the parity-extended version of this problem, defined by the symmetric linear potential, V(z) = F|z| and find new classes of constraints on the zeros of the Airy function, Ai({zeta}), and its derivative, Ai'({zeta}). We also consider the parity-restricted version of the harmonic oscillator and find completely new classes of mathematical relations, unrelated to those of the ordinary oscillator problem. These two soluble quantum-mechanical systems defined by power-law potentials provide examples of how the form of the potential (both parity and continuity properties) affects the convergence of quantum-mechanical sum rules. We also discuss semi-classical predictions for expectation values and the Stark effect for these systems.
New identities from quantum-mechanical sum rules of parity-related potentials
Ayorinde, O. A.; Chisholm, K.; Belloni, M.; Robinett, R. W.
2010-06-01
We apply quantum-mechanical sum rules to pairs of one-dimensional systems defined by potential energy functions related by parity. Specifically, we consider symmetric potentials, V(x) = V(- x), and their parity-restricted partners, ones with V(x) but defined only on the positive half-line. We extend recent discussions of sum rules for the quantum bouncer by considering the parity-extended version of this problem, defined by the symmetric linear potential, V(z) = F|z| and find new classes of constraints on the zeros of the Airy function, Ai(ζ), and its derivative, Ai'(ζ). We also consider the parity-restricted version of the harmonic oscillator and find completely new classes of mathematical relations, unrelated to those of the ordinary oscillator problem. These two soluble quantum-mechanical systems defined by power-law potentials provide examples of how the form of the potential (both parity and continuity properties) affects the convergence of quantum-mechanical sum rules. We also discuss semi-classical predictions for expectation values and the Stark effect for these systems.
Predictions for the Dirac Phase in the Neutrino Mixing Matrix and Sum Rules
Girardi, I.; Petcov, S. T.; Titov, A. V.
2015-07-01
Using the fact that the neutrino mixing matrix U = U†eUν, where Ue and Uv result from the diagonalisation of the charged lepton and neutrino mass matrices, we analyse the sum rules which the Dirac phase δ present in U satisfies when Uv has a form dictated by, or associated with, discrete symmetries and Ue has a “minimal” form (in terms of angles and phases it contains) that can provide the requisite corrections to Uv, so that reactor, atmospheric and solar neutrino mixing angles θ13, θ23 and θ12 have values compatible with the current data. The following symmetry forms are considered: i) tri-bimaximal (TBM), ii) bimaximal (BM) (or corresponding to the conservation of the lepton charge L' = Le — Lμ — Lτ (LC)), iii) golden ratio type A (GRA), iv) golden ratio type B (GRB), and v) hexagonal (HG). We investigate the predictions for 5 in the cases of TBM, BM (LC), GRA, GRB and HG forms using the exact and the leading order sum rules for cos δ proposed in the literature, taking into account also the uncertainties in the measured values of sin2 θ12, sin2 θ23 and sin2 θ13. This allows us, in particular, to assess the accuracy of the predictions for cos δ based on the leading order sum rules and its dependence on the values of the indicated neutrino mixing parameters when the latter are varied in their respective 3σ experimentally allowed ranges.
Determining the Dirac CP violation phase in the neutrino mixing matrix from sum rules
Girardi, I.; Petcov, S. T.; Titov, A. V.
2015-05-01
Using the fact that the neutrino mixing matrix U = Ue† Uν, where Ue and Uν result from the diagonalisation of the charged lepton and neutrino mass matrices, we analyse the sum rules which the Dirac phase δ present in U satisfies when Uν has a form dictated by, or associated with, discrete symmetries and Ue has a "minimal" form (in terms of angles and phases it contains) that can provide the requisite corrections to Uν, so that reactor, atmospheric and solar neutrino mixing angles θ13, θ23 and θ12 have values compatible with the current data. The following symmetry forms are considered: i) tri-bimaximal (TBM), ii) bimaximal (BM) (or corresponding to the conservation of the lepton charge L‧ =Le -Lμ -Lτ (LC)), iii) golden ratio type A (GRA), iv) golden ratio type B (GRB), and v) hexagonal (HG). We investigate the predictions for δ in the cases of TBM, BM (LC), GRA, GRB and HG forms using the exact and the leading order sum rules for cos δ proposed in the literature, taking into account also the uncertainties in the measured values of sin2 θ12, sin2 θ23 and sin2 θ13. This allows us, in particular, to assess the accuracy of the predictions for cos δ based on the leading order sum rules and its dependence on the values of the indicated neutrino mixing parameters when the latter are varied in their respective 3σ experimentally allowed ranges.
Nature of the X(5568) : a critical Laplace sum rule analysis at N2LO
Albuquerque, R; Rabemananjara, A; Rabetiarivony, D
2016-01-01
We scrutinize recent QCD spectral sum rules (QSSR) results to lowest order (LO) predicting the masses of the BK molecule and (su)\\bar(bd) four-quark states. We improve these results by adding NLO and N2LO corrections to the PT contributions giving a more precise meaning on the b-quark mass definition used in the analysis. We extract our optimal predictions using Laplace sum rule (LSR) within the standard stability criteria versus the changes of the external free parameters (\\tau-sum rule variable, t_c continuum threshold and subtraction constant \\mu). The smallness of the higher order PT corrections justifies (a posteriori) the LO order results + the uses of the ambiguous heavy quark mass to that order. However, our predicted spectra in the range (5173- 5226) GeV, summarized in Table 7, for exotic hadrons built with four different flavours (buds), do not support some previous interpretations of the D0 candidate [1], X(5568), as a pure molecule or a four-quark state. If experimentally confirmed, it could resul...
Cabrera-Trujillo, R.
2017-08-01
Sum rule relations over the excitation spectrum of a quantum system contain information about both the energy spectrum and eigenfunctions of the system in a compact form, particularly regarding closure relations. In this work, the effects of pressure induced by a spherical cavity on an atomic hydrogen impurity on the dipole oscillator strength (DOS) sum rule, S k , and its logarithmic version, L k , are studied by means of a numerical approach based on a finite-difference solution to the Schrödinger equation. Pressure effects are accounted for by means of a spherical cavity of radius R 0 immersed in a medium characterized by a penetrable potential height V 0. The DOS sum rules S k and L k are investigated as a function of these cavity parameters and thus directly related to the impurity static pressure and surrounding material. One finds that the sum rules are fulfilled within the numerical precision for low pressure conditions. However, when the barrier height is large or infinite (a non-penetrable cavity), the sum rule, for positive k, differs from its closure relation. One finds that this occurs for a cavity radius {R}0important and this behavior is not presented. As the {S}-2 sum rule is the static dipole polarizability, the results are compared to available data in the literature, showing excellent agreement. This behavior in the sum rule and oscillator strength in electron-impurity excitations affects optical transitions of importance in semiconductor nanostructures.
Effective restoration of dipole sum rules within the renormalized random-phase approximation
Hung, N. Quang; Dang, N. Dinh; Hao, T. V. Nhan; Phuc, L. Tan
2016-12-01
The dipole excitations for calcium and zirconium isotopes are studied within the fully self-consistent Hartree-Fock mean field incorporated with the renormalized random-phase approximation (RRPA) using the Skyrme interaction SLy5. The RRPA takes into account the effect of ground-state correlations beyond RPA owing to the Pauli principle between the particle-hole pairs that form the RPA excitations as well as the correlations due to the particle-particle and hole-hole transitions, whose effects are treated here in an effective way. By comparing the RPA results with the RRPA ones, which are obtained for isoscalar (IS) and isovector (IV) dipole excitations in 48,52,58Ca and 90,96,110Zr, it is shown that ground-state correlations beyond the RPA reduce the IS transition strengths. They also shift up the energy of the lowest IV dipole state and slightly push down the peak energy of the IV giant dipole resonance. As the result, the energy-weighted sums of strengths of both IS and IV modes decrease, causing the violation of the corresponding energy-weighted sum rules (EWSR). It is shown that this sum rule violation can be eliminated by taking into account the contribution of the particle-particle and hole-hole excitations together with the particle-hole ones in a simple and perturbative way. Consequently, the ratio of the energy-weighted sum of strengths of the pygmy dipole resonance to that of the giant dipole resonance increases.
QCD corrections to B→π form factors from light-cone sum rules
Yu-Ming Wang
2015-09-01
Full Text Available We compute perturbative corrections to B→π form factors from QCD light-cone sum rules with B-meson distribution amplitudes. Applying the method of regions we demonstrate factorization of the vacuum-to-B-meson correlation function defined with an interpolating current for pion, at one-loop level, explicitly in the heavy quark limit. The short-distance functions in the factorization formulae of the correlation function involves both hard and hard-collinear scales; and these functions can be further factorized into hard coefficients by integrating out the hard fluctuations and jet functions encoding the hard-collinear information. Resummation of large logarithms in the short-distance functions is then achieved via the standard renormalization-group approach. We further show that structures of the factorization formulae for fBπ+(q2 and fBπ0(q2 at large hadronic recoil from QCD light-cone sum rules match that derived in QCD factorization. In particular, we perform an exploratory phenomenological analysis of B→π form factors, paying attention to various sources of perturbative and systematic uncertainties, and extract |Vub|=(3.05−0.38+0.54|th.±0.09|exp.×10−3 with the inverse moment of the B-meson distribution amplitude ϕB+(ω determined by reproducing fBπ+(q2=0 obtained from the light-cone sum rules with π distribution amplitudes. Furthermore, we present the invariant-mass distributions of the lepton pair for B→πℓνℓ (ℓ=μ,τ in the whole kinematic region. Finally, we discuss non-valence Fock state contributions to the B→π form factors fBπ+(q2 and fBπ0(q2 in brief.
Determining the Dirac CP violation phase in the neutrino mixing matrix from sum rules
I. Girardi
2015-05-01
Full Text Available Using the fact that the neutrino mixing matrix U=Ue†Uν, where Ue and Uν result from the diagonalisation of the charged lepton and neutrino mass matrices, we analyse the sum rules which the Dirac phase δ present in U satisfies when Uν has a form dictated by, or associated with, discrete symmetries and Ue has a “minimal” form (in terms of angles and phases it contains that can provide the requisite corrections to Uν, so that reactor, atmospheric and solar neutrino mixing angles θ13, θ23 and θ12 have values compatible with the current data. The following symmetry forms are considered: i tri-bimaximal (TBM, ii bimaximal (BM (or corresponding to the conservation of the lepton charge L′=Le−Lμ−Lτ (LC, iii golden ratio type A (GRA, iv golden ratio type B (GRB, and v hexagonal (HG. We investigate the predictions for δ in the cases of TBM, BM (LC, GRA, GRB and HG forms using the exact and the leading order sum rules for cosδ proposed in the literature, taking into account also the uncertainties in the measured values of sin2θ12, sin2θ23 and sin2θ13. This allows us, in particular, to assess the accuracy of the predictions for cosδ based on the leading order sum rules and its dependence on the values of the indicated neutrino mixing parameters when the latter are varied in their respective 3σ experimentally allowed ranges.
In-medium QCD sum rules for D mesons: A projection method for higher order contributions
Buchheim, Thomas; Kampfer, Burkhard
2014-01-01
D mesons serve as excellent probes of hot and/or dense strongly interacting matter. They can provide insight into the restoration of chiral symmetry. The chiral condensate as well as other chirally odd condensates, such as certain four-quark condensates, are linked to order parameters of spontaneous chiral symmetry breaking. Thus, the evaluation of these higher order condensate contributions in the framework of QCD sum rules is of high interest. We present a general method for projecting Lorentz indices of ground state expectation values providing a crucial step towards a comprehensive calculation of higher order corrections to the operator product expansion of hadrons, especially D mesons, in a strongly interacting medium.
Low-energy sum rules and large-N$_{c}$ consistency conditions
Broniowski, W
1994-01-01
The large-$N_c$ consistency conditions for axial vector and isovector magnetic couplings of pions to baryons are discussed from the point of view of low-energy current-algebra sum rules (Adler-Weisberger, Cabibbo-Radicati). In particular, we show how the result that ratios of axial vector and isovector magnetic coupling constants get corrections only at the order $1/N_c^2$ follows from the $N_c$-counting of appropriate cross sections. This counting is performed using various approaches at the quark and hadronic level. Other implications of our method are also presented.
Analysis of 1/2+ baryon states containing fourth-family quarks from QCD sum rules
YOU Fu-Yi; WANG Zhi-Gang; WAN Shao-Long
2012-01-01
When the fourth generation of quarks have sufficiently small mixing with ordinary standard-model quarks,the hadrons made up from these quarks can be long-lived enough.We analyze the 1/2+ baryon statescontaining fourth-generation quarks and standard-model quarks,i.e.the charm or bottom quarks,in the QCD sum rules approach.Considering the perturbative and two gluon condensate contributions in the calculation,we give the numerical results of the masses and pole residues.
Analysis of $\\Omega_b^-(bss)$ and $\\Omega_c^0(css)$ with QCD sum rules
Wang, Zhi-Gang
2008-01-01
In this article, we calculate the masses and the pole residues of the ${1/2}^+$ heavy baryons $\\Omega_c^0(css)$ and $\\Omega_b^-(bss)$ with the QCD sum rules. The numerical values $M_{\\Omega_c^0}=(2.72\\pm0.18) \\rm{GeV}$ (or $M_{\\Omega_c^0}=(2.71\\pm0.18) \\rm{GeV}$) and $M_{\\Omega_b^-}=(6.13\\pm0.12) \\rm{GeV}$ (or $M_{\\Omega_b^-}=(6.18\\pm0.13) \\rm{GeV}$) are in good agreement with the experimental data.
B ---> pi and B ---> K transitions from QCD sum rules on the light cone
Ball, Patricia
1998-09-01
I calculate the form factors describing semileptonic and penguin-induced decays of B mesons into light pseudoscalar mesons. The form factors are calculated from QCD sum rules on the light-cone including contributions up to twist 4, radiative corrections to the leading twist contribution and SU(3)-breaking effects. The theoretical uncertainty is estimated to be \\sim 15%. The heavy-quark-limit relations between semileptonic and penguin form factors are found to be valid in the full accessible range of momentum transfer.
Leutwyler-Smilga sum rules for Ginsparg-Wilson lattice fermions
Farchioni, F
1999-01-01
We argue that lattice QCD with Ginsparg-Wilson fermions satisfies the Leutwyler-Smilga sum rules for the eigenvalues of the chiral Dirac operator. The result is obtained in the one flavor case, by rephrasing Leutwyler and Smilga's original analysis for the finite volume partition function. This is a further evidence that Ginsparg-Wilson fermions, even if breaking explicitly the chirality on the lattice in accordance to the Nielsen-Ninomiya theorem, mimic the main features of the continuum theory related to chiral symmetry.
Magnetic moment for the negative parity Λ → Σ0 transition in light cone QCD sum rules
Aliev, T. M.; Savcı, M.
2016-07-01
The magnetic moment of the Λ →Σ0 transition between negative parity baryons is calculated in framework of the QCD sum rules approach by using the general form of the interpolating currents. The pollution arising from the positive-to-positive, and positive-to-negative parity baryons is eliminated by constructing the sum rules for different Lorentz structures. A comparison of our result with the predictions of the results of other approaches for the positive parity baryons is presented.
Aliev, T M
2015-01-01
The magnetic moment of the $\\Lambda \\to \\Sigma^0$ transition between negative parity, baryons is calculated in framework of the QCD sum rules approach, using the general form of the interpolating currents. The pollution arising from the positive--to--positive, and positive to negative parity baryons are eliminated by constructing the sum rules for different Lorentz structures. Nonzero value of the considered magnetic moment can be attributed to the violation of the $SU(3)$ symmetry.
Kumar, Ashok; Thakkar, Ajit J.
2011-11-01
Experimental photoabsorption cross-sections combined with constraints provided by the Kuhn-Reiche-Thomas sum rule and the high-energy behavior of the dipole-oscillator-strength density are used to construct dipole oscillator strength distributions for buckminsterfullerene (C60). The distributions are used to predict dipole sum rules Sk, mean excitation energies Ik, the frequency dependent polarizability, and C6 coefficients for the long-range dipole-dipole interactions of C60 with a variety of atoms and molecules.
New Sum Rule Determination of the Mass and Strangeness Content of the Nucleon
Nasrallah, Nasrallah F
2013-01-01
A new QCD calculation of the mass of the nucleon is presented. It makes use of a polynomial kernel in the dispersion integrals tailored to practically eliminate the contribution of the unknown 1=2+ and 1=2- continuum. This approach avoids the arbitrariness and instability attached to the Borel kernel used in previous sum rules calculations. Our method yields stable results for the nucleon mass and coupling. For standard values of the condensates, the prediction of the nucleon mass in the chiral limit is mN = (830+/-50)MeV. With the pion-nucleon sigma-term given by chiral perturbation theory and the strange sigma-term estimated by the Zweig rule we get mN = (990+/-50)MeV.
Searching for hidden-charm baryonium signals in QCD sum rules
Chen, Hua-Xing; Zhou, Dan [Beihang University, School of Physics, Beijing Key Laboratory of Advanced Nuclear Materials and Physics, Beijing (China); Chen, Wei [University of Saskatchewan, Department of Physics and Engineering Physics, Saskatoon, SK (Canada); Liu, Xiang [Lanzhou University, School of Physical Science and Technology, Lanzhou (China); Lanzhou University, Research Center for Hadron and CSR Physics, Institute of Modern Physics of CAS, Lanzhou (China); Zhu, Shi-Lin [Peking University, School of Physics, State Key Laboratory of Nuclear Physics and Technology, Beijing (China); Collaborative Innovation Center of Quantum Matter, Beijing (China); Peking University, Center of High Energy Physics, Beijing (China)
2016-11-15
We give an explicit QCD sum rule investigation for hidden-charm baryonium states with the quark content u anti ud anti dc anti c, spin J = 0/1/2/3, and of both positive and negative parities. We systematically construct the relevant local hidden-charm baryonium interpolating currents, which can actually couple to various structures, including hidden-charm baryonium states, charmonium states plus two pions, and hidden-charm tetraquark states plus one pion, etc. We do not know which structure these currents couple to at the beginning, but after sum rule analyses we can obtain some information. We find some of them can couple to hidden-charm baryonium states, using which we evaluate the masses of the lowest-lying hidden-charm baryonium states with quantum numbers J{sup P} = 2{sup -}/3{sup -}/0{sup +}/1{sup +}/2{sup +} to be around 5.0 GeV. We suggest to search for hidden-charm baryonium states, especially the one of J = 3{sup -}, in the D-wave J/ψππ and P-wave J/ψρ and J/ψω channels in this energy region. (orig.)
Exclusive radiative b-decays in the light-cone QCD sum rule approach
Ali, A; Simma, H
1994-01-01
We carry out a detailed study of exclusive radiative rare $B$-decays in the framework of the QCD sum rules on the light cone, which combines the traditional QCD sum rule technique with the description of final state vector mesons in terms of the light-cone wave functions of increasing twist. The decays considered are: $B_{u,d} \\to K^* +\\gamma, B_{u,d}\\to \\rho+\\gamma, B_d\\to \\omega+\\gamma$ and the corresponding decays of the $B_s$ mesons, $B_s\\to \\phi+\\gamma$ and $B_s\\to K^*+\\gamma$. Based on our estimate of the transition form factor $F_1^{B \\to K^*\\pg}(0) =0.32\\pm0.05$, we find for the branching ratio $BR(B \\to K^* + \\gamma) = (4.8\\pm 1.5)\\times 10^{-5}$, which is in agreement with the observed value measured by the CLEO collaboration. We present detailed estimates for the ratios of the radiative decay form factors, which are then used to predict the rates for the exclusive radiative B-decays listed above. This in principle allows the extraction of the CKM matrix element $|V_{td}|$ from the penguin-dominated...
Reanalysis of the $X(3915)$, $X(4500)$ and $X(4700)$ with QCD sum rules
Wang, Zhi-Gang
2016-01-01
In this article, we study the $C\\gamma_5\\otimes \\gamma_5C$ type and $C\\otimes C$ type scalar $cs\\bar{c}\\bar{s}$ tetraquark states with the QCD sum rules by calculating the contributions of the vacuum condensates up to dimension 10 in a consistent way. The ground state masses $M_{C\\gamma_5\\otimes \\gamma_5C}=3.89\\pm 0.05\\,\\rm{GeV}$ and $M_{C\\otimes C}=5.48\\pm0.10\\,\\rm{GeV}$ support assigning the $X(3915)$ to be the ground state $C\\gamma_5\\otimes \\gamma_5C$ type tetraquark state with $J^{PC}=0^{++}$, but do not support assigning the $X(4700)$ to be the ground state $C\\otimes C$ type $cs\\bar{c}\\bar{s}$ tetraquark state with $J^{PC}=0^{++}$. Then we tentatively assign the $X(3915)$ and $X(4500)$ to be the 1S and 2S $C\\gamma_5\\otimes \\gamma_5C$ type scalar $cs\\bar{c}\\bar{s}$ tetraquark states respectively, and obtain the 1S mass $M_{\\rm 1S}=3.85^{+0.18}_{-0.17}\\,\\rm{GeV}$ and 2S mass $M_{\\rm 2S}=4.35^{+0.10}_{-0.11}\\,\\rm{GeV}$ from the QCD sum rules, which support assigning the $X(3915)$ to be the 1S $C\\gamma_5\\oti...
XYZ-like Spectra from Laplace Sum Rule at N2LO in the Chiral Limit
Albuquerque, R; Fanomezana, F; Rabemananjara, A; Rabetiarivony, D; Randriamanatrika, G
2016-01-01
We present new compact integrated expressions of QCD spectral functions of heavy-light molecules and four-quark $XYZ$-like states at lowest order (LO) of perturbative (PT) QCD and up to $d=8$ condensates of the Operator Product Expansion (OPE). Then, we improve previous LO results from QCD spectral sum rules (QSSR), on the $XYZ$-like masses and decay constants (which suffer from the ill-defined heavy quark mass) by including up to next-to-next leading order (N2LO) PT QCD corrections, which we have estimated by assuming the factorization of the four-quark spectral functions. PT N3LO corrections are estimated using a geometric growth of the PT series and are included in the systematic errors. Our optimal results based on stability criteria with respect to the variations of the $\\tau$-Laplace sum rule (LSR) variable, QCD continuum threshold $t_c $ and subtraction constant $\\mu$ are summarized in Tables 11 to 14. We conclude that the masses of the $XZ$ observed states are compatible with (almost) pure $J^{PC}=1^{...
Calculation of heavy meson decay form factors using QCD light cone sum rules
Klein, Christoph; Faller, Sven; Khodjamirian, Alexander; Mannel, Thomas [Theoretische Physik 1, Fachbereich Physik, Universitaet Siegen (Germany); Offen, Nils [Laboratoire de Physique Theorique CNRS/Univ. Paris-Sud 11, Orsay (France)
2009-07-01
For the determination of CKM-matrix elements from exclusive semileptonic heavy meson decays it is important to know the corresponding form factors, which describe the hadronic dynamics. Since the form factors need some theoretical input, it is crucial to have a few independent calculations to extract the CKM-parameters from experimental data. One of these is the method of QCD sum rules, which will be applied here. In this talk we present our results from the use of different versions of the method of light cone sum rules (LCSR) for the determination of the B{yields} D{sup (*)}- as well as the D{yields}{pi} and D{yields}K-form factors. For B{yields}D{sup (*)} we use the new version of LCSR with B-meson-distribution amplitudes, which is applicable in the kinematical region of high recoil of the produced meson. The results are compared with recent experimental data and their expansion in the heavy quark mass is discussed. Concerning D{yields} {pi},K we employ and update the conventional LCSR with {pi}/K-distribution amplitudes. With the calculated form factors we determine the ratio vertical stroke V{sub cd} vertical stroke / vertical stroke V{sub cs} vertical stroke from new experimental data.
Heavy-light diquark masses from QCD sum rules and constituent diquark models of tetraquarks
Kleiv, R. T.; Steele, T. G.; Zhang, Ailin; Blokland, Ian
2013-06-01
Diquarks with JP=0±, 1± containing a heavy (charm or bottom) quark and a light quark are investigated using QCD Laplace sum rules. Masses are determined using appropriately constructed gauge invariant correlation functions, including for the first time next-to-leading order perturbative contributions. The JP=0+ and 1+ charm-light diquark masses are, respectively, found to be 1.86±0.05 and 1.87±0.10GeV, while those of the 0+ and 1+ bottom-light diquarks are both determined to be 5.08±0.04GeV. The sum rules derived for heavy-light diquarks with negative parity are poorly behaved and do not permit unambiguous mass predictions, in agreement with previous results for negative parity light diquarks. The scalar and axial vector heavy-light diquark masses are degenerate within uncertainty, as expected by heavy quark symmetry considerations. Furthermore, these mass predictions are in good agreement with masses extracted in constituent diquark models of the tetraquark candidates X(3872) and Yb(10890). Thus these results provide QCD support for the interpretation of the X(3872) and Yb(10890) as JPC=1++ tetraquark states composed of diquark clusters. Further implications for tetraquarks among the heavy quarkoniumlike XYZ states are discussed.
Study of the $D^*\\rho$ system using QCD sum rules
Torres, A Martinez; Nielsen, M; Navarra, F S; Oset, E
2013-01-01
In this talk I present a study of the $D^* \\rho$ system made by using the method of QCD sum rules. Considering isospin and spin projectors, we investigate the different configurations and obtain three $D^*$ mesons with isospin $I=1/2$, spin $S=0$, $1$, $2$ and with masses $2500\\pm 67$ MeV, $2523\\pm60$ MeV, and $2439\\pm119$ MeV, respectively. The last state can be related to $D^*_2(2460)$ (spin 2) listed by the Particle Data Group, while one of the first two might be associated with $D^*(2640)$, whose spin-parity is unknown. In the case of $I=3/2$ we also find evidences of three states with spin 0, 1 and 2, respectively, with masses $2467\\pm82$ MeV, $2420\\pm128$ MeV, and $2550\\pm56$ MeV.
Reanalysis of X(4140) as axial-vector tetraquark state with QCD sum rules
Wang, Zhi-Gang
2016-12-01
In this article, we take X(4140) as the diquark-antidiquark type csbar{c}bar{s} tetraquark state with J^{PC}=1^{++}, and we study the mass and pole residue with the QCD sum rules in detail by constructing two types of interpolating currents. The numerical results M_{X_{L,+}}=3.95± 0.09 GeV and M_{X_{H,+}}=5.00± 0.10 GeV disfavor assigning the X(4140) to the J^{PC}=1^{++} diquark-antidiquark type csbar{c}bar{s} tetraquark state. Moreover, we obtain the masses of the J^{PC}=1^{+-} diquark-antidiquark type csbar{c}bar{s} tetraquark states as a byproduct. The present predictions can be confronted to the experimental data in the future.
Third family corrections to tri-bimaximal lepton mixing and a new sum rule
Antusch, Stefan [Max-Planck-Institut fuer Physik (Werner-Heisenberg-Institut) Foehringer Ring 6, D-80805 Muenchen (Germany)], E-mail: antusch@mppmu.mpg.de; King, Stephen F. [School of Physics and Astronomy, University of Southampton, SO16 1BJ Southampton (United Kingdom)], E-mail: sfk@hep.phys.soton.ac.uk; Malinsky, Michal [School of Physics and Astronomy, University of Southampton, SO16 1BJ Southampton (United Kingdom)], E-mail: malinsky@phys.soton.ac.uk
2009-01-19
We investigate the theoretical stability of the predictions of tri-bimaximal neutrino mixing with respect to third family wave-function corrections. Such third family wave-function corrections can arise from either the canonical normalisation of the kinetic terms or renormalisation group running effects. At leading order both sorts of corrections can be subsumed into a single universal parameter. For hierarchical neutrinos, this leads to a new testable lepton mixing sum rule s=rcos{delta}+2/3 a (where s,r,a describe the deviations of solar, reactor and atmospheric mixing angles from their tri-bimaximal values, and {delta} is the observable Dirac CP phase) which is stable under all leading order third family wave-function corrections, as well as Cabibbo-like charged lepton mixing effects.
Mass Predictions of Open-Flavour Hybrid Mesons from QCD Sum Rules
Ho, Jason; Steele, Tom
2016-01-01
Within QCD, colourless states may be constructed corresponding to exotic matter outside of the traditional quark model. Experiments have recently observed tetraquark and pentaquark states, but no definitive hybrid meson signals have been observed. With the construction of the PANDA experiment at FAIR, and with full commissioning of the GlueX experiment at JLab expected to be completed this year, the opportunity for the observation of hybrid mesons has greatly increased. However, theoretical calculations are necessary to ascertain the identity of any experimental resonances that may be observed. We present selected QCD sum rule results from a full range of quantum numbers for open-flavour hybrid mesons with heavy valence quark content, including non-perturbative condensate contributions up to six-dimensions.
Sum rules and spectral density flow in QCD and in superconformal theories
Costantini Antonio
2014-01-01
Full Text Available We discuss the signature of the anomalous breaking of the superconformal symmetry in N${\\cal N}$ = 1 super Yang Mills theory and its manifestation in the form of anomaly poles. Moreover, we describe the massive deformations of the N${\\cal N}$ = 1 theory and the spectral densities of the corresponding anomaly form factors. These are characterized by spectral densities which flow with the mass deformation and turn the continuum contributions from the two-particle cuts of the intermediate states into poles, with a single sum rule satisfied by each component. The poles can be interpreted as signaling the exchange of a composite axion/dilaton/dilatino (ADD multiplet in the effective Lagrangian. We conclude that global anomalous currents characterized by a single flow in the perturbative picture always predict the existence of composite interpolating fields.
Study of the D*ρ system using QCD sum rules
Torres, A. Martínez; Khemchandani, K. P.; Nielsen, M.; Navarra, F. S. [Instituto de Física, Universidade de São Paulo, C. P. 66318, 05389-970 São Paulo, SP (Brazil); Oset, E. [Departamento de Física Teórica and IFIC, Centro Mixto Universidad de Valencia-CSIC, Institutos de Investigación de Paterna, Apartado 22085, 46071 Valencia (Spain)
2014-11-11
In this proceeding we present a study of the D*ρ system made by using the method of QCD sum rules. Considering isospin and spin projectors, we investigate the different configurations and obtain three D* mesons with isospin I = 1/2, spin S = 0, 1, 2 and with masses 2500±67 MeV, 2523±60 MeV, and 2439±119 MeV, respectively. The last state can be related to D{sub 2}{sup *} (2460) (spin 2) listed by the Particle Data Group, while one of the first two might be associated with D*(2640), whose spin-parity is unknown. In the case of I = 3/2 we also find evidences of three states with spin 0, 1 and 2, respectively, with masses 2467±82 MeV, 2420±128 MeV, and 2550±56 MeV.
Masses of Open-Flavour Heavy-Light Hybrids from QCD Sum Rules
Ho, Jason; Harnett, Derek; Steele, Tom
2017-01-01
Our current understanding of the strong interaction (QCD) permits the construction of colour singlet states with novel structures that do not fit within the traditional quark model, including hybrid mesons. To date, though other exotic structures such as pentaquark and tetraquark states have been confirmed, no unambiguous hybrid meson signals have been observed. However, with data collection at the GlueX experiment ongoing and with the construction of the PANDA experiment at FAIR, the opportunity to observe hybrid states has never been better. As theoretical calculations are a necessary piece for the identification of any observed experimental resonance, we present our mass predictions of heavy-light open-flavour hybrid mesons using QCD Laplace sum-rules for all scalar and vector JP channels, and including non-perturbative condensate contributions up to six-dimensions.
Malila, Jussi; McGraw, Robert; Laaksonen, Ari; Lehtinen, Kari E. J.
2015-01-01
Despite recent advances in monitoring nucleation from a vapor at close-to-molecular resolution, the identity of the critical cluster, forming the bottleneck for the nucleation process, remains elusive. During past twenty years, the first nucleation theorem has been often used to extract the size of the critical cluster from nucleation rate measurements. However, derivations of the first nucleation theorem invoke certain questionable assumptions that may fail, e.g., in the case of atmospheric new particle formation, including absence of sub-critical cluster losses and heterogeneous nucleation on pre-existing nanoparticles. Here, we extend the kinetic derivation of the first nucleation theorem to give a general framework to include such processes, yielding sum rules connecting the size dependent particle formation and loss rates to the corresponding loss-free nucleation rate and the apparent critical size from a naïve application of the first nucleation theorem that neglects them.
QCD Sum Rules for the {lambda}{sub b} semileptonic decay
Marques de Carvalho, R.S.; Nielsen, M. [Sao Paulo Univ., SP (Brazil). Inst. de Fisica. Grupo de Fisica Nuclear Teorica e Fenomenologia de Particulas Elementares
2001-07-01
We use the QCD Sum Rule approach to evaluate the form factors and decay rates of {lambda}{sub b} {yields} {lambda}{sub c}{sup +} + l + {nu}-bar{sub l} decay. This decay is represented by a three point function of the weak transition current and the interpolating fields of {lambda}{sub b} and {lambda}{sub c}. We calculate the theoretical part by performing the Operator Product Expansion of this three point function. In the phenomenological side, we use the experimental information of the decay amplitude. As usual we perform a Borel transform in these two sides in order to obtain the form factors. With this information we can obtain the decay rates. After the calculation of these quantities we compare our results with the experimental ones. (author)
Reanalysis of the $X(4140)$ as axialvector tetraquark state with QCD sum rules
Wang, Zhi-Gang
2016-01-01
In this article, we take the $X(4140)$ as the diquark-antidiquark type $cs\\bar{c}\\bar{s}$ tetraquark state with $J^{PC}=1^{++}$, and study the mass and pole residue with the QCD sum rules in details by constructing two types interpolating currents. The numerical results $M_{X_{L,+}}=3.95\\pm0.09\\,\\rm{GeV}$ and $M_{X_{H,+}}=5.00\\pm0.10\\,\\rm{GeV}$ disfavor assigning the $X(4140)$ to be the $J^{PC}=1^{++}$ diquark-antidiquark type tetraquark state. Furthermore, we obtain the masses of the $J^{PC}=1^{+-}$ diquark-antidiquark type $cs\\bar{c}\\bar{s}$ tetraquark states as a byproduct. The present predictions can be confronted to the experimental data in the future.
QCD sum rules study of {xi}{sub c} and {xi}{sub b} baryons
Duraes, Francisco O. [Centro de Ciencias e Humanidades, Universidade Presbiteriana Mackenzie, R. da Consolacao 930, 01302-907 Sao Paulo, SP (Brazil)], E-mail: duraes@mackenzie.com.br; Nielsen, Marina [Instituto de Fisica, Universidade de Sao Paulo, C.P. 66318, 05389-970 Sao Paulo, SP (Brazil)], E-mail: mnielsen@if.usp.br
2007-12-13
We use QCD sum rules to study the masses of the baryons {xi}{sub c} and {xi}{sub b}. We work with a current where the strange and the light quarks are in a relative spin zero, at leading order in {alpha}{sub s}. We consider the contributions of condensates up to dimension six. For {xi}{sub b} we get m{sub {xi}{sub b}}=(5.75{+-}0.25) GeV, and for {xi}{sub c} we get m{sub {xi}{sub c}}=(2.5{+-}0.2) GeV, both in excellent agreement with the experimental values. We also make predictions to the state {omega}{sub b}(ssb) obtaining m{sub {omega}{sub b}}=(5.82{+-}0.23) GeV.
Understanding close-lying exotic charmonia states within QCD sum rules
Martínez Torres, A.; Khemchandani, K. P.; Dias, J. M.; Navarra, F. S.; Nielsen, M.
2017-10-01
Motivated by the experimental findings of some new exotic states decaying into channels like J / ψϕ, we investigate the formation of resonances/bound states in the Ds* Dbars* system using QCD sum rules. To do this we start with a current of the type vector times vector and use spin projectors to separate the spin 0, 1 and 2 contributions to the correlation function. We find three states with isospin 0, nearly spin degenerate, with a mass around 4.1 GeV. We have also investigated the decay of these states to J / ψϕ and provide the corresponding partial widths. Such information should be useful for experimental studies in future.
D+→η(')l+νl semileptonic decays in light-cone sum rules
LI Jing-Wu; XUE Dan-Qing; XU Qing-Qiang; WU Xiang-Yao
2011-01-01
We calculate the D→η transition form factor in light-cone sum rules by taking improved current correlators to avoid the pollution from the twist-3 wave function. We get consistent results of the D →η lν decays with the experimental data. By comparing the difference between the results of the branching ratios of D+ →ηlν from a two-pole parameterization model and from a BZ parameterization model, we find that the two-pole model and the BZ model are comparably believable. One way is supposed for the determination of the η-η' mixing angle from the dependence of the branching ratios of D →ηlν decays on the η-η' mixing angle.
Reanalysis of the (0+,1+) States Bs0 and Bs1 with QCD Sum Rules
WANG Zhi-Gang
2008-01-01
We calculate the masses and decay constants of the P-wave strange-bottomed mesons Bs0 and Bs1 with the QCD sum rules, and observe that the central values of the masses Bs0 and Bs1 are smaller than the corresponding BK and B* K thresholds respectively, the strong decays Bs0 → BK and Bs1 → B* K are kinematically forbidden.They can decay through the isospin violation processes Bs0 → Bsη→, Bsπ0 and Bs1 → Bsη→, Bs*π0. The bottomed mesons Bs0 and Bs1, just like their charmed cousins Ds0(2317) and Ds1(2460), may be very narrow.
Liu, C; Liu, J; Yao, Y X; Wu, P; Wang, C Z; Ho, K M
2016-10-11
We recently proposed the correlation matrix renormalization (CMR) theory to treat the electronic correlation effects [Phys. Rev. B 2014, 89, 045131 and Sci. Rep. 2015, 5, 13478] in ground state total energy calculations of molecular systems using the Gutzwiller variational wave function (GWF). By adopting a number of approximations, the computational effort of the CMR can be reduced to a level similar to Hartree-Fock calculations. This paper reports our recent progress in minimizing the error originating from some of these approximations. We introduce a novel sum-rule correction to obtain a more accurate description of the intersite electron correlation effects in total energy calculations. Benchmark calculations are performed on a set of molecules to show the reasonable accuracy of the method.
Masses of Open-Flavour Heavy-Light Hybrids from QCD Sum-Rules
Ho, J; Steele, T G
2016-01-01
We use QCD Laplace sum-rules to predict masses of open-flavour heavy-light hybrids where one of the hybrid's constituent quarks is a charm or bottom and the other is an up, down, or strange. We compute leading-order, diagonal correlation functions of several hybrid interpolating currents, taking into account QCD condensates up to dimension-six, and extract mass predictions for all $J^P\\in\\{0^{\\pm},\\,1^{\\pm}\\}$. Within theoretical uncertainties, we find degeneracy between the heavy-nonstrange and heavy-strange hybrids in all $J^P$ channels. Also, our mass predictions are nearly degenerate under parity flips. For the charm-light hybrids there is a clear mass hierarchy of heavier scalar states which becomes less pronounced for the bottom-light hybrids. Possible effects of mixing with conventional quark-antiquark mesons are also explored.
QCD sum rule calculation of quark-gluon three-body components in the B-meson wave function
Nishikawa, Tetsuo; Tanaka, Kazuhiro
2011-10-01
We discuss the QCD sum rule calculation of the heavy-quark effective theory parameters λE and λH, which represent quark-gluon three-body components in the B-meson wave function. We update the sum rules for λE,H calculating the new higher-order contributions to the operator product expansion for the corresponding correlator, i.e., the order αs radiative corrections to the Wilson coefficients associated with the dimension-5 quark-gluon mixed condensate, and the power corrections due to the dimension-6 vacuum condensates. We find that the new radiative corrections significantly improve stability of the corresponding Borel sum rules, modifying the values of λE,H.
Lower and upper bounds on the mass of light quark-antiquark scalar resonance in the SVZ sum rules
Afonin, S S
2016-01-01
The calculation of the mass of light scalar isosinglet meson within the Shifman--Vainshtein--Zakharov (SVZ) sum rules is revisited. We develop simple analytical methods for estimation of hadron masses in the SVZ approach and try to reveal the origin of their numerical values. The calculations of hadron parameters in the SVZ sum rules are known to be heavily based on a choice of the perturbative threshold. This choice requires some important ad hoc information. We show analytically that the scalar mass under consideration has a lower and upper bound which are independent of this choice. The lower limit lies around the $\\omega$-meson mass and the upper one does near the $f_1$-meson mass. Our analysis seems to finally exclude the interpretation of the $f_0(500)$ (called also $\\sigma$) meson as a quark-antiquark state in the SVZ sum rules.
Buchheim, Thomas; Kampfer, Burkhard
2014-01-01
Wilson coefficients of light four-quark condensates in QCD sum rules are evaluated for pseudo-scalar $D$ mesons, thus, pushing the sum rules toward mass dimension six. Contrary to the situation for $\\bar{q}q$ mesons the impact of the four-quark condensates for vacuum as well as in-medium situations is found to be rather small within the Borel window used in previous analyses. The complete four-quark condensate contributions enable to identify candidates for an order parameter of spontaneous chiral symmetry breaking/restoration as well as to evaluate stability criteria of operator product expansions.
Bernard, V; Meißner, Ulf G; Kubis, Bastian; Mei{\\ss}ner, Ulf-G.
2005-01-01
We analyze the Fubini-Furlan-Rosetti sum rule in the framework of covariant baryon chiral perturbation theory to leading one-loop accuracy and including next-to-leading order polynomial contributions. We discuss the relation between the subtraction constants in the invariant amplitudes and certain low-energy constants employed in earlier chiral perturbation theory studies of threshold neutral pion photoproduction off nucleons. In particular, we consider the corrections to the sum rule due to the finite pion mass and show that below the threshold they agree well with determinations based on fixed-t dispersion relations. We also discuss the energy dependence of the electric dipole amplitude E_{0+}.
Magnetic moment for the negative parity Λ→Σ0 transition in light cone QCD sum rules
T.M. Aliev
2016-07-01
Full Text Available The magnetic moment of the Λ→Σ0 transition between negative parity baryons is calculated in framework of the QCD sum rules approach by using the general form of the interpolating currents. The pollution arising from the positive-to-positive, and positive-to-negative parity baryons is eliminated by constructing the sum rules for different Lorentz structures. A comparison of our result with the predictions of the results of other approaches for the positive parity baryons is presented.
YAN Xin-Hu; YE Yun-Xiu; CHEN Jian-Ping; LU Hai-Jiang; ZHU Peng-Jia; JIANG Feng-Jian
2015-01-01
The radiation and ionization energy loss are presented for single arm Monte Carlo simulation for the GDH sum rule experiment in Hall-A at the Jefferson Lab.Radiation and ionization energy loss are discussed for 12C elastic scattering simulation.The relative momentum ratio-Ap and 12C elastic cross section are compared without and with radiative energy loss and a reasonable shape is obtained by the simulation.The total energy loss distribution is obtained,showing a Landau shape for 12C elastic scattering.This simulation work will give good support for radiation correction analysis of the GDH sum rule experiment.
Renormalization group improved bottom mass from {Upsilon} sum rules at NNLL order
Hoang, Andre H.; Stahlhofen, Maximilian [Wien Univ. (Austria). Fakultaet fuer Physik; Ruiz-Femenia, Pedro [Wien Univ. (Austria). Fakultaet fuer Physik; Valencia Univ. - CSIC (Spain). IFIC
2012-09-15
We determine the bottom quark mass from non-relativistic large-n {Upsilon} sum rules with renormalization group improvement at next-to-next-to-leading logarithmic order. We compute the theoretical moments within the vNRQCD formalism and account for the summation of powers of the Coulomb singularities as well as of logarithmic terms proportional to powers of {alpha}{sub s} ln(n). The renormalization group improvement leads to a substantial stabilization of the theoretical moments compared to previous fixed-order analyses, which did not account for the systematic treatment of the logarithmic {alpha}{sub s} ln(n) terms, and allows for reliable single moment fits. For the current world average of the strong coupling ({alpha}{sub s}(M{sub Z})=0.1183{+-}0.0010) we obtain M{sub b}{sup 1S}=4.755{+-}0.057{sub pert} {+-}0.009{sub {alpha}{sub s}}{+-}0.003{sub exp} GeV for the bottom 1S mass and anti m{sub b}(anti m{sub b})=4.235{+-}0.055{sub pert}{+-}0.003{sub exp} GeV for the bottom MS mass, where we have quoted the perturbative error and the uncertainties from the strong coupling and the experimental data.
Cvetic, G
2001-01-01
A renormalization-scale-invariant generalization of the diagonal Pade approximants (dPA), developed previously, is extended so that it becomes renormalization-scheme-invariant as well. We do this explicitly when two terms beyond the leading order (NNLO,$\\sim {\\alpha}_s^3$) are known in the truncated perturbation series (TPS). Invariance under the change of the leading scheme parameter c_2 is achieved via a variant of the principle of minimal sensitivity. The subleading parameter c_3 is fixed so that a scale- and scheme-invariant Borel transform of the resummation approximant gives the correct location of the leading infrared renormalon pole. The leading higher-twist contribution, or a part of it, is thus believed to be contained implicitly in the resummation. We applied the approximant to the Bjorken polarized sum rule (BjPSR) at $Q^2 = 3 GeV^2$ and obtained in {bar MS} scheme ${\\alpha}_s(M_Z)=0.111^{+0.005}_{-0.012}$ or $0.113^{+0.004}_{-0.019}$, for two frameworks of extraction of the BjPSR-integral values ...
Gaunt, Jonathan R
2009-01-01
It is anticipated that hard double parton scatterings will occur frequently in the collisions of the LHC, producing interesting signals and significant backgrounds to certain single scattering processes. For double scattering processes in which the same hard scale t = ln(Q^2) is involved in both collisions, we require the double parton distributions (dPDFs) D_h^{j_1j_2}(x_1,x_2;t) in order to make theoretical predictions of their rates and properties. We describe the development of a new set of leading order dPDFs that represents an improvement on approaches used previously. First, we derive momentum and number sum rules that the dPDFs must satisfy. The fact that these must be obeyed at any scale is used to construct improved dPDFs at the input scale Q_0, for a particular choice of input scale (Q_0^2 = 1 GeV^2) and corresponding single PDFs (the MSTW2008LO set). We then describe a novel program which uses a direct x-space method to numerically integrate the LO DGLAP equation for the dPDFs, and which may be us...
QCD sum rules and thermal properties of Charmonium in the vector channel
Dominguez, C.A., E-mail: Cesareo.Dominguez@uct.ac.z [Centre for Theoretical Physics and Astrophysics, University of Cape Town, Rondebosch 7700 (South Africa); Department of Physics, Stellenbosch University, Stellenbosch 7600 (South Africa); Loewe, M., E-mail: mloewe@fis.puc.c [Facultad de Fisica, Pontificia Universidad Catolica de Chile, Casilla 306, Santiago 22 (Chile); Rojas, J.C., E-mail: jurojas@ucn.c [Departamento de Fisica, Universidad Catolica del Norte, Casilla 1280, Antofagasta (Chile); Zhang, Y., E-mail: Yingwen.Zhang@uct.ac.z [Department of Physics, Stellenbosch University, Stellenbosch 7600 (South Africa)
2010-10-15
The thermal evolution of the hadronic parameters of charmonium in the vector channel, i.e. the J/{psi} resonance mass, coupling (leptonic decay constant), total width, and continuum threshold is analyzed in the framework of thermal Hilbert moment QCD sum rules. The continuum threshold s{sub 0}, as in other hadronic channels, decreases with increasing temperature until the PQCD threshold s{sub 0}=4m{sub Q}{sup 2} is reached at T{approx_equal}1.22T{sub c} (m{sub Q} is the charm quark mass) and the J/{psi} mass is essentially constant in a wide range of temperatures. The other hadronic parameters behave in a very different way from those of light-light and heavy-light quark systems. The total width grows with temperature up to T{approx_equal}1.04T{sub c} beyond which it decreases sharply with increasing T. The resonance coupling is also initially constant beginning to increase monotonically around T{approx_equal}T{sub c}. This behavior strongly suggests that the J/{psi} resonance might survive beyond the critical temperature for deconfinement, in agreement with lattice QCD results.
Low-x contribution to the Bjorken sum rule within double logarithmic $ln^2x$ approximation
Kotlorz, D; Kotlorz, Dorota; Kotlorz, Andrzej
2004-01-01
The small-$x$ contributions to the Bjorken sum rule within double logarithmic $ln^2x$ approximation for different input parametrisations $g_1^{NS}(x,Q_0^2)$ are presented. Analytical solutions of the evolution equations for full and truncated moments of the unintegrated structure function $f^{NS}(x,Q^2)$ are used. Theoretical predictions for $\\int_{0}^{0.003} g_1^{NS}(x,Q^2=10) dx$ are compared with the SMC small-$x$ data. Rough estimation of the slope $\\lambda$, controlling the small-$x$ behaviour of $g_1^{NS}\\sim x^{-\\lambda}$ from the SMC data is performed. Double logarithmic terms $\\sim (\\alpha_s ln^2x)^n$ become leading when $x\\to 0$ and imply the singular behaviour of $g_1^{NS}\\sim x^{-0.4}$. This seems to be confirmed by recent experimental SMC and HERMES data. Advantages of the unified $ln^2x$+LO DGLAP approach and the crucial role of the running coupling $\\alpha_s=\\alpha_s(Q^2/z)$ at low-$x$ are also discussed.
Twist neutrality, a zero sum rule for oriented closed space curves with applications to circular DNA
Bohr, Jakob
2013-01-01
The interplay between global constraints and local material properties of chain molecules is a subject of emerging interest. Molecules that are intrinsically chiral, such as double-stranded DNA, is one example. They exhibit a non-vanishing strain-twist coupling, which depends on the local geometry, i.e. on curvature and torsion, yet the paths of closed loops are restricted by White's theorem. We suggest that the reciprocation of these principles leads to a twist neutrality condition. I.e. to a zero sum rule for the incremental change in the rate of winding along the curve. This has direct implications for plasmids. For small circular microDNAs it follows that there must exist a minimum length for these to be double-stranded. A first estimate of this minimum length is 120 base pairs. This is not far from the 80 base pairs which is about the smallest length observed in experimental studies. Slightly longer microDNAs are better described as an ellipse and a relationship between length and eccentricity for these ...
Precise f_{D*,B*} and f_{B_c} from QCD spectral sum rules
Narison, Stephan
2014-01-01
Anticipating future precise measurements of the B-like leptonic decays for alternative determinations of the CKM mixing angles or/and for predicting their semi-leptonic and hadronic decays, we pursue our program on the B-like mesons by improving the estimates of f_D* and f_B* [analogue to f_\\pi=130.4(2) MeV] using suitable ratios of the well-established (inverse) Laplace sum rules less affected by the systematics and known to N2LO pQCD and where the full d=6 non-perturbative condensate contributions are included. An estimate of the N3LO terms based on geometric growth of the pQCD series is included in the error calculations. Our optimal results based on stability criteria and on an (in)dependence on the choice of the QCD subtraction point read: f_D*/f_D=1.209(22),f_B*/f_B=1.031(8) which imply : f_D*=246(7) MeV and f_B*=212(8) MeV if we use our recent results in [1] for f_D and f_B. We complete the analysis by a direct estimate of f_Bc using the complete NLO + N2LO for massless m_c pQCD expression and complete...
Charm-quark mass from weighted finite energy QCD sum rules
Bodenstein, S; Dominguez, C A; Peñarrocha, J; Schilcher, K
2010-01-01
The running charm-quark mass in the $\\bar{MS}$ scheme is determined from weighted finite energy QCD sum rules (FESR) involving the vector current correlator. Only the short distance expansion of this correlator is used, together with integration kernels (weights) involving positive powers of $s$, the squared energy. The optimal kernels are found to be a simple {\\it pinched} kernel, and polynomials of the Legendre type. The former kernel reduces potential duality violations near the real axis in the complex s-plane, and the latter allows to extend the analysis to energy regions beyond the end point of the data. These kernels, together with the high energy expansion of the correlator, weigh the experimental and theoretical information differently from e.g. inverse moments FESR. Current, state of the art results for the vector correlator up to four-loop order in perturbative QCD are used in the FESR, together with the latest experimental data. The integration in the complex s-plane is performed using three diffe...
Precision calculation of threshold pi^- d scattering, pi N scattering lengths, and the GMO sum rule
Baru, V; Hoferichter, M; Kubis, B; Nogga, A; Phillips, D R
2011-01-01
We use chiral perturbation theory (ChPT) to calculate the $\\pi^- d$ scattering length with an accuracy of a few percent, including isospin-violating corrections both in the two- and three-body sector. In particular, we provide the technical details of a recent letter, where we used data on pionic deuterium and pionic hydrogen atoms to extract the isoscalar and isovector pion-nucleon scattering lengths $a^+$ and $a^-$. We study isospin-breaking contributions to the three-body part of $a_{\\pi^-d}$ due to mass differences, isospin violation in the $\\pi N$ scattering lengths, and virtual photons. This last class of effects is ostensibly infrared enhanced due to the smallness of the deuteron binding energy. However, we show that the leading virtual-photon effects that might undergo such enhancement cancel, and hence the standard ChPT counting provides a reliable estimate of isospin violation in $a_{\\pi^- d}$ due to virtual photons. Finally, we discuss the validity of the Goldberger-Miyazawa-Oehme sum rule in the p...
Stellar delta matter with delta-meson coupling constants constrained by QCD sum rule
Silva, Antonio Ferreira da [Secretaria de Educacao, Cultura e Desportos do Estado de Roraima (SECD/RR), Boa Vista, RR (Brazil); Oliveira, Jose Carlos Teixeira de [Universidade Federal de Roraima (UFRR), Boa Vista, RR (Brazil); Rodrigues, Hilario [Centro Federal de Educacao Tecnologica (CEFET-RJ), Rio de Janeiro, RJ (Brazil); Duarte, Sergio Barbosa [Centro Brasileiro de Pesquisas Fisicas (CBPF), Rio de Janeiro, RJ (Brazil); Chiapparini, Marcelo [Universidade do Estado do Rio de Janeiro (UERJ), RJ (Brazil)
2010-07-01
The considerable presence of delta-resonances (30% of baryonic population) in the dense phase of relativistic heavy ion collisions leads to a great interest in the study of the delta matter formation in the deep interior of compact stars. In the present work we determine the equation of state and the population of baryons and leptons and discuss the effects of the baryon-meson coupling constants to the formation of delta matter in the stellar medium. We use the non-linear Walecka model consisting of the octet of baryons of spin 1=2 (n, p, {Lambda}{sup 0}, {Sigma}{sup -}, {Sigma}{sup 0}, {Sigma}{sup +}, {Xi}{sup -}, {Xi}{sup 0}) and baryonic resonances of spin 3=2, represented by the delta resonances ({Delta}{sup -}, ({Delta}{sup 0}, ({Delta}{sup +}, ({Delta}{sup ++}) and {Omega}{sup -}, in the baryonic sector. In the leptonic sector we consider the electrons and muons. The coupling constants between the hyperons {Lambda}, {Sigma}, and {Xi} and the mesons {omega} and {rho} are fixed by using SU(6) symmetry, while the hyperons-{sigma} coupling constants are constrained by the consistence of the hypernuclear potential in the nuclear matter with hypernuclear data. In addition, we use the finite density QCD sum rule to determine the possible values of delta-meson coupling constants. (author)
Oliver, Luis
2014-01-01
In the heavy quark limit of QCD, using the Operator Product Expansion and the non-forward amplitude, as proposed by Nikolai Uraltsev, we formulate sum rules that generalize Bjorken and Uraltsev sum rules. We recover the Uraltsev lower bound for the slope of the Isgur-Wise (IW) function, that we generalize to higher derivatives. We show that these results have a clear interpretation in terms of the Lorentz group, since the IW function is given by an overlap between the initial and final light clouds, related by Lorentz transformations. Both the Lorentz group and the Sum Rules approach are equivalent. Moreover, we formulate an integral representation of the IW function with a positive measure. Inverting this integral formula, we obtain the measure in terms of the IW function, allowing to formulate criteria to decide if a given ansatz for the IW function is compatible or not with the sum rule constraints. We compare these theoretical constraints to some forms proposed in the literature.
The Polarised Photon $g_1^\\gamma$ Sum Rule at the Linear Collider and High Luminosity B Factories
Shore, G M
2004-01-01
The sum rule for the first moment of the polarised (virtual) photon structure function $g_1^\\gamma(x,Q^2;K^2)$ is revisited in the light of proposals for future $e^+ e^-$ colliders. The sum rule exhibits an array of phenomena characteristic of QCD: for real photons ($K^2=0$) electromagnetic gauge invariance constrains the first moment to vanish; the limit for asymptotic photon virtuality ($m_\\rho^2 \\ll K^2 \\ll Q^2$) is governed by the electromagnetic $U_A(1)$ axial anomaly and the approach to asymptopia by the gluonic anomaly; for intermediate values of $K^2$, it reflects the realisation of chiral symmetry and is determined by the off-shell radiative couplings of the pseudoscalar mesons; finally, like many polarisation phenomena in QCD, the first moment of $g_1^\\gamma$ involves the gluon topological susceptibility. In this paper, we review the original sum rule proposed by Narison, Shore and Veneziano and extend the relation with pseudoscalar mesons. The possibility of measuring the sum rule in future polaris...
Analysis of the Light-Flavor Scalar and Axial-Vector Diquark States with QCD Sum Rules
WANG Zhi-Gang
2013-01-01
In this article,we study the light-flavor scalar and axial-vector diquark states in the vacuum and in the nuclear matter using the QCD sum rules in a systematic way,and make reasonable predictions for their masses in the vacuum and in the nuclear matter.
Effect of Coulomb interaction on the X-ray magnetic circular dichroism spin sum rule in rare earths
Teramura, Y; Tanaka, A; Thole, BT; Jo, T
A deviation from the spin sum rule, which relates the integrated intensity of the X-ray magnetic circular dichroism (MCD) signal to the expectation value of the spin operator S-z ((S-z)), is numerically calculated in the case of the 3d --> 4f absorption for rare earths from the trivalent Ce to Tm.
Analysis of diffractive pd to Xd and pp to Xp interactions and test of the finite-mass sum rule
Akimov, Y; Golovanov, L B; Goulianos, K; Gross, D; Malamud, E; Melissinos, A C; Mukhin, S; Nitz, D; Olsen, S; Sticker, H; Tsarev, V A; Yamada, R; Zimmerman, P
1976-01-01
The first moment finite mass sum rule is tested by utilising cross- sections for pp to Xp extracted from recent Fermilab data on pd to Xd and also comparing with CERN ISR data. The dependences on M/sub x//sup 2/, t and s are also discussed. (11 refs).
WU Xing-Gang; YU Yao; CHEN Gu; HAN Hua-Yong
2011-01-01
The B-meson decay constant fB is an important component for studying the B-meson decays, which can be studied through QCD sum rules.We make a detailed discussion on fB from two sum rules up to next-to-leading order, i.e.sum rules Ⅰ and Ⅱ, which are derived from the conventional correlator and the correlator with chiral currents respectively.It is found that these two sum rules are consistent with each other.The sum rules Ⅱ involves less non-perturbative condensates as that of sum rules Ⅰ, and in principle, it can be more accurate if we know the dimensionfour gluon condensate well.It is found that fB decreases with the increment of mb, and to compare with the Belle experimental data on fB, both sum rules Ⅰ and Ⅱ prefer smaller pole b-quark mass, mb = 4.68 ± 0.07 GeV.By varying all the input parameters within their reasonable regions and by adding all the uncertainties in quadrature, we obtain fB = 172+23-25 MeV for sum rules Ⅰ and fB = 214+26-34 MeV for sum rules Ⅱ.PACS numbers: 11.55.Hx, 12.38.-t, 13.20.He, 12.38.Lg
XYZ-like spectra from Laplace sum rule at N2LO in the chiral limit
Albuquerque, R.; Narison, S.; Fanomezana, F.; Rabemananjara, A.; Rabetiarivony, D.; Randriamanatrika, G.
2016-12-01
We present new compact integrated expressions of QCD spectral functions of heavy-light molecules and four-quark XY Z-like states at lowest order (LO) of perturbative (PT) QCD and up to d = 8 condensates of the Operator Product Expansion (OPE). Then, by including up to next-to-next leading order (N2LO) PT QCD corrections, which we have estimated by assuming the factorization of the four-quark spectral functions, we improve previous LO results from QCD spectral sum rules (QSSR), on the XY Z-like masses and decay constants which suffer from the ill-defined heavy quark mass. PT N3LO corrections are estimated using a geometric growth of the PT series and are included in the systematic errors. Our optimal results based on stability criteria are summarized in Tables 11-14 and compared, in Sec. 10, with experimental candidates and some LO QSSR results. We conclude that the masses of the XZ observed states are compatible with (almost) pure JPC = 1+±, 0++ molecule or/and four-quark states. The ones of the 1-±, 0-± molecule/four-quark states are about 1.5 GeV above the Yc,b mesons experimental candidates and hadronic thresholds. We also find that the couplings of these exotics to the associated interpolating currents are weaker than that of ordinary D,B mesons (fDD ≈ 10-3f D) and may behave numerically as 1/m¯b3/2 (respectively 1/m¯b) for the 1+, 0+ (respectively 1-, 0-) states which can stimulate further theoretical studies of these decay constants.
Unitarity sum rules, three-site moose model, and the ATLAS 2 TeV diboson anomalies
Abe, Tomohiro; Nagai, Ryo; Okawa, Shohei; Tanabashi, Masaharu
2015-09-01
We investigate W' interpretations for the ATLAS 2 TeV diboson anomalies. The roles of the unitarity sum rules, which ensure the perturbativity of the longitudinal vector boson scattering amplitudes, are emphasized. We find the unitarity sum rules and the custodial symmetry are powerful enough to predict various nontrivial relations among W W Z', W Z W', W W h , W W'h and Z Z'h coupling strengths in a model independent manner. We also perform surveys in the general parameter space of W' models and find the ATLAS 2 TeV diboson anomalies may be interpreted as a W' particle of the three-site moose model, i.e., a Kaluza-Klein like particle in a deconstructed extra dimension model. It is also shown that the nonstandard-model-like Higgs boson is favored by the present data to interpret the ATLAS diboson anomalies as the consequences of the W' and Z' bosons.
$\\mu-H$ Lamb shift: dispersing the nucleon-excitation uncertainty with a finite energy sum rule
Gorchtein, Mikhail; Szczepaniak, Adam P
2013-01-01
We assess the two-photon exchange contribution to the Lamb shift in muonic hydrogen with forward dispersion relations. The subtraction constant $\\bar T(0,Q^2)$ that is necessary for a dispersive evaluation of the forward doubly-virtual Compton amplitude, through a finite energy sum rule, is related to the fixed J=0 pole generalized to the case of virtual photons. We evaluated this sum rule using excellent virtual photoabsorption data that are available. We find that the "proton polarizability correction" to the Lamb shift in muonic hydrogen is $-(40\\pm5)\\mu$eV. We conclude that nucleon structure-dependent uncertainty by itself is unlikely to resolve the large (300$\\mu$eV) discrepancy between direct measurement of the Lamb shift in $\\mu H$ and expectations based on conventional Hydrogen measurements.
Peters, Gerhard
2008-05-15
In this work the leading-twist next-to-leading order (NLO) correction to the light-cone sum rules prediction for the electromagnetic form factors of the nucleon are calculated. Here the Ioffe nucleon interpolation current is used and it is worked in the M{sub N}=0 approximation, with M{sub N} being the mass of the nucleon. In this approximation, only the Pauli form factor F{sub 2} receives a correction and the calculated correction is quite sizable. The numerical results for the proton form factors show the improved agreement with the experimental data. Furthermore the problems encountered when going away from M{sub N}=0 approximation at NLO, as well as, gauge invariance of the perturbative results are discussed. This work presents the first step towards the NLO accuracy in the light-cone sum rules for baryon form factors. (orig.)
Franta, Daniel, E-mail: franta@physics.muni.cz [Department of Physical Electronic, Faculty of Science, Masaryk University, Kotlářská 2, 61137 Brno (Czech Republic); Plasma Technologies, CEITEC — Central European Institute of Technology, Masaryk University Kamenice 5, 62500 Brno (Czech Republic); Nečas, David; Zajíčková, Lenka [Department of Physical Electronic, Faculty of Science, Masaryk University, Kotlářská 2, 61137 Brno (Czech Republic); Plasma Technologies, CEITEC — Central European Institute of Technology, Masaryk University Kamenice 5, 62500 Brno (Czech Republic); Ohlídal, Ivan [Department of Physical Electronic, Faculty of Science, Masaryk University, Kotlářská 2, 61137 Brno (Czech Republic)
2014-11-28
The distribution of the total transition strength, i.e. the right hand side of the integral form of Thomas–Reiche–Kuhn sum rule, into individual absorption processes is described for crystalline silicon containing interstitial oxygen. Utilization of the sum rule allows the construction of a dispersion model covering all elementary excitations from phonon absorption to core electron excitations. The dependence of transition strength of individual electronic and phonon contributions on temperature and oxygen content is described. - Highlights: • Distribution of transition strength for c-Si containing interstitial oxygen • Temperature dependence of transition strength of individual contributions • Dependence of transition strength on concentration of interstitial oxygen • Consideration of interband electronic transitions, free carriers, and phonons.
Magnetic moment of $X_Q$ state with $J^{PC}=1^{+\\pm}$ in light cone QCD sum rules
Agamaliev, A K; Savcı, M
2016-01-01
The magnetic moments of the recently observed resonance $X_b(5568)$ by DO Collaboration and its partner with charm quark are calculated in the framework of the light cone QCD sum rules, by assuming that these resonances are represented as tetra--quark states with quantum numbers $J^{PC}=1^{+\\pm}$. The magnetic moment can play critical role in determination of the quantum numbers, as well as giving useful information about the inner structure of these mesons.
Analysis of the decay B0→χc1π0 with light-cone QCD sum rules
Wang Zhi-Gang
2009-01-01
In this article,we calculate the contribution from the nonfactorizable soft hadronic matrix element to the decay B0→ Xc1π0 with the light-cone quantum chromo-dynamic (QCD) sum rules. The numerical results show that its contribution is rather large and should not be neglected. The total amplitudes lead to a branching fraction which is in agreement with the experimental data marginally.
How Precisely can we Determine the $\\piNN$ Coupling Constant from the Isovector GMO Sum Rule?
Loiseau, B; Thomas, A W
1999-01-01
The isovector GMO sum rule for zero energy forward pion-nucleon scattering iscritically studied to obtain the charged pion-nucleon coupling constant usingthe precise negatively charged pion-proton and pion-deuteron scattering lengthsdeduced recently from pionic atom experiments. This direct determination leadsto a pseudoscalar charged pion-nucleon coupling constant of 14.23 +- 0.09(statistic) +- 0.17 (systematic). We obtain also accurate values for thepion-nucleon scattering lengths.
Chen, Wei; Jin, Hong-ying; Kleiv, R. T.; Steele, T. G.; Wang, Meng; Xu, Qing
2013-08-01
QCD sum rules are employed to determine whether the X(3872) can be described as a mixed state that couples to JPC=1++ charmonium hybrid and D¯D* molecular currents. After calculating the mixed correlator of hybrid and molecular currents, we formulate the sum rule in terms of a mixing parameter that interpolates between the pure molecular and hybrid scenarios. As the mixing parameter is increased from the pure molecular case, the predicted mass increases until it reaches a maximum value in good agreement with the X(3872) and the resulting sum-rule analysis appears more robust than the pure molecular case.
Kivel, N A
2000-01-01
We applied QCD Light Cone Sum Rules to estimate power corrections to the helicity-conserving amplitude in the process $\\gamma^*\\gamma\\to \\pi\\pi$. We found that above $Q^2 \\sim 4$ GeV$^2$ power corrections are numerically small and the twist-2 part dominates.The amplitude can be reliably calculated in this region using models of $2 \\pi$ distribution amplitudes as an input. We found that the magnitude of the NLO corrections depends rather strongly on the normalization of the gluonic distribution amplitude.
Aliev, T M
2016-01-01
The strong coupling constants of the $\\pi$ and $K$ mesons with negative parity octet baryons are estimated within the light cone QCD sum rules. It is observed that all strong coupling constants, similar to the case for the positive parity baryons, can be described in terms of three invariant functions, where two of them correspond to the well known $F$ and $D$ couplings in the $SU(3)_f$ symmetry, and the third function describes the $SU(3)_f$ symmetry violating effects. We compare our predictions on the strong coupling constants of pseudoscalar mesons of negative parity baryons with those corresponding to the strong coupling constants for the positive parity baryons.
Higher-twist effects in the B → π transition form factor from QCD light-cone sum rules
Khodjamirian, Alexander; Rusov, Aleksey [Universitaet Siegen (Germany). Fakultaet IV, Department Physik, Theoretische Physik 1 Walter-Flex-Strasse 3 57068 Siegen
2016-07-01
I report on the progress in calculating new higher-twist corrections to the QCD light-cone sum rule for the B → π transition form factor. First, the expansion of the massive heavy-quark propagator in the external gluonic field near the light-cone was extended to include new terms containing the gluon-field strength derivatives. The resulting analytical expressions for the twist-5 and twist-6 contributions to the correlation function were obtained in a factorized approximation, expressed via the product of the quark-condensate density and the lower-twist pion distribution amplitudes. The numerical analysis of new higher-twist effects is in progress.
A measurement of $\\alpha_{s}$ (M$_{Z}^{2}$) from the Gross Llewellyn Smith sum rule
Harris, D A; Auchincloss, P S; De Barbaro, P; Bazarko, A O; Bernstein, R H; Bodek, A; Bolton, T; Budd, H; Conrad, J; Drucker, R B; Johnson, R A; Kim, J H; King, B J; Kinnel, T; Koizumi, G; Koutsoliotas, S; Lamm, M J; Lefmann, W C; Marsh, W; McFarland, K S; McNulty, C; Mishra, S R; Naples, D; Nienaber, P; Nussbaum, M; Oreglia, M J; Perera, L; Quintas, P Z; Romosan, A; Sakumoto, W K; Schumm, B A; Sciulli, F J; Seligman, W G; Shaevitz, M H; Smith, W H; Spentzouris, P; Steiner, R; Stern, E G; Vakili, M; Yang, U K
1995-01-01
The Gross Llewellyn Smith sum rule has been measured at different values of four-momentum transfer squared (Q^{2}) by combining the precise CCFR neutrino data with data from other deep-inelastic scattering experiments at lower values of Q^{2}. A comparison with the {\\cal O}(\\alpha^{3}_{s}) predictions of perturbative QCD yields a determination of \\alpha_{s} and its dependence on Q^{2} in the range 1\\,GeV^2 < Q^{2} < 20 \\,GeV^{2}. Low \\qsq\\ tests have greater sensitivity to \\alfs(\\mztwo) than high \\qsq\\ tests, since at low Q^2, \\alpha_s is large and changing rapidly.
Analysis of the X(3872), Zc(3900), and Zc(3885) as axial-vector tetraquark states with QCD sum rules
Wang, Zhi-Gang; Huang, Tao
2014-03-01
In this article, we distinguish the charge conjunctions of the interpolating currents, calculate the contributions of the vacuum condensates up to dimension 10 in a consistent way in the operator product expansion, study the masses and pole residues of the JPC=1+± hidden charmed tetraquark states with the QCD sum rules, and explore the energy-scale dependence in detail for the first time. The predictions MX=3.87-0.09+0.09 GeV and MZ=3.91-0.09+0.11 GeV support assigning the X(3872) and Zc(3900) [or Zc(3885)] as the 1++ and 1+- diquark-antidiquark type tetraquark states, respectively.
Relation between (e, e') sum rules in {sup 6,7}Li and {sup 4}He nuclei: Experiment and cluster model
Efros, V.D. [National Research Center ' ' Kurchatov Institute' ' , Moscow (Russian Federation); National Research Nuclear University MEPhI (Moscow Engineering Physics Institute), Moscow (Russian Federation); Timchenko, I.S.; Buki, A.Yu. [National Science Center ' ' Kharkov Institute of Physics and Technology' ' , Kharkov (Ukraine)
2016-09-15
The sums over (e, e') spectra of {sup 6}Li and {sup 7}Li nuclei which correspond to the longitudinal sum rule are studied. It is suggested that due to the cluster structure of the lithium isotopes these sums may approximately be expressed in terms of such a sum pertaining to the α-particle. Calculation of these sums is performed in the framework of cluster models with antisymmetrization done with respect to all the nucleons. At momentum transfers higher than 0.8 fm{sup -1} the relations expressing the A = 6 or 7 sum in terms of the A = 4 sum prove to be valid with rather high accuracy. In the region of momentum transfers around 1 fm{sup -1} the longitudinal correlation functions of {sup 6}Li and {sup 7}Li nuclei are found to be close to that of the α-particle. Basing on this, the difference between the q values at which the high-q limit of the inelastic sum rule is reached in the {sup 6,7}Li cases and the {sup 4}He case is explained. The experimental longitudinal sums in the range between 0.450 and 1.625 fm{sup -1} are employed to perform comparison with the theoretical sum rule calculated in the framework of cluster models. Out of the experimental sums, those in the range between 0.750 and 1.000 fm{sup -1} in the {sup 6}Li case and between 0.750 and 1.125 fm{sup -1} in the {sup 7}Li case are obtained in the present work. In the {sup 6}Li case a complete agreement between experiment and the calculated sum rule is found while in the {sup 7}Li case an agreement only at a qualitative level is observed. (orig.)
Kim, H; Oka, M; Lee, S H
2000-01-01
Using QCD sum rules, we compute the diagonal meson-baryon couplings, pi NN , eta NN , pi XI XI , eta XI XI , pi SIGMA SIGMA and eta SIGMA SIGMA , from the baryon-baryon correlation function with a meson: i integral d sup 4 x e sup i sup q supcentre dot sup x . The calculations are performed to leading order in p submu by considering the two separate Dirac structures, i gamma sub 5 gamma submu p supmu and gamma sub 5 sigma submu subnu q supmu p supnu separately. We first improve the previous sum rule calculations on these Dirac structures for the pi NN coupling by including three-particle pion wave functions of twist 4 and then extend the formalism to calculate the other couplings, eta NN , pi XI XI , eta XI XI , pi SIGMA SIGMA and eta SIGMA SIGMA . In the SU(3) symmetric limit, we identify the terms responsible for the F/D ratio in the OPE by matching the obtained couplings with their SU(3) relations. Depending on the Dirac structure considered, we find different identifications for the F/D ratio. The coupli...
Ikawa, Shun-ichi; Yamazaki, Shuichi; Kimura, Masao
1981-06-01
Another form of the sum rule for dipolar absorptions has been derived by means of quantum statistics. The difference between this and usually used form results from a quantum effect on the molecular rotational motion. By the joint use of the two forms, average rotational kinetic energies of water molec in the liquid and solid phases and some dipolar molecules in solutions have been estimated. It has been shown that the average rotational kinetic energ larger than the value expected from the classical equipartition rule, with an increase in the hindering potential for the rotational motion of the mole The dipole moments of water molecules in liquid and solid water have been estimated. These are considerably smaller than the gas-phase value.
Improved QCD sum rule study of $Z_{c}(3900)$ as a $\\bar{D}D^{*}$ molecular state
Zhang, Jian-Rong
2013-01-01
In the framework of QCD sum rules, we present an improved study of our previous work [Phys. Rev. D {\\bf80}, 056004 (2009)] particularly on the $\\bar{D}D^{*}$ molecular state to investigate that the possibility of the newly observed $Z_{c}(3900)$ as a $S$-wave $\\bar{D}D^{*}$ molecular state. To ensure the quality of QCD sum rule analysis, contributions of up to dimension nine are calculated to test the convergence of operator product expansion (OPE). We find that the two-quark condensate $$ is very large and makes the standard OPE convergence (i.e. the perturbative at least larger than each condensate contribution) happen at very large values of Borel parameters. By releasing the rigid OPE convergence criterion, one could find that the OPE convergence is still under control. We arrive at the numerical result $3.86\\pm0.27 {GeV}$ for $\\bar{D}D^{*}$, which agrees with the mass of $Z_{c}(3900)$ and could support the explanation of $Z_{c}(3900)$ in terms of a $S$-wave $\\bar{D}D^{*}$ molecular state.
Thermal Spectrum of Heavy Vector and Axial Vector Mesons in the Framework of QCD Sum Rules Method
Yazici, Enis
2016-01-01
The masses and the leptonic decay constants of vector and axial vector heavy-heavy mesons are calculated using the thermal QCD sum rules approach. While obtaining the QCD sum rules, additional operators in the Wilson expansion and also temperature dependency of the continuum threshold are taken into account. The masses and the decay constants remained unchanged up to $T\\simeq100~MeV$. After that point, they start to diminish. At the critical temperature, the masses decreased about $3\\%$, $5\\%$ and $14\\%$ for the vector mesons $\\Upsilon$, $B_{c}$ and $J/\\psi$; $6\\%$, $7\\%$ and $22\\%$ for the axial vector mesons $\\chi_{b1}$, $B_{c}$ and $\\chi_{c1}$, respectively. The decay constants reached about less than $20\\%$ of their vacuum values. The obtained results of the thermal mass and decay constant calculations at zero temperature are in a very good agreement with the other non-perturbative calculations at vacuum as well as with the experimental data.
The spin structure function g1p of the proton and a test of the Bjorken sum rule
C. Adolph
2016-02-01
Full Text Available New results for the double spin asymmetry A1p and the proton longitudinal spin structure function g1p are presented. They were obtained by the COMPASS Collaboration using polarised 200 GeV muons scattered off a longitudinally polarised NH3 target. The data were collected in 2011 and complement those recorded in 2007 at 160 GeV, in particular at lower values of x. They improve the statistical precision of g1p(x by about a factor of two in the region x≲0.02. A next-to-leading order QCD fit to the g1 world data is performed. It leads to a new determination of the quark spin contribution to the nucleon spin, ΔΣ, ranging from 0.26 to 0.36, and to a re-evaluation of the first moment of g1p. The uncertainty of ΔΣ is mostly due to the large uncertainty in the present determinations of the gluon helicity distribution. A new evaluation of the Bjorken sum rule based on the COMPASS results for the non-singlet structure function g1NS(x,Q2 yields as ratio of the axial and vector coupling constants |gA/gV|=1.22±0.05 (stat.±0.10 (syst., which validates the sum rule to an accuracy of about 9%.
Perturbative Corrections to $\\Lambda_b \\to \\Lambda$ Form Factors from QCD Light-Cone Sum Rules
Wang, Yu-Ming
2015-01-01
We compute radiative corrections to $\\Lambda_b \\to \\Lambda$ from factors, at next-to-leading logarithmic accuracy, from QCD light-cone sum rules with $\\Lambda_b$-baryon distribution amplitudes. Employing the diagrammatic approach factorization of the vacuum-to-$\\Lambda_b$-baryon correlation function is justified at leading power in $\\Lambda/m_b$, with the aid of the method of regions. Hard functions entering the factorization formulae are identical to the corresponding matching coefficients of heavy-to-light currents from QCD onto soft-collinear effective theory. The universal jet function from integrating out the hard-collinear fluctuations exhibits richer structures compared with the one involved in the factorization expressions of the vacuum-to-$B$-meson correlation function. Based upon the QCD resummation improved sum rules we observe that the perturbative corrections at ${\\cal O}(\\alpha_s)$ shift the $\\Lambda_b \\to \\Lambda$ from factors at large recoil significantly and the dominant contribution originat...
Effective restoration of dipole sum rules within the renormalized random-phase approximation
Hung, N Quang; Hao, T V Nhan; Phuc, L Tan
2016-01-01
The dipole excitations for calcium and zirconium isotopes are studied within the fully self-consistent Hartree-Fock mean field incorporated with the renormalized random-phase approximation (RRPA) using the Skyrme interaction SLy5. The RRPA takes into account the effect of ground-state correlations beyond RPA owing to the Pauli principle between the particle-hole pairs that form the RPA excitations as well as the correlations due to the particle-particle and hole-hole transitions, whose effects are treated here in an effective way. By comparing the RPA results with the RRPA ones, which are obtained for isoscalar (IS) and isovector (IV) dipole excitations in $^{48, 52, 58}$Ca and $^{90, 96, 110}$Zr, it is shown that ground-state correlations beyond the RPA reduce the IS transition strengths. They also shift up the energy of the lowest IV dipole state and slightly push down the peak energy of the IV giant dipole resonance. As the result, the energy-weighted sums of strengths of both IS and IV modes decrease, cau...
Low-x contribution to the Bjorken sum rule within unified $ln^2x+$LO DGLAP approximation
Kotlorz, D
2004-01-01
The small-$x$ contributions to the Bjorken sum rule within unified picture $ln^2x+$LO DGLAP for different input parametrisations $g_1^{NS}(x,Q_0^2)$ are presented. Theoretical predictions for $\\int_{0}^{0.003} g_1^{NS}(x,Q^2=10) dx$ are compared with the SMC small-$x$ data. Rough estimation of the slope $\\lambda$, controlling the small-$x$ behaviour of $g_1^{NS}\\sim x^{-\\lambda}$ from the obtained results and SMC data is performed. The crucial role of the running coupling $\\alpha_s=\\alpha_s(Q^2/z)$ at low-$x$ is taken into account.
Analysis of the (1)/(2){sup ±} pentaquark states in the diquark model with QCD sum rules
Wang, Zhi-Gang [North China Electric Power University, Department of Physics, Baoding (China); Huang, Tao [Chinese Academy of Sciences, Institute of High Energy Physics and Theoretical Physics Center for Science Facilities, Beijing (China)
2016-01-15
In this article, we present the scalar-diquark-scalar-diquark-antiquark type and scalar-diquark-axialvector-diquark-antiquark type pentaquark configurations in the diquark model, and study the masses and pole residues of the J{sup P} = (1)/(2){sup ±} hidden-charm pentaquark states in detail with the QCD sum rules by extending our previous work on the J{sup P} = (3)/(2){sup -} and (5)/(2){sup +} hidden-charm pentaquark states. We calculate the contributions of the vacuum condensates up to dimension-10 in the operator product expansion by constructing both the scalar-diquark-scalar-diquark-antiquark type and the scalar-diquark-axialvector-diquark-antiquark type interpolating currents. The present predictions of the masses can be confronted to the LHCb experimental data in the future. (orig.)
F-wave heavy-light meson spectroscopy in QCD sum rules and heavy quark effective theory
Zhou, Dan; Geng, Li-Sheng; Liu, Xiang; Zhu, Shi-Lin
2015-01-01
We study the F-wave c_bar s heavy meson doublets (2+,3+) and (3+,4+). They have large orbital excitations L=3, and may be good challenges (tests) for theoretical studies. To study them we use the method of QCD sum rule in the framework of heavy quark effective theory. Their masses are predicted to be m_{(2+,3+)} = (3.45 \\pm 0.25, 3.50 \\pm 0.26) GeV and m_{(3+,4+)} = (3.20 \\pm 0.22, 3.26 \\pm 0.23) GeV, with mass splittings Delta m_{(2+,3+)} = m_{3+} - m_{2+} = 0.046 \\pm 0.030 GeV and Delta m_{(3+,4+)} = 0.053 \\pm 0.044 GeV, respectively.
Pion Form Factor in QCD Sum Rules with Nonlocal Condensates and in the Local-Duality Approach
Bakulev, Alexander P; Stefanis, N G
2009-01-01
We discuss the QCD sum-rule approach for the spacelike electromagnetic pion form factor in the $O(\\alpha_s)$ approximation. We show that the nonlocality of the condensates is a key point to include nonperturbative contributions to the pion form factor. We compare our results with the Local-Duality predictions and show that the continuum threshold $s_0(Q^2)$ parameter is highly underestimated in the Local-Duality approach at $Q^2\\gtrsim 2$ GeV$^2$. Using our fit for this parameter, $s_0^\\text{LD}(Q^2)$, and applying the fractional analytic perturbation theory, we estimate with an accuracy of the order of 1% the $O(\\alpha_s^2)$ contribution to the pion's form factor.
Azizi, K.; Sarac, Y.; Sundu, H.
2017-05-01
To better understand the nature and internal structure of the exotic states discovered by many collaborations, more information on their electromagnetic properties and their strong and weak interactions with other hadrons is needed. The residue or current coupling constant of these states together with their mass are the main inputs in determinations of such properties. We perform QCD sum rules analyses on the hidden-charm pentaquark states with spin parities JP=3/2± and JP=5/2± to calculate their residue and mass. In the calculations, we adopt a molecular picture for JP=3/2± states and a mixed current in a molecular form for JP=5/2±. Our analyses show that the Pc+(4380 ) and Pc+(4450 ), observed by the LHCb Collaboration, can be considered as hidden-charm pentaquark states with JP=3/2- and JP=5/2+, respectively.
Holas, A; March, N H; Rubio, Angel
2005-11-15
Holas and March [Phys. Rev. A. 51, 2040 (1995)] gave a formally exact theory for the exchange-correlation (xc) force F(xc)(r)= -inverted Deltaupsilon(xc)(r) associated with the xc potential upsilon(xc)(r) of the density-functional theory in terms of low-order density matrices. This is shown in the present study to lead, rather directly, to the determination of a sum rule nF(xc)=0 relating the xc force with the ground-state density n(r). Some connection is also made with an earlier result relating to the external potential by Levy and Perdew [Phys. Rev. A. 32, 2010 (1985)] and with the quite recent study of Joubert [J. Chem. Phys. 119, 1916 (2003)] relating to the separation of the exchange and correlation contributions.
$D \\rightarrow a_1, f_1$ transition form factors and semileptonic decays via 3-point QCD sum rules
Zuo, Yabing; He, Linlin; Yang, Wei; Chen, Yan; Hao, Yannan
2016-01-01
By using the 3-point QCD sum rules, we calculate the transition form factors of $D$ decays into the spin triplet axial vector mesons $a_1(1260)$, $f_1(1285) $, $f_1(1420)$. In the calculations, we consider the quark contents of each meson in detail. In view of the fact that the isospin of $a_1(1260)$ is one, we calculate the $D^+ \\rightarrow a_1^0 (1260)$ and $D^0 \\rightarrow a_1^- (1260)$ transition form factors separately. In the case of $ f_1(1285), f_1(1420)$, the mixing between light flavor $SU(3)$ singlet and octet is taken into account. Based on the form factors obtained here, we give predictions for the branching ratios of relevant semileptonic decays, which can be tested in the future experiments.
Shen, Yue-Long; Lü, Cai-Dian
2016-01-01
Within the framework of $B$-meson light-cone sum rules, we compute the one-loop level QCD corrections to $B\\to \\pi$ transition form factors at small $ q^{2}$ region, in implement of a complete renormalization group equation evolution. To solve the renormalization group equations, we work at the "dual" space where the anomalous dimensions of the jet function and the light-cone distribution amplitudes are diagonal. With the complete renormalization group equation evolution, the form factors are almost independent of the factorization scale, which is shown numerically. We also extrapolate the results of the form factors to the whole $q^2$ region, and compare their behavior with other studies.
Analysis of X(5568) as Scalar Tetraquark State in Diquark-Antidiquark Model with QCD Sum Rules
Wang, Zhi-Gang
2016-09-01
In this article, we take the X(5568) as the diquark-antidiquark type tetraquark state with the spin-parity JP = 0+, construct the scalar-diquark-scalar-antidiquark type current, carry out the operator product expansion up to the vacuum condensates of dimension-10, and study the mass and pole residue in details with the QCD sum rules. We obtain the value MX = (5.57±0.12) GeV, which is consistent with the experimental data. The present prediction favors assigning the X(5568) to be the scalar tetraquark state. Supported by National Natural Science Foundation under Grant No. 11375063, and Natural Science Foundation of Hebei Province under Grant No. A2014502017
Yazici, E.; Sundu, H.; Veliev, E.V. [Kocaeli University, Department of Physics, Izmit (Turkey)
2016-02-15
The strong form factor of the B{sub c}B{sub c}J/ψ vertex is calculated in the framework of the QCD sum rules method at finite temperature. Taking into account additional operators appearing at finite temperature, a thermal Wilson expansion is obtained and QCD sum rules are derived. While increasing the temperature, the strong form factor remains unchanged up to T ≅ 100 MeV but slightly increases after this point. After T ≅ 160 MeV, the form factor suddenly decreases up to T ≅ 170 MeV. The obtained result of the coupling constant by fitting the form factor at Q{sub 2} = -m{sup 2}{sub offshell} at T = 0 is in a very good agreement with the QCD sum rules calculations in the case of vacuum. Our prediction can be checked in future experiments. (orig.)
Analysis of the Vertexes ΣQ([I])*QK* and ([1])'Q*Σ*QK* within Light-Cone QCD Sum Rules
YOU Fu-Yi; WANG Zhi-Gang; WAN Shao-Long
2012-01-01
We parameterize the vertexes Σq[1]*qK* and [1]'qΣq*K* with three tensor structures due to Lorentz invariance, and calculate the corresponding three coupling constants within light-cone QCD sum rules. We then obtain their numerical values taking into account all the uncertainties of the relevant parameters.%We parameterize the vertexes ΣQ([1])*QK* and ([1])'QΣ*QK* with three tensor structures due to Lorentz invariance,and calculate the corresponding three coupling constants within light-cone QCD sum rules.We then obtain their numerical values taking into account all the uncertainties of the relevant parameters.
Kamohara, Masumi; Izumi, Yudai; Tanaka, Masafumi; Okamoto, Keiko; Tanaka, Masahito; Kaneko, Fusae; Kodama, Yoko; Koketsu, Toshiyuki; Nakagawa, Kazumichi
2008-10-01
Absorption spectra of thin films of glycine (Gly), alanine (Ala), valine (Val), serine (Ser), leucine (Leu), phenylalanine (Phe) and methinine (Met) were measured in absolute values of absorption cross section σ( E) for the photon energy E from 3 to 250 eV. We translated σ( E) into the optical oscillator strength distribution df/dE and we examined the Thomas-Reiche-Kuhn sum rule [Hirschfelder, J.O., Curtiss, C.F., Bird, R.B., 1954. Molecular Theory of Gases and Liquids. Wiley, New York, p. 890]. We concluded that T-R-K sum rule was correctly applicable for such relatively large size of biomolecules.
Aliev, T M; Savcı, M
2016-01-01
The light cone sum rules method is used in studying the radiative decays $\\Sigma_Q \\to \\Lambda_Q \\gamma$ and $\\Xi^\\prime_Q \\to \\Xi_Q \\gamma$. Firstly, the sum rules for the form factor $F_2(Q^2=0)$ responsible for these transitions is constructed. Using this result the decay widths of the above--mentioned decays are calculated and analyzed. A comparison of our predictions on the decay widths of considered transitions with the predictions of the other approaches is presented.
Kondratyuk, S; Myhrer, F; Scholten, O
2004-01-01
The Adler-Weisberger and Goldberger-Miyazawa-Oehme sum rules are calculated within a relativistic, unitary and crossing symmetric dynamical model for pion-nucleon scattering using two different methods: 1) by evaluating of the scattering amplitude at the corresponding low-energy kinematics and 2) by evaluating the sum-rule integrals with the calculated total cross section. The discrepancy between the results of the two methods provides a measure of the breaking of analyticity and chiral symmetry in the model. The contribution of the $\\Delta$ resonance, including its dressing with meson loops, is discussed in some detail and found to be small.
Nuclear physics with laser-electron-photons. Developments and perspectives at SPring-8
Fujiwara, Mamoru [Osaka Univ., Ibaraki (Japan). Research Center for Nuclear Physics
1998-03-01
By the Compton scattering with ultraviolet laser beam using the 8 GeV electron beam of the SPring-8, the photon beam which is polarized by nearly 100% is obtained in 1-3.5 GeV region. The quark nuclear physics research at this facility is unique in the world, and it is expected that in the experiment at the SPring-8, the collision phenomena of polarized, high energy gamma-ray and the quarks in nucleons and the knockout phenomena of quarks are observed. Also the polarization experiment for clarifying ``the origin of nucleon spin`` has been proposed. Japan can stand at the top in the world in the research of quark nuclear physics with leptons. In the inverse Compton scattering using far infrared laser, the gamma-ray with good directionality of MeV range is obtained, and it will be applied widely to the research on E1 resonance and M1 excitation of atomic nuclei. In this report, the medium energy quark nuclear physics developed at the SPring-8 is outlined, and the nuclear physics which is expected to be developed when the high intensity, high polarization gamma-ray of about 10 MeV is generated is discussed. The detection of s, anti-s components in nucleons, research on baryon deformation and baryon spectra, verification of the Gerasimov, Drell-Hearn law of sum, meson structure, test of quark model by the photolysis of deuterons, dual Ginzburg Landau theory exploration, research on the mass and behavior of mesons in nuclear media are discussed. (K.I.)
Nuclear physics with laser-electron-photons. Developments and perspectives at SPring-8
Fujiwara, Mamoru [Osaka Univ., Ibaraki (Japan). Research Center for Nuclear Physics
1998-03-01
By the Compton scattering with ultraviolet laser beam using the 8 GeV electron beam of the SPring-8, the photon beam which is polarized by nearly 100% is obtained in 1-3.5 GeV region. The quark nuclear physics research at this facility is unique in the world, and it is expected that in the experiment at the SPring-8, the collision phenomena of polarized, high energy gamma-ray and the quarks in nucleons and the knockout phenomena of quarks are observed. Also the polarization experiment for clarifying ``the origin of nucleon spin`` has been proposed. Japan can stand at the top in the world in the research of quark nuclear physics with leptons. In the inverse Compton scattering using far infrared laser, the gamma-ray with good directionality of MeV range is obtained, and it will be applied widely to the research on E1 resonance and M1 excitation of atomic nuclei. In this report, the medium energy quark nuclear physics developed at the SPring-8 is outlined, and the nuclear physics which is expected to be developed when the high intensity, high polarization gamma-ray of about 10 MeV is generated is discussed. The detection of s, anti-s components in nucleons, research on baryon deformation and baryon spectra, verification of the Gerasimov, Drell-Hearn law of sum, meson structure, test of quark model by the photolysis of deuterons, dual Ginzburg Landau theory exploration, research on the mass and behavior of mesons in nuclear media are discussed. (K.I.)
The Spin-dependent Structure Function of the Proton $g_{1}^p$ and a Test of the Bjorken Sum Rule
Alekseev, M G; Alexandrov, Yu; Alexeev, G D; Amoroso, A; Austregesilo, A; Badelek, B; Balestra, F; Ball, J; Barth, J; Baum, G; Bedfer, Y; Bernhard, J; Bertini, R; Bettinelli, M; Birsa, R; Bisplinghoff, J; Bordalo, P; Bradamante, F; Bravar, A; Bressan, A; Brona, G; Burtin, E; Bussa, M P; Chaberny, D; Cotic, D; Chiosso, M; Chung, S U; Cicuttin, A; Colantoni, M; Crespo, M L; Dalla Torre, S; Das, S; Dasgupta, S S; Denisov, O Yu; Dhara, L; Diaz, V; Donskov, S V; Doshita, N; Duic, V; Dünnweber, W; Efremov, A; El Alaoui, A; Eversheim, P D; Eyrich, W; Faessler, M; Ferrero, A; Filin, A; Finger, M; Finger, M Jr; Fischer, H; Franco, C; Friedrich, J M; Garfagnini, R; Gautheron, F; Gavrichtchouk, O P; Gazda, R; Gerassimov, S; Geyer, R; Giorgi, M; Gnesi, I; Gobbo, B; Goertz, S; Grabmüller, S; Grasso, A; Grube, B; Gushterski, R; Guskov, A; Haas, F; von Harrach, D; Hasegawa, T; Heinsius, F H; Hermann, R; Herrmann, F; Heß, C; Hinterberger, F; Horikawa, N; Höppner, Ch; d'Hose, N; Ilgner, C; Ishimoto, S; Ivanov, O; Ivanshin, Yu; Iwata, T; Jahn, R; Jasinski, P; Jegou, G; Joosten, R; Kabuß, E; Käfer, W; Kang, D; Ketzer, B; Khaustov, G V; Khokhlov, Yu A; Kisselev, Yu; Klein, F; Klimaszewski, K; Koblitz, S; Koivuniemi, J H; Kolosov, V N; Kondo, K; Königsmann, K; Konopka, R; Konorov, I; Konstantinov, V F; Korzenev, A; Kotzinian, A M; Kouznetsov, O; Kowalik, K; Krämer, M; Kral, A; Kroumchtein, Z V; Kuhn, R; Kunne, F; Kurek, K; Lauser, L; Le Goff, J M; Lednev, A A; Lehmann, A; Levorato, S; Lichtenstadt, J; Liska, T; Maggiora, A; Maggiora, M; Magnon, A; Mallot, G K; Mann, A; Marchand, C; Marroncle, J; Martin, A; Marzec, J; Massmann, F; Matsuda, T; Maximov, A N; W Meyer, W; Michigami, T; Mikhailov, Yu V; Moinester, M A; Mutter, A; Nagaytsev, A; Nagel, T; Nassalski, J; Negrini, T; Nerling, F; Neubert, S; Neyret, D; Nikolaenko, V I; Olshevsky, A G; Ostrick, M; Padee, A; Panknin, R; Panzieri, D; Parsamyan, B; Paul, S; Pawlukiewicz-Kaminska, B; Perevalova, E; Pesaro, G; Peshekhonov, D V; Piragino, G; Platchkov, S; Pochodzalla, J; Polak, J; Polyakov, V A; Pontecorvo, G; Pretz, J; Quintans, C; Rajotte, J F; Ramos, S; Rapatsky, V; Reicherz, G; Richter, A; Robinet, F; Rocco, E; Rondio, E; Ryabchikov, D I; Samoylenko, V D; Sandacz, A; Santos, H; Sapozhnikov, M G; Sarkar, S; Savin, I A; Sbrizzai, G; Schiavon, P; Schill, C; Schmitt, L; Schlüter, T; Schopferer, S; Schröder, W; Shevchenko, O Yu; Siebert, H W; Silva, L; Sinha, L; Sissakian, A N; Slunecka, M; Smirnov, G I; Sosio, S; Sozzi, F; Srnka, A; Stolarski, M; Sulc, M; Sulej, R; Takekawa, S; Tessaro, S; Tessarotto, F; Teufel, A; Tkatchev, L G; Uhl, S; Uman, I; Virius, M; Vlassov, N V; Vossen, A; Weitzel, Q; Windmolders, R; Wislicki, W; Wollny, H; Zaremba, K; Zavertyaev, M; Zemlyanichkina, E; Ziembicki, M; Zhao, J; Zhuravlev, N; Zvyagin, A
2010-01-01
The inclusive double-spin asymmetry, $A_{1}^{p}$, has been measured at COMPASS in deepinelastic polarised muon scattering off a large polarised NH3 target. The data, collected in the year 2007, cover the range Q2 > 1 (GeV/c)^2, 0.004 < x < 0.7 and improve the statistical precision of g_{1}^{p}(x) by a factor of two in the region x < 0.02. The new proton asymmetries are combined with those previously published for the deuteron to extract the non-singlet spin-dependent structure function g_1^NS(x,Q2). The isovector quark density, Delta_q_3(x,Q2), is evaluated from a NLO QCD fit of g_1^NS. The first moment of Delta_q3 is in good agreement with the value predicted by the Bjorken sum rule and corresponds to a ratio of the axial and vector coupling constants g_A/g_V = 1.28+-0.07(stat)+-0.10(syst).
Analysis of the strong decays $D_{s3}^*(2860)\\to DK$, $D^{*}K$ with QCD sum rules
Wang, Zhi-Gang
2016-01-01
In this article, we assign the $D_{s3}^*(2860)$ to be a D-wave $c\\bar{s}$ meson, study the vertices $D_{s3}^*(2860)DK$ and $D_{s3}^*(2860)D^*K$ in details to select the pertinent tensor structures, calculate the hadronic coupling constants $G_{D_{s3}^*(2860)DK}$ and $G_{D_{s3}^*(2860)D^*K}$ with the three-point QCD sum rules and obtain the decay widths $\\Gamma\\left(D_{s3}^*(2860)\\to D^{*}K\\right)$ and $\\Gamma\\left(D_{s3}^*(2860)\\to DK\\right)$. The predicted ratio $R=\\Gamma\\left(D_{s3}^*(2860)\\to D^{*}K\\right)/\\Gamma\\left(D_{s3}^*(2860)\\to DK\\right)=0.57\\pm0.38$ cannot reproduce the experimental data $R={\\rm Br}\\left(D_{sJ}^*(2860)\\to D^{*}K\\right)/{\\rm Br}\\left(D_{sJ}^*(2860)\\to DK\\right)=1.10 \\pm 0.15 \\pm 0.19$.
Reanalysis of the Zc(4020), Zc(4025), Z(4050) and Z(4250) as Tetraquark States with QCD Sum Rules
Wang, Zhi-Gang
2015-04-01
In this article, we calculate the contributions of the vacuum condensates up to dimension-10 in the operator product expansion, and study the Cγμ — Cγν type scalar, axial-vector and tensor tetraquark states in details with the QCD sum rules. In calculations, we use the formula to determine the energy scales of the QCD spectral densities. The predictions MJ=2 = ({4.02}+0.09-0.09)GeV, MJ=1 =(4.02+0.07-0.08)GeV favor assigning the Zc(4020) and Zc(4025) as the JPC = 1+- or 2++ diquark-antidiquark type tetraquark states, while the prediction MJ=0 = (3.85+0.15-0.09)GeV disfavors assigning the Z(4050) and Z(4250) as the JPC = 0++ diquark-antidiquark type tetraquark states. Furthermore, we discuss the strong decays of the 0++, 1+-, 2++ diquark-antidiquark type tetraquark states in details. Supported by National Natural Science Foundation of Chian under Grant No. 11375063, and Natural Science Foundation of Hebei Province under Grant No. A2014502017
The Spin Structure Function $g_1^{\\rm p}$ of the Proton and a Test of the Bjorken Sum Rule
Adolph, C.; Alexeev, M.G.; Alexeev, G.D.; Amoroso, A.; Andrieux, V.; Anosov, V.; Austregesilo, A.; Azevedo, C.; Badelek, B.; Balestra, F.; Barth, J.; Baum, G.; Beck, R.; Bedfer, Y.; Bernhard, J.; Bicker, K.; Bielert, E.R.; Birsa, R.; Bisplinghoff, J.; Bodlak, M.; Boer, M.; Bordalo, P.; Bradamante, F.; Braun, C.; Bressan, A.; Buchele, M.; Burtin, E.; Capozza, L.; Chang, W.C.; Chiosso, M.; Choi, I.; Chung, S.U.; Cicuttin, A.; Crespo, M.L.; Curiel, Q.; Dalla Torre, S.; Dasgupta, S.S.; Dasgupta, S.; Denisov, O.Yu.; Dhara, L.; Donskov, S.V.; Doshita, N.; Duic, V.; Dziewiecki, M.; Efremov, A.; Eversheim, P.D.; Eyrich, W.; Ferrero, A.; Finger, M.; M. Finger jr; Fischer, H.; Franco, C.; von Hohenesche, N. du Fresne; Friedrich, J.M.; Frolov, V.; Fuchey, E.; Gautheron, F.; Gavrichtchouk, O.P.; Gerassimov, S.; Giordano, F.; Gnesi, I.; Gorzellik, M.; Grabmuller, S.; Grasso, A.; Grosse-Perdekamp, M.; Grube, B.; Grussenmeyer, T.; Guskov, A.; Haas, F.; Hahne, D.; von Harrach, D.; Hashimoto, R.; Heinsius, F.H.; Herrmann, F.; Hinterberger, F.; Horikawa, N.; d'Hose, N.; Hsieh, C.Yu; Huber, S.; Ishimoto, S.; Ivanov, A.; Ivanshin, Yu.; Iwata, T.; Jahn, R.; Jary, V.; Jorg, P.; Joosten, R.; Kabuss, E.; Ketzer, B.; Khaustov, G.V.; Khokhlov, Yu. A.; Kisselev, Yu.; Klein, F.; Klimaszewski, K.; Koivuniemi, J.H.; Kolosov, V.N.; Kondo, K.; Konigsmann, K.; Konorov, I.; Konstantinov, V.F.; Kotzinian, A.M.; Kouznetsov, O.; Kramer, M.; Kremser, P.; Krinner, F.; Kroumchtein, Z.V.; Kuchinski, N.; Kunne, F.; Kurek, K.; Kurjata, R.P.; Lednev, A.A.; Lehmann, A.; Levillain, M.; Levorato, S.; Lichtenstadt, J.; Longo, R.; Maggiora, A.; Magnon, A.; Makins, N.; Makke, N.; Mallot, G.K.; Marchand, C.; Martin, A.; Marzec, J.; Matousek, J.; Matsuda, H.; Matsuda, T.; Meshcheryakov, G.; Meyer, W.; Michigami, T.; Mikhailov, Yu. V.; Miyachi, Y.; Nagaytsev, A.; Nagel, T.; Nerling, F.; Neyret, D.; Nikolaenko, V.I.; Novy, J.; Nowak, W.D.; Nunes, A.S.; Olshevsky, A.G.; Orlov, I.; Ostrick, M.; Panzieri, D.; Parsamyan, B.; Paul, S.; Peng, J.C.; Pereira, F.; Pesek, M.; Peshekhonov, D.V.; Platchkov, S.; Pochodzalla, J.; Polyakov, V.A.; Pretz, J.; Quaresma, M.; Quintans, C.; Ramos, S.; Regali, C.; Reicherz, G.; Riedl, C.; Rocco, E.; Rossiyskaya, N.S.; Ryabchikov, D.I.; Rychter, A.; Samoylenko, V.D.; Sandacz, A.; Santos, C.; Sarkar, S.; Savin, I.A.; Sbrizzai, G.; Schiavon, P.; Schmidt, K.; Schmieden, H.; Schonning, K.; Schopferer, S.; Selyunin, A.; Shevchenko, O.Yu.; Silva, L.; Sinha, L.; Sirtl, S.; Slunecka, M.; Sozzi, F.; Srnka, A.; Stolarski, M.; Sulc, M.; Suzuki, H.; Szabelski, A.; Szameitat, T.; Sznajder, P.; Takekawa, S.; Wolbeek, J. ter; Tessaro, S.; Tessarotto, F.; Thibaud, F.; Tosello, F.; Tskhay, V.; Uhl, S.; Veloso, J.; Virius, M.; Weisrock, T.; Wilfert, M.; Windmolders, R.; Zaremba, K.; Zavertyaev, M.; Zemlyanichkina, E.; Ziembicki, M.; Zink, A.
2016-01-01
New results for the double spin asymmetry $A_1^{\\rm p}$ and the proton longitudinal spin structure function $g_1^{\\rm p}$ are presented. They were obtained by the COMPASS collaboration using polarised 200 GeV muons scattered off a longitudinally polarised NH$_3$ target. The data were collected in 2011 and complement those recorded in 2007 at 160\\,GeV, in particular at lower values of $x$. They improve the statistical precision of $g_1^{\\rm p}(x)$ by about a factor of two in the region $x\\lesssim 0.02$. A next-to-leading order QCD fit to the $g_1$ world data is performed. It leads to a new determination of the quark spin contribution to the nucleon spin, $\\Delta \\Sigma$ ranging from 0.26 to 0.36, and to a re-evaluation of the first moment of $g_1^{\\rm p}$. The uncertainty of $\\Delta \\Sigma$ is mostly due to the large uncertainty in the present determinations of the gluon helicity distribution. A new evaluation of the Bjorken sum rule based on the COMPASS results for the non-singlet structure function $g_1^{\\rm...
Kumar, Manoj; Banerjee, Varsha; Puri, Sanjay
2017-01-01
We perform comprehensive Monte Carlo (MC) simulations to study ordering dynamics in the random field Ising model with conserved order parameter (C-RFIM) in d=2,3 . The observations from this study are: a) For a fixed value of the disorder Δ, the correlation function C(r,t;Δ) exhibits dynamical scaling. b) The scaling function is not robust with respect to Δ, i.e., super-universality (SU) is violated by C(r,t;Δ) . c) At early times, the domains follow the algebraic growth with a disorder-dependent exponent: L(t,Δ)∼ t1/\\bar{z(Δ)} . At late times, there is a crossover to logarithmic growth: L(t,Δ) ∼ (\\ln t)1/\\varphi , where φ is a disorder-independent exponent. d) The small-r behavior of the correlation function exhibits a cusp singularity: 1-C(r) ∼ rα(Δ) , where α is the cusp exponent signifying rough fractal interfaces. e) The corresponding structure factor exhibits a non-Porod tail: S(k,t;Δ)∼ k-(d+α) , and obeys a generalized Tomita sum rule \\int_0^∞ {d}p p1-α≤ft[pd+αf(p)-C\\right]=0 , where f(p) is the appropriate scaling function, and C is a constant.
$B\\to V\\ell^+\\ell^-$ in the Standard Mode from Light-Cone Sum Rules
Straub, Aoife Bharucha David M
2015-01-01
We present $B_q\\to\\rho$, $B_q\\to\\omega$, $B_q\\to K^*$, $B_s\\to K^*$ and $B_s\\to \\phi$ form factors from light-cone sum rules using updated hadronic input parameters. It is argued that the, generally valid, equations of motion constrain the uncertainty of tensor-to-vector form factor ratios. This improves the prediction of zeros of helicity amplitudes which is of major importance for $B\\to K^*\\ell\\ell$ angular observables. We provide easy-to-use fits to the LCSR results, including the full error correlation matrix, in all modes at low $q^2$ as well as combined fits to LCSR and lattice results covering the entire kinematic range for $B_q\\to K^*$, $B_s\\to K^*$ and $B_s\\to \\phi$. The error correlation matrix avoids the problem of overestimating the uncertainty in phenomenological applications. Using the new form factors and recent computations of non-factorisable contributions we provide Standard Model predictions for $B\\to K^*\\gamma$ as well as $B\\to K^*\\ell^+\\ell^-$ and $B_s\\to\\phi\\mu^+\\mu^-$ at low dilepton in...
Zhou, Juefei
This dissertation combines theoretical and experimental studies of organic molecules to understand light-matter interactions with the goal of making more efficient nonlinear-optical molecules. We use a finite element method to numerically calculate and optimize the nonlinear-optical susceptibilities of 1-dimensional molecules, which resulted in a new paradigm for fabricating molecules with better nonlinear properties. This approach was used as a guide by researchers to identify and characterize a record-high intrinsic hyperpolarizability. Using the results of a sum rule analysis, we propose a new method for modeling the nonlinear-optical spectra of molecules. We apply our theory to the two-photon absorption cross section of the Air Force dye called AF455, and find that it is consistent with our measurements. The properties of the first two excited states of AF455 determined with a combination of linear absorption spectroscopy and hyper-Rayleigh scattering measurements are sufficient to predict, within experimental uncertainty, the full two-photon absorption spectrum.
The Zb(10 610) and Zb(10 650) as axial-vector tetraquark states in the QCD sum rules
Wang, Zhi-Gang; Huang, Tao
2014-10-01
In this article, we study the axial-vector mesons Zb(10 610) and Zb(10 650) with the Cγμ-Cγ5 type and Cγμ-Cγν type interpolating currents, respectively, by carrying out the operator product expansion to the vacuum condensates up to dimension 10. In calculations, we explore the energy scale dependence of the QCD spectral densities of the hidden bottom tetraquark states in detail for the first time, and suggest a formula μ=√{MX/Y/Z2-(2} with the effective mass Mb=5.13 GeV to determine the energy scales. The numerical results favor assigning the Zb(10 610) and Zb(10 650) as the Cγμ-Cγ5 type and Cγμ-Cγν type hidden bottom tetraquark states, respectively. We obtain the mass of the JPC=1 hidden bottom tetraquark state as a byproduct, which can be compared to the experimental data in the futures. Furthermore, we study the strong decays Zb±(10 610)→ϒπ±,ηbρ± with the three-point QCD sum rules, the decay widths also support assigning the Zb(10 610) as the Cγμ-Cγ5 type hidden bottom tetraquark state.
Precision calculation of threshold πd scattering, πN scattering lengths, and the GMO sum rule
Baru, V.; Hanhart, C.; Hoferichter, M.; Kubis, B.; Nogga, A.; Phillips, D. R.
2011-12-01
We use chiral perturbation theory (ChPT) to calculate the πd scattering length with an accuracy of a few percent, including isospin-violating corrections in both the two- and three-body sectors. In particular, we provide the technical details of a recent letter (Baru et al., 2011) [1], where we used data on pionic deuterium and pionic hydrogen atoms to extract the isoscalar and isovector pion-nucleon scattering lengths a and a. We study isospin-breaking contributions to the three-body part of a due to mass differences, isospin violation in the πN scattering lengths, and virtual photons. This last class of effects is ostensibly infrared enhanced due to the smallness of the deuteron binding energy. However, we show that the leading virtual-photon effects that might undergo such enhancement cancel, and hence the standard ChPT counting provides a reliable estimate of isospin violation in a due to virtual photons. Finally, we discuss the validity of the Goldberger-Miyazawa-Oehme sum rule in the presence of isospin violation, and use it to determine the charged-pion-nucleon coupling constant.
Baru, V. [Institut fuer Theoretische Physik II, Ruhr-Universitaet Bochum, D-44870 Bochum (Germany); Institut fuer Kernphysik and Juelich Center for Hadron Physics, Forschungszentrum Juelich, D-52425 Juelich (Germany); Institute for Theoretical and Experimental Physics, B. Cheremushinskaya 25, 117218 Moscow (Russian Federation); Hanhart, C. [Institut fuer Kernphysik and Juelich Center for Hadron Physics, Forschungszentrum Juelich, D-52425 Juelich (Germany); Institute for Advanced Simulation, Forschungszentrum Juelich, D-52425 Juelich (Germany); Hoferichter, M., E-mail: hoferichter@hiskp.uni-bonn.de [Helmholtz-Institut fuer Strahlen- und Kernphysik and Bethe Center for Theoretical Physics, Universitaet Bonn, D-53115 Bonn (Germany); Institute of Nuclear and Particle Physics and Department of Physics and Astronomy, Ohio University, Athens, OH 45701 (United States); Kubis, B. [Helmholtz-Institut fuer Strahlen- und Kernphysik and Bethe Center for Theoretical Physics, Universitaet Bonn, D-53115 Bonn (Germany); Nogga, A. [Institut fuer Kernphysik and Juelich Center for Hadron Physics, Forschungszentrum Juelich, D-52425 Juelich (Germany); Institute for Advanced Simulation, Forschungszentrum Juelich, D-52425 Juelich (Germany)
2011-12-15
We use chiral perturbation theory (ChPT) to calculate the {pi}{sup -}d scattering length with an accuracy of a few percent, including isospin-violating corrections in both the two- and three-body sectors. In particular, we provide the technical details of a recent letter (Baru et al., 2011) , where we used data on pionic deuterium and pionic hydrogen atoms to extract the isoscalar and isovector pion-nucleon scattering lengths a{sup +} and a{sup -}. We study isospin-breaking contributions to the three-body part of a{sub {pi}}{sup -}{sub d} due to mass differences, isospin violation in the {pi}N scattering lengths, and virtual photons. This last class of effects is ostensibly infrared enhanced due to the smallness of the deuteron binding energy. However, we show that the leading virtual-photon effects that might undergo such enhancement cancel, and hence the standard ChPT counting provides a reliable estimate of isospin violation in a{sub {pi}}{sup -}{sub d} due to virtual photons. Finally, we discuss the validity of the Goldberger-Miyazawa-Oehme sum rule in the presence of isospin violation, and use it to determine the charged-pion-nucleon coupling constant.
Nath, N. M.; Mukharjee, A.; Das, M. K.; Sarma, J. K.
2016-12-01
We present an analysis of the xF3(x,Q2) structure function and Gross-Llewellyn Smith(GLS) sum rule taking into account the nuclear effects and higher twist correction. This analysis is based on the results presented in [N.M. Nath, et al, Indian J. Phys. 90 (2016) 117]. The corrections due to nuclear effects predicted in several earlier analysis are incorporated to our results of xF3(x,Q2) structure function and GLS sum rule for free nucleon, corrected upto next-next-to-leading order (NNLO) perturbative order and calculate the nuclear structure function as well as sum rule for nuclei. In addition, by means of a simple model we have extracted the higher twist contributions to the non-singlet structure function xF3(x,Q2) and GLS sum rule in NNLO perturbative orders and then incorporated them to our results. Our NNLO results along with nuclear effect and higher twist corrections are observed to be compatible with corresponding experimental data and other phenomenological analysis. Support from DAE-BRNS, India, as Major Research Project under Sanction No. 2012/37P/36/BRNS/2018 dated 24 Nov. 2012
Hudspith, R J; Maltman, K; Wolfe, C E; Zanotti, J
2015-01-01
Continuum and lattice methods are used to investigate systematic issues in the sum rule determination of $V_{us}$ using inclusive hadronic $\\tau$ decay data. Results for $V_{us}$ employing assumptions for $D>4$ OPE contributions used in previous conventional implementations of this approach are shown to display unphysical dependence on the sum rule weight, $w$, and choice of upper limit, $s_0$, of the relevant experimental spectral integrals. Continuum and lattice results suggest a new implementation of the sum rule approach with not just $\\vert V_{us}\\vert$, but also $D>4$ effective condensates, fit to data. Lattice results are also shown to provide a quantitative assessment of truncation uncertainties for the slowly converging $D=2$ OPE series. The new sum rule implementation yields $\\vert V_{us}\\vert$ results free of unphysical $s_0$- and $w$-dependences and $\\sim 0.0020$ higher than that obtained using the conventional implementation. With preliminary new experimental results for the $K\\pi$ branching frac...
Polanco-Euán, E N; Sánchez-Colón, G; Bambah, B A
2016-01-01
The SU(3) octet states with baryon number B = 2, hexaquark dibaryons, are considered. Decay coupling constants sum rules for dibaryon octet into two ordinary baryon octets with ?$\\lambda_8$ first order SU(3) symmetry breaking are given. An SU(4) extension of the analysis is commented upon. Possibilities for the experimental observation of multibaryon and anti-multibaryon states are pointed out.
Kondratyuk, S; Kubodera, K; Myhrer, F; Scholten, O
2004-01-01
The Adler-Weisberger and Goldberger-Miyazawa-Oehme sum rules are calculated within a relativistic, unitary and crossing symmetric dynamical model for pion-nucleon scattering using two different methods: (1) by evaluating the scattering amplitude at the corresponding low-energy kinematics and (2) by
Final COMPASS results on the deuteron spin-dependent structure function g1d and the Bjorken sum rule
C. Adolph
2017-06-01
Full Text Available Final results are presented from the inclusive measurement of deep-inelastic polarised-muon scattering on longitudinally polarised deuterons using a 6LiD target. The data were taken at 160 GeV beam energy and the results are shown for the kinematic range 1(GeV/c24GeV/c2 in the mass of the hadronic final state. The deuteron double-spin asymmetry A1d and the deuteron longitudinal-spin structure function g1d are presented in bins of x and Q2. Towards lowest accessible values of x, g1d decreases and becomes consistent with zero within uncertainties. The presented final g1d values together with the recently published final g1p values of COMPASS are used to again evaluate the Bjorken sum rule and perform the QCD fit to the g1 world data at next-to-leading order of the strong coupling constant. In both cases, changes in central values of the resulting numbers are well within statistical uncertainties. The flavour-singlet axial charge a0, which is identified in the MS‾ renormalisation scheme with the total contribution of quark helicities to the nucleon spin, is extracted at next-to-leading order accuracy from only the COMPASS deuteron data: a0(Q2=3(GeV/c2=0.32±0.02stat±0.04syst±0.05evol. Together with the recent results on the proton spin structure function g1p, the results on g1d constitute the COMPASS legacy on the measurements of g1 through inclusive spin-dependent deep inelastic scattering.
Kontturi, Ville; Silfsten, Pertti; Peiponen, Kai-Erik
2011-07-01
Absorption spectra from colloids containing different concentrations of spherical gold nanoparticles in water were measured with a spectrophotometer. The absorption spectra were used to calculate the number density of nanoparticles (NPs) with the aid of an unconventional finite spectral band f-sum rule applied for gold colloid. Good correlation between the number density of dispersion electrons, obtained from the f-sum rule, and the number density of nanoparticles was found. The effective absolute refractive index of the gold colloid was obtained with the aid of a singly subtractive Kramers-Kronig relation, and in addition the refractive index change due to the nanoparticles was obtained with the aid of a conventional Kramers-Kronig relation. Such optical properties are valuable in studies of light interaction with nanoparticles.
Hilger, Thomas Uwe
2012-04-11
The interplay of hadron properties and their modification in an ambient nuclear medium on the one hand and spontaneous chiral symmetry breaking and its restoration on the other hand is investigated. QCD sum rules for D and B mesons embedded in cold nuclear matter are evaluated. We quantify the mass splitting of D- anti D and B- anti B mesons as a function of the nuclear matter density and investigate the impact of various condensates in linear density approximation. The analysis also includes D{sub s} and D{sup *}{sub 0} mesons. QCD sum rules for chiral partners in the open-charm meson sector are presented at nonzero baryon net density or temperature. We focus on the differences between pseudo-scalar and scalar as well as vector and axial-vector D mesons and derive the corresponding Weinberg type sum rules. Based on QCD sum rules we explore the consequences of a scenario for the ρ meson, where the chiral symmetry breaking condensates are set to zero whereas the chirally symmetric condensates remain at their vacuum values. The complementarity of mass shift and broadening is discussed. An alternative approach which utilizes coupled Dyson-Schwinger and Bethe-Salpeter equations for quark-antiquark bound states is investigated. For this purpose we analyze the analytic structure of the quark propagators in the complex plane numerically and test the possibility to widen the applicability of the method to the sector of heavy-light mesons in the scalar and pseudo-scalar channels, such as the D mesons, by varying the momentum partitioning parameter. The solutions of the Dyson-Schwinger equation in the Wigner-Weyl phase of chiral symmetry at nonzero bare quark masses are used to investigate a scenario with explicit but without dynamical chiral symmetry breaking.
Mannel, T. [Siegen Univ. (Germany). FB 7, Theoretische Physik; Pecjak, B.D. [Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany); Pivovarov, A.A. [Siegen Univ. (Germany). FB 7, Theoretische Physik]|[Russian Academy of Sciecnes, Moscow (Russian Federation). Inst. for Nuclear Research
2007-03-15
We use QCD sum rules to compute matrix elements of the {delta}B=2 operators appearing in the heavy-quark expansion of the width difference of the B{sub s} mass eigenstates. Our analysis includes the leading-order operators Q and Q{sub S}, as well as the subleading operators R{sub 2} and R{sub 3}, which appear at next-to-leading order in the 1/m{sub b} expansion. We conclude that the violation of the factorization approximation for these matrix elements due to non-perturbative vacuum condensates is as low as 1-2%. (orig.)
Cvetič, Gorazd
2016-01-01
We consider a new form of analytical perturbation theory expansion in the massless $SU(N_c)$ theory, for the $e^+e^-$-annihilation to hadrons Adler function, and the Bjorken sum rule of the polarized lepton-hadron deep-inelastic scattering, and demonstrate its validity at the $O(\\alpha_s^4)$-level at least. It is expressed through a two-fold series in terms of powers of the conformal anomaly and the coupling constant $\\alpha_s$ of the $SU(N_c)$ gauge model. Subsequently, explicit expressions are obtained for the $\\{\\beta\\}$-expanded perturbation coefficients at $O(\\alpha_s^4)$ level in $\\overline{\\rm MS}$ scheme, for the nonsinglet contribution to the Adler function and the Bjorken polarized sum rule. Comparisons of the obtained terms in the $\\{\\beta\\}$-expanded perturbation coefficients are made with the corresponding terms obtained by using extra gluino degrees of freedom, or skeleton-motivated expansion, or $R_{\\delta}$-scheme motivated expansion in the Principle of Maximal Conformality. Relations are pres...
Cvetič, Gorazd; Kataev, A. L.
2016-07-01
We consider a new form of analytical perturbation theory expansion in the massless S U (Nc) theory, for the nonsinglet part of the e+e--annihilation to hadrons Adler function Dn s and of the Bjorken sum rule of the polarized lepton-hadron deep-inelastic scattering Cns B j p, and demonstrate its validity at the O (αs4)-level at least. It is a two-fold series in powers of the conformal anomaly and of S U (Nc) coupling αs. Explicit expressions are obtained for the {β }-expanded perturbation coefficients at O (αs4) level in MS ¯ scheme, for both considered physical quantities. Comparisons of the terms in the {β }-expanded coefficients are made with the corresponding terms obtained by using extra gluino degrees of freedom, or skeleton-motivated expansion, or Rδ-scheme motivated expansion in the Principle of Maximal Conformality. Relations between terms of the {β }-expansion for the Dn s- and Cns B j p-functions, which follow from the conformal symmetry limit and its violation, are presented. The relevance to the possible new analyses of the experimental data for the Adler function and Bjorken sum rule is discussed.
Kumar, Ashok; Thakkar, Ajit J.
2010-02-01
The construction of the dipole oscillator strength distribution (DOSD) from theoretical and experimental photoabsorption cross sections combined with constraints provided by the Kuhn-Reiche-Thomas sum rule and molar refractivity data is a well-established technique that has been successfully applied to more than 50 species. Such DOSDs are insufficiently accurate at large photon energies. A novel iterative procedure is developed that rectifies this deficiency by using the high-energy asymptotic behavior of the dipole oscillator strength density as an additional constraint. Pilot applications are made for the neon, argon, krypton, and xenon atoms. The resulting DOSDs improve the agreement of the predicted S2 and S1 sum rules with ab initio calculations while preserving the accuracy of the remainder of the moments. Our DOSDs exploit new and more accurate experimental data. Improved estimates of dipole properties for these four atoms and of dipole-dipole C6 and triple-dipole C9 dispersion coefficients for the interactions among them are reported.
Representations of the U$_{q}$(u$_{4,1}$) and a q-polynomial that determines baryon mass sum rules
Gavrilik, A M; Tertychnyj, A V; Gavrilik, A M; Kachurik, I I; Tertychnyj, A V
1995-01-01
With quantum groups U_q(su_n) taken as classifying symmetries for hadrons of n flavors, we calculate within irreducible representation D^+_{12}(p-1,p-3,p-4;p,p-2) (p \\in {\\bf Z}) of 'dynamical' quantum group U_q(u_{4,1}) the masses of baryons {1\\over 2}^+ that belong to {\\it 20}-plet of U_q(su_4). The obtained q-analog of mass relation (MR) for U_q(su_3)-octet contains unexpected mass-dependent term multiplied by the factor {A_q\\over B_q} where A_q, B_q are certain polynomials (resp. of 7-th and 6-th order) in the variable q+q^{-1}\\equiv [2]_q. Both values q=1 and q=e^{i\\pi \\over 6} turn the polynomial A_q into zero. But, while q=1 results in well-known Gell-Mann--Okubo (GMO) baryon MR, the second root of A_q reduces the q-MR to some novel mass sum rule which has irrational coefficients and which holds, for empirical masses, even with better accuracy than GMO mass sum rule.
Kataev, A L
2013-01-01
Conformal symmetry based relations between the concrete perturbative QED and QCD approximations of the polarized Bjorken, the Ellis-Jaffe, the Gross-Llewellyn Smith sum rules and of the Adler functions of the axial vector and vector channels are derived. They are based on application of the operator product expansion to three triangle AVV Green functions, constructed from the non-singlet axial vector-vector-vector currents, the {\\it singlet} axial-vector and two {\\it non-singlet} vector currents and the {\\it non-singlet} axial-vector-vector and {\\it singlet} vector currents, in the limit when the conformal symmetry of gauge models with fermions is unbroken. We specify the conditions when the conformal symmetry is valid in the U(1) and $SU(N_c)$ models. The identity between perturbative approximations of the Bjorken, Ellis-Jaffe and the Gross-Llewellyn Smith sum rules, which follow from this theoretical limit, is proved. The expressions for the $O(\\alpha^4)$ and $O(\\alpha_s^3)$ conformal symmetry based contrib...
Zhang, J.-Z.; Galbraith, I.
2008-05-01
Using perturbation theory, intraband magneto-optical absorption is calculated for InAs/GaAs truncated pyramidal quantum dots in a magnetic field applied parallel to the growth direction z . The effects of the magnetic field on the electronic states as well as the intraband transitions are systematically studied. Selection rules governing the intraband transitions are discussed based on the symmetry properties of the electronic states. While the broadband z -polarized absorption is almost insensitive to the magnetic field, the orbital Zeeman splitting is the dominant feature in the in-plane polarized spectrum. Strong in-plane polarized magneto-absorption features are located in the far-infrared region, while z -polarized absorption occurs at higher frequencies. This is due to the dot geometry (the base length is much larger than the height) yielding different quantum confinement in the vertical and lateral directions. The Thomas-Reiche-Kuhn sum rule, including the magnetic field effect, is applied together with the selection rules to the absorption spectra. The orbital Zeeman splitting depends on both the dot size and the confining potential—the splitting decreases as the dot size or the confining potential decreases. Our calculated Zeeman splittings are in agreement with experimental data.
A QCD sum rules calculation of the ηcD*D and ηc Ds* Ds form factors and strong coupling constants
Rodrigues, B. Osório; Bracco, M. E.; Zanetti, C. M.
2017-10-01
We use the QCD sum rules for the three point correlation functions to compute the strong coupling constants of the meson vertices ηcD* D and ηc Ds* Ds. We consider perturbative and non-perturbative contributions, working up to dimension five on the OPE. The vertices were studied considering that each one of its three mesons are off-shell alternately. The vertex coupling constant is evaluated through the extrapolation of the three different form factors. The results obtained for the coupling constants are gηcD*D =5.23-1.38+1.80 and g ηc Ds* Ds =5.55-1.55+1.29.
Analysis of the $D_{s3}^*(2860)$ as a D-wave $c\\bar{s}$ meson with QCD sum rules
Wang, Zhi-Gang
2016-01-01
In this article, we take the $D_{s3}^*(2860)$ as a D-wave $c\\bar{s}$ meson, and study the mass and decay constant of the $D_{s3}^*(2860)$ with the QCD sum rules by calculating the contributions of the vacuum condensates up to dimension-6 in the operator product expansion. The predicted mass $M_{D_{s3}^*}=(2.86\\pm0.10)\\,\\rm{GeV}$ is in excellent agreement with the experimental value $M_{D_{s3}^*}=(2860.5\\pm 2.6 \\pm 2.5\\pm 6.0)\\,\\rm{ MeV}$ from the LHCb collaboration. The prediction supports assigning the $D_{s3}^*(2860)$ to be the D-wave $c\\bar{s}$ meson.
Wang, Zhi-Gang [North China Electric Power University, Department of Physics, Baoding (China)
2016-03-15
In this article, we construct both the axialvector-diquark-axialvector-diquark-antiquark type and the axialvector-diquark-scalar-diquark-antiquark type interpolating currents, then calculate the contributions of the vacuum condensates up to dimension 10 in the operator product expansion, and we study the masses and pole residues of the J{sup P} = (1)/(2){sup ±} hidden-charm pentaquark states with the QCD sum rules in a systematic way. In calculations, we use the formula μ = √(M{sub P}{sup 2}-(2M{sub c}){sup 2}) to determine the energy scales of the QCD spectral densities. We take into account the SU(3) breaking effects of the light quarks, and we obtain the masses of the hidden-charm pentaquark states with the strangeness S = 0, -1, -2, -3, which can be confronted with the experimental data in the future. (orig.)
Wang, Zhi-Gang [North China Electric Power University, Department of Physics, Baoding (China)
2016-02-15
In this article,we construct the diquark-diquark- antiquark type interpolating currents, and we study the masses and pole residues of the J{sup P} = (3)/(2){sup -} and (5)/(2){sup +} hidden charm pentaquark states in detail with the QCD sum rules by calculating the contributions of the vacuum condensates up to dimension-10 in the operator product expansion. In the calculations, we use the formula μ = √(M{sup 2}{sub P{sub c}}-(2M{sub c}){sup 2}) to determine the energy scales of the QCD spectral densities. The present predictions favor assigning P{sub c}(4380) and P{sub c}(4450) to be the (3)/(2){sup -} and (5)/(2){sup +} pentaquark states, respectively. (orig.)
Analysis of the strong decay X(5568) → B{sub s}{sup 0}π{sup +} with QCD sum rules
Wang, Zhi-Gang [North China Electric Power University, Department of Physics, Baoding (China)
2016-05-15
In this article, we take the X(5568) to be the scalar diquark-antidiquark type tetraquark state, study the hadronic coupling constant g{sub XB{sub sπ}} with the three-point QCD sum rules by carrying out the operator product expansion up to the vacuum condensates of dimension-6 and including both the connected and the disconnected Feynman diagrams; then we calculate the partial decay width of the strong decay X(5568) → B{sub s}{sup 0}π{sup +} and obtain the value Γ{sub X} = (20.5 ± 8.1) MeV, which is consistent with the experimental data Γ{sub X} = (21.9 ± 6.4{sup +5.0}{sub -2.5}) MeV from the D0 collaboration. (orig.)
Analysis of the strong coupling form factors of $\\Sigma_bNB$ and $\\Sigma_c ND$ in QCD sum rules
Yu, Guo Liang; Li, Zhen Yu
2016-01-01
In this article, we study the strong interaction of the vertexes $\\Sigma_bNB$ and $\\Sigma_c ND$ using the three-point QCD sum rules under two different dirac structures. Considering the contributions of the vacuum condensates up to dimension $5$ in the operation product expansion, the form factors of these vertexes are calculated. Then, we fit the form factors into analytical functions and extrapolate them into time-like regions, which giving the coupling constant. Our analysis indicates that the coupling constant for these two vertexes are $G_{\\Sigma_bNB}=0.43\\pm0.01GeV^{-1}$ and $G_{\\Sigma_cND}=3.76\\pm0.05GeV^{-1}$.
Johnson, R.A.; Vakili, M. [University of Cincinnati, Cincinnati, Ohio 45221 (United States); Kim, J.H.; Arroyo, C.G.; Bazarko, A.O.; Conrad, J.; King, B.J.; Lefmann, W.C.; McNulty, C.; Mishra, S.R.; Quintas, P.Z.; Romosan, A.; Schellman, H.; Sciulli, F.J.; Seligman, W.G.; Shaevitz, M.H.; Spentzouris, P.; Stern, E.G. [Columbia University, New York, New York 10027 (United States); Bernstein, R.H.; Lamm, M.J.; Marsh, W.; McFarland, K.S.; Yu, J. [Fermi National Accelerator Laboratory, Batavia, Illinois 60510 (United States); Bolton, T.; Naples, D. [Kansas State University, Manhattan, Kansas 66506 (United States); de Barbaro, L. [Northwestern University, Evanston, Illinois 60208 (United States); Harris, D.A.; de Barbaro, P.; Bodek, A.; Budd, H.; Sakumoto, W.K.; Yang, U.K. [University of Rochester, Rochester, New York 14627 (United States); Kinnel, T.; Smith, W.H. [University of Wisconsin, Madison, Wisconsin 53706 (United States)
1998-10-01
We extract a set of values for the Gross{endash}Llewellyn Smith sum rule at different values of 4-momentum transfer squared (Q{sup 2} ), by combining revised CCFR neutrino data with data from other neutrino deep-inelastic scattering experiments for 1{lt}Q{sup 2}{lt}15 GeV{sup 2}/c{sup 2} . A comparison with the order {alpha}{sup 3}{sub s} theoretical predictions yields a determination of {alpha}{sub s} at the scale of the Z -boson mass of 0.114{plus_minus}{sup 0.009}{sub 0.012} . This measurement provides a new and useful test of perturbative QCD at low Q{sup 2} , because of the low uncertainties in the higher order calculations. {copyright} {ital 1998} {ital The American Physical Society }
Application of the QCD light cone sum rule to tetraquarks: The strong vertices XbXbρ and XcXcρ
Agaev, S. S.; Azizi, K.; Sundu, H.
2016-06-01
The full version of the QCD light-cone sum rule method is applied to tetraquarks containing a single heavy b or c quark. To this end, investigations of the strong vertices XbXbρ and XcXcρ are performed, where Xb=[s u ][b ¯ d ¯ ] and Xc=[s u ][c ¯d ¯] are the exotic states built of four quarks of different flavors. The strong coupling constants GXbXbρ and GXcXcρ corresponding to these vertices are found using the ρ -meson leading- and higher-twist distribution amplitudes. In the calculations, Xb and Xc are treated as scalar bound states of a diquark and antidiquark.
Jeffries, J R; Moore, K T; Butch, N P; Maple, M B
2010-05-19
We examine the degree of 5f electron localization in URu{sub 2}Si{sub 2} using spin-orbit sum rule analysis of the U N{sub 4,5} (4d {yields} 5f) edge. When compared to {alpha}-U metal, US, USe, and UTe, which have increasing localization of the 5f states, we find that the 5f states of URu{sub 2}Si{sub 2} are more localized, although not entirely. Spin-orbit analysis shows that intermediate coupling is the correct angular momentum coupling mechanism for URu{sub 2}Si{sub 2} when the 5f electron count is between 2.6 and 2.8. These results have direct ramifications for theoretical assessment of the hidden order state of URu{sub 2}Si{sub 2}, where the degree of localization of the 5f electrons and their contribution to the Fermi surface are critical.
Moore, K; der Laan, G v; Haire, R; Wall, M; Schwartz, A
2005-10-07
Transmission electron microscopy is used to acquire electron energy-loss spectra from phase-specific regions of Pu and U metal, PuO{sub 2} and UO{sub 2}, and aged, self-irradiated Pu metal. The N{sub 4,5} (4d {yields} 5f) spectra are analyzed using the spin-orbit sum rule. Our results show that the technique is sensitive enough to detect changes in the branching ratio of the white-line peaks between the metal and dioxide of both U and Pu. There is a small change in the branching ratio between different Pu metals, and the data trends as would be expected for varying f electron localization, i.e., {alpha}-Pu, {delta}-Pu, aged {delta}-Pu. Moreover, our results suggest that the metal-oxide bonds in UO{sub 2} and PuO{sub 2} are strongly covalent in nature and do not exhibit an integer valence change as would be expected from purely ionic bonding.
Grebennikov, Vladimir I.; Bebenin, Nikolai G.; Zainullina, Rimma I.; Kuepper, Karsten; Kuznetsova, Tatyana V.
2017-10-01
The problem of determining the magnitude of the atomic magnetic moments in compounds with rare-earth and transition elements using the X-ray magnetic circular dichroism (XMCD) is investigated. The standard sum rules approach usually gives the moment values by several times smaller than their bulk values obtained from the direct magnetic measurements. We attribute this to the strong spin fluctuations in the surface layer which actually formed the soft XMCD signal. A method of determining the value of the local magnetic moments in the presence of strong fluctuations is proposed. The magnetic interactions in La0.5Pr0.2Ca0.3MnO3 are investigated by x-ray absorption spectroscopy, XMCD and bulk magnetization measurements. The proposed procedure is used to determine the values of atomic magnetic moments of transition and rare-earth elements as well as net magnetization on the surface and in the bulk from experimental Mn L2,3 and Pr M4,5 XMCD spectra.
Fu, Hai-Bing; Han, Hua-Yong; Ma, Yang
2014-01-01
The QCD light-cone sum rules (LCSR) provides an effective way for dealing with the heavy-to-light transition form factors (TFFs), whose non-perturbative dynamics are parameterized into the light-meson's light-cone distribution amplitudes (LCDAs) with various twist structures. By taking the chiral correlator as the starting point, we calculate the LCSRs for the $B\\to\\rho$ TFFs up to twist-4 accuracy. As for the TFFs at the large recoil region, we observe that the twist-2 transverse DA $\\phi_{2;\\rho}^\\bot$ provides the dominant contribution, while the contributions from the remaining twist-3 and twist-4 terms are $\\delta^2$-suppressed. Thus, our present improved LCSRs provides a good platform for testing the $\\phi_{2;\\rho}^\\bot$ behavior. For the purpose, we suggest a convenient WH-model for the $\\rho$-meson leading-twist wavefunction, in which the parameter $B_{2;\\rho}^\\bot\\sim a^\\bot_2$ dominantly controls its longitudinal distribution. Typically, its DA $\\phi_{2;\\rho}^\\bot$ is CZ-like as $B_{2;\\rho}^\\bot\\sim...
Kim, S
2001-01-01
We calculate the Wilson coefficients of all dimension-6 gluon operators with nonzero spin in the correlation function between two heavy vector currents. For the twist-4 part, we first identify the three independent gluon operators, and then proceed with the calculation of the Wilson coefficients using the fixed-point gauge. Together with the previous calculation of the Wilson coefficients for the dimension-6 scalar gluon operators by Nikolaev and Radyushkin, our result completes the list of all the Wilson coefficients of dimension-6 gluon operators in the correlation function between heavy vector currents. We apply our results to investigate the mass of J/psi in nuclear matter using QCD sum rules. Using an upper-bound estimate on the matrix elements of the dimension-6 gluon operators to linear order in density, we find that the density-dependent contribution from dimension-6 operators is less than 40% of the dimension-4 operators with opposite sign. The final result gives about -4 MeV mass shift for the charm...
The generalized GDH sum for He-3
Karl Slifer
2004-06-02
The Burkhardt-Cottingham, Bjorken and generalized GDH sum rules are all consequences of the Q^2-dependent dispersion relations for the virtual photon Compton amplitudes. These integrals are investigated for a He-3 target at low Q^2.
Wang, Z G
2006-01-01
In this article, we analyze the vertexes $D^*D_sK$, $D^*_sDK$, $D_0D_sK$ and $D_{s0}DK$ within the framework of the light-cone QCD sum rules approach in an unified way. The strong coupling constants $G_{D^*D_sK}$ and $G_{D^*_sDK}$ are important parameters in evaluating the charmonium absorption cross sections in searching for the quark-gluon plasmas, our numerical values for the $G_{D^*D_sK}$ and $G_{D^*_sDK}$ are compatible with the existing estimations although somewhat smaller, the SU(4) symmetry breaking effects are very large, about 60%. For the charmed scalar mesons $D_0$ and $D_{s0}$, we take the point of view that they are the conventional $c\\bar{u}$ and $c\\bar{s}$ mesons respectively, and calculate the strong coupling constants $G_{D_0 D_s K}$ and $G_{D_{s0} D K}$ with the vector interpolating currents. The numerical values for the scalar-$D_sK$ and -$DK$ coupling constants $G_{D_0 D_s K}$ and $G_{D_{s0} D K}$ are compatible with the existing estimations, the large values support the hadronic dressin...
Pong, Wai Yan
2007-01-01
We begin by answering the question, "Which natural numbers are sums of consecutive integers?" We then go on to explore the set of lengths (numbers of summands) in the decompositions of an integer as such sums.
Bluemlein, Johannes; Falcioni, Giulio; Freitas, Abilio de
2016-05-15
We calculate analytically the flavor non-singlet O(α{sup 2}{sub s}) massive Wilson coefficients for the inclusive neutral current non-singlet structure functions F{sup ep}{sub 1,2,L}(x, Q{sup 2}) and g{sup ep}{sub 1,2}(x, Q{sup 2}) and charged current non-singlet structure functions F{sup ν(anti} {sup ν)p}{sub 1,2,3}(x, Q{sup 2}), at general virtualities Q{sup 2} in the deep-inelastic region. Numerical results are presented. We illustrate the transition from low to large virtualities for these observables, which may be contrasted to basic assumptions made in the so-called variable flavor number scheme. We also derive the corresponding results for the Adler sum rule, the unpolarized and polarized Bjorken sum rules and the Gross-Llewellyn Smith sum rule. There are no logarithmic corrections at large scales Q{sup 2} and the effects of the power corrections due to the heavy quark mass are of the size of the known O(α{sup 2}{sub s}) corrections in the case of the sum rules. The complete charm and bottom corrections are compared to the approach using asymptotic representations in the region Q{sup 2} >> m{sup 2}{sub c,b}. We also study the target mass corrections to the above sum rules.
Brodal, Gerth Stølting; Jørgensen, Allan Grønlund
2008-01-01
In an array of n numbers each of the \\binomn2+nUnknown control sequence '\\binom' contiguous subarrays define a sum. In this paper we focus on algorithms for selecting and reporting maximal sums from an array of numbers. First, we consider the problem of reporting k subarrays inducing the k larges...... an algorithm with this running time and by proving a matching lower bound. Finally, we combine the ideas and obtain an O(n· max {1,log(k/n)}) time algorithm that selects a subarray storing the k’th largest sum among all subarrays of length at least l and at most u....
U.S. Geological Survey, Department of the Interior — The GIS layer "Census_sum_15" provides a standardized tool for examining spatial patterns in abundance and demographic trends of the southern sea otter (Enhydra...
Multiparty Symmetric Sum Types
Nielsen, Lasse; Yoshida, Nobuko; Honda, Kohei
2010-01-01
This paper introduces a new theory of multiparty session types based on symmetric sum types, by which we can type non-deterministic orchestration choice behaviours. While the original branching type in session types can represent a choice made by a single participant and accepted by others...... determining how the session proceeds, the symmetric sum type represents a choice made by agreement among all the participants of a session. Such behaviour can be found in many practical systems, including collaborative workflow in healthcare systems for clinical practice guidelines (CPGs). Processes...... with the symmetric sums can be embedded into the original branching types using conductor processes. We show that this type-driven embedding preserves typability, satisfies semantic soundness and completeness, and meets the encodability criteria adapted to the typed setting. The theory leads to an efficient...
A FEW MORE PROPERTIES OF SUM AND INTEGRAL SUM GRAPHS
V Vilfred
2014-10-01
Full Text Available The concepts of sum graph and integral sum graph were introduced by Harary [7], [8]. A sum graph is a graph whose vertices can be labeled with distinct positive integers so that the sum of the labels on each pair of adjacent vertices is the label of some other vertex. Integral sum graphs have the same definition except that the labels may be any integers. Harary [7], [8], gave examples of all orders of sum graphs and integral sum graphs , nÎN. The family of integral sum graph was extended by Vilfred (see [14], and in this paper, we obtain a few properties of sum and integral sum graphs and two new families of integral sum graphs.
Structure-property correlation study through sum-over-state approach
Nandi, P. K.; Hatua, K.; Bansh, A. K.; Panja, N.; Ghanty, T. K.
2015-01-01
The use of Thomas Kuhn (TK) sum rule in the expanded sum-over-state (SOS) expression of hyperpolarizabilities leads to various relationships between different order of polarizabilities and ground state dipole moment etc.
Beck, Matthias
2010-01-01
Let $p_1,p_2,\\dots,p_n, a_1,a_2,\\dots,a_n \\in \\N$, $x_1,x_2,\\dots,x_n \\in \\R$, and denote the $k$th periodized Bernoulli polynomial by $\\B_k(x)$. We study expressions of the form \\[ \\sum_{h \\bmod{a_k}} \\ \\prod_{\\substack{i=1\\\\ i\
Languasco, Alessandro
2011-01-01
Assuming that the Generalized Riemann Hypothesis (GRH) holds, we prove an explicit formula for the number of representations of an integer as a sum of $k\\geq 5$ primes. Our error terms in such a formula improve by some logarithmic factors an analogous result by Friedlander-Goldston.
Bounds for Certain Character Sums
杨锦; 郑志勇
2003-01-01
This paper shows a connection between exponential sums and character sums. In particular, we introduce a character sum that is an analog of the classical Kloosterman sums and establish the analogous Weil-Estermann's upper bound for it. The paper also analyzes a generalized Hardy-Littlewood example for character sums, which shows that the upper bounds given here are the best possible. The analysis makes use of local bounds for the exponential sums and character sums. The basic theorems have been previously established.
A Few Finite Trigonometric Sums
Chandan Datta
2017-02-01
Full Text Available Finite trigonometric sums occur in various branches of physics, mathematics, and their applications. These sums may contain various powers of one or more trigonometric functions. Sums with one trigonometric function are known; however, sums with products of trigonometric functions can become complicated, and may not have a simple expression in a number of cases. Some of these sums have interesting properties, and can have amazingly simple values. However, only some of them are available in the literature. We obtain a number of such sums using the method of residues.
Kumar, Alok
2010-01-01
We cannot use directly the results of zero-temperature at finite temperature, for at finite temperature the average is to be carried over all highly degenerate excited states unlike zero-temperature average is only on unique ground state. One of the formal way to take into account the finite temperature into quantum field theory is due to Matsubara, to replace temporal component of eigenvalues $k_{4}$ by $\\omega_{n}=\\frac{2\\pi n}{\\beta}$ $(\\frac{2\\pi (n+{1/2})}{\\beta})$ with summation over all integer values of $n$. The summation is done with the infinite series expansion of $\\coth (\\pi y)$. With the chemical potential $\\mu$, $\\omega_{n}$ will be replaced by $\\omega_{n} - \\mu$ in the eigenvalues and the summation over $n$ cannot be done easily. Various methods exist to evaluate it. We use the infinite series expansion of $\\coth (\\pi y)$ to work operationally for such Matsubara frequency sums.
贺丽; 余增强
2016-01-01
Sum rules for the dynamic structure factors are powerful tools to explore the collective behaviors in many-body systems at zero temperature as well as at finite temperatures. The recent remarkable realization of synthetic spin-orbit (SO) coupling in quantum gases is opening up new perspective to study the intriguing SO effects with ultracold atoms. So far, a specific type of SO coupling, which is generated by a pair of Raman laser beams, has been experimentally achieved in Bose-Einstein condensates of 87Rb and degenerate Fermi gases of 40K and 6Li. In the presence of SO coupling, the dynamic structure factors for the density fluctuation and spin fluctuation satisfy different sum rules. In particular, in the two-component quantum gases with inter-species Raman coupling, the f-sum rule for the spin fluctuation has an additional term proportional to the transverse spin polarization. Due to the coupling between the momentum and spin, the first moment of the dynamic structure factor does not necessarily possess the inversion symmetry, which is in strong contrast to the conventional system without SO coupling. Such an asymmetric behavior could be observed in both Fermi gases and Bose gases with Raman coupling. As a demonstration, we focus on the uniform case at zero temperature in this work. For the non-interacting Fermi gases, the asymmetric first moment appears only when the Raman detuning is finite. The asymmetric amplitude is quite limited, and it vanishes at both zero detuning and infinite detuning. For the weakly interacting Bose gases, the first moment is asymmetric in momentum space even at zero detuning, when the ground state spontaneously breaks the Z2 symmetry in the plane-wave condensation phase. Using the Bogoliubov method, the dynamic structure factor and its first moment are explicitly calculated for various interaction parameters. We find that the asymmetric behavior in the spin channel could be much more significant than in the density channel, and the
Sums of multiplicative characters analogue of Kloosterman sums
Xi, Ping
2010-01-01
Let $q$ be a positive integer, $\\chi$ a nontrivial character mod $q$. In this paper the authors prove some estimates for the character sum which is analogue of incomplete Kloostermann sums\\[\\sum_{\\substack{a\\in\\mathcal{I}\\\\ \\gcd(a,q)=1}}\\chi(ma+n\\overline{a}),\\] where $\\overline{a}$ is the multiplicative inverse of $a\\bmod q$, and $\\mathcal{I}$ is a subinterval of $[x+1,x+q]$ for certain integer $x.$
Social Security Administration — Staging Instance for all SUMs Counts related projects including: Redeterminations/Limited Issue, Continuing Disability Resolution, CDR Performance Measures, Initial...
Recurrence Formulas for Fibonacci Sums
Brandao, Adilson J V
2008-01-01
In this article we present a new recurrence formula for a finite sum involving the Fibonacci sequence. Furthermore, we state an algorithm to compute the sum of a power series related to Fibonacci series, without the use of term-by-term differentiation theorem
2007-01-01
In this paper,we first introduce a concept of L_p-dual Quermassintegral sum function of convex bodies and establish the polar projection Minkowski inequality and the polar projection Aleksandrov-Fenchel inequality for L_p-dual Quermassintegral sums.Moreover,by using Lutwak’s width-integral of index i,we establish the L_p-Brunn-Minkowski inequality for the polar mixed projec- tion bodies.As applications,we prove some interrelated results.
Comment concerning Leonardo's rule
Sotolongo-Costa, O; Oseguera-Manzanilla, T; Díaz-Guerrero, D S
2016-01-01
In this comment we propose a novel explanation for the Leonardo's rule concerning the tree branching. According to Leonardo's notebooks he observed that if one observes the branches of a tree, the squared radius of the principal branch is equal to the sum of the squared radius of the branch daughters.
Sum rules for the T-odd fragmentation functions
Schäfer, A
2000-01-01
The conservation of the intrinsic transverse momentum during parton fragmentation imposes non-trivial constraints on T-odd fragmentation functions. These significantly enhance the differences between the favoured and unfavoured fragmentation functions, which could be relevant to understand the azimuthal asymmetries of charged pion production observed recently by the HERMES collaboration.
Understanding the X(3872 with QCD sum rules
Zanetti C.M.
2010-04-01
Full Text Available The nature of the meson X(3872 is still under debate. Here we assume it to be a mixture between charmonium and exotic molecular [cq][qc] states with JPC = 1++ . We ﬁnd that there is only a small range for the values of the mixing angle, θ, that can provide simultaneously good agreement with the experimental value of the mass and the decay width, and this range is 50 ≤ θ ≤ 130 . In this range we get mX = (3.77 ± 0.18 GeV and Γ(X → J/ψπ+π− = (9.3 ± 6.9 MeV, which are compatible, within the errors, with the experimental values. We, therefore, conclude that the X(3872 is approximately 97% a charmonium state with 3% admixture of ∼88% D0 D∗0 molecule and ∼12% D+ D∗− molecule.
Sum Rules for Optical Extinction and Scattering by Small Particles.
1986-03-18
and some areas of optics, particularly optical properties of solids (e.g., Stern, 1963), they have been largely ignored by workers in the field of...Elementary theory of the optical properties of solids . Sold State Phys. 15, 299-408. A , a. - . - . A - - .4 4 ) J N
Three nucleon forces in nuclear matter in QCD sum rules
Drukarev, E. G.; Ryskin, M. G.; Sadovnikova, V. A.
2017-03-01
We calculate the single-particle nucleon characteristics in symmetric nuclear matter with inclusion of the 3N interactions. The contributions of the 3N forces to nucleon self energies are expressed in terms of the nonlocal scalar condensate (d = 3) and of the configuration of the four-quark condensates (d = 6) in which two diquark operators act on two different nucleons of the matter. The most important part of the contribution of the four-quark condensate is calculated in a model-independent way. We employed a relativistic quark model of nucleon for calculation of the other parts. The density dependence of the vector and scalar nucleon self energies and of the single-particle potential energy are obtained. Estimations on contributions of the 4N forces to the nucleon self energies are made.
Yu, Guo-Liang; Wang, Zhi-Gang [North China Electric Power University, Department of Mathematics and Physics, Baoding (China); Li, Zhen-Yu [Guizhou Normal College, School of Physics and Electronic Science, Guiyang (China)
2015-06-15
In this article, we calculate the form factors and the coupling constant of the vertex D{sub s}{sup *}D{sub s}φ using the three-point QCD sum rules. We consider the contributions of the vacuum condensates up to dimension 7 in the operator product expansion. And all possible off-shell cases are considered, φ, D{sub s} and D{sub s}{sup *}, resulting in three different form factors. Then we fit the form factors into analytical functions and extrapolate them into time-like regions, which giving the coupling constant for the process. Our analysis indicates that the coupling constant for this vertex is G{sub D{sub s{sup *}D{sub sφ}}} = 4.12 ± 0.70 GeV{sup -1}1. The results of this work are very useful in the other phenomenological analysis. As an application, we calculate the coupling constant for the decay channel D{sub s}{sup *} → D{sub s}γ and analyze the width of this decay with the assumption of the vector meson dominance of the intermediate φ(1020). Our final result about the decay width of this decay channel is Γ = 0.59 ± 0.15 keV. (orig.)
Large even order character sums
Goldmakher, Leo
2012-01-01
A classical theorem of Paley asserts the existence of an infinite family of quadratic characters whose character sums become exceptionally large. In this paper, we establish an analogous result for characters of any fixed even order. Previously our bounds were only known under the assumption of the Generalized Riemann Hypothesis.
Some Alternating Double Binomial Sums
ZHENG De-yin; TANG Pei-pei
2013-01-01
We consider some new alternating double binomial sums. By using the Lagrange inversion formula, we obtain explicit expressions of the desired results which are related to a third-order linear recursive sequence. Furthermore, their recursive relation and generating functions are obtained.
EXTENSIONS OF EULER HARMONIC SUMS
Djurdje Cvijović
2012-10-01
Full Text Available Three new closed-form summation formulae involving harmonic numbers are established using simple arguments and they are very general extensions of Euler’s famous harmonic sum identity. Some illustrative special cases as well as immediate consequences of the main results are also considered.
2008-06-23
Jun 23, 2008 ... Access to financial services is one of the important ways to protect and build economic ... Thus, HIV and AIDS service NGOs have been increasingly getting ..... Rules and regulations: As explained by the participants in.
Borwein, J M; McPhedran, R C
2013-01-01
The study of lattice sums began when early investigators wanted to go from mechanical properties of crystals to the properties of the atoms and ions from which they were built (the literature of Madelung's constant). A parallel literature was built around the optical properties of regular lattices of atoms (initiated by Lord Rayleigh, Lorentz and Lorenz). For over a century many famous scientists and mathematicians have delved into the properties of lattices, sometimes unwittingly duplicating the work of their predecessors. Here, at last, is a comprehensive overview of the substantial body of
CONVERGENCE RATE OFDISTRIBUTIONS OF TRIMMED SUMS
QIYONGCHENG; CHENGSHIHONG
1996-01-01
The authors first derive the normal expansion of the joint density function of two orderstatistics from the uniform distribution and then, using the approximation, establish a wayto estimate the normal convergence rate for trimmed sums. For applications, the convergence rates for the intermediately trimmed sums and heavily trimmed sums are found out.
The hybrid mean value of Dedekind sums and two-term exponential sums
Leran Chang
2016-01-01
Full Text Available In this paper, we use the mean value theorem of Dirichlet L-functions, the properties of Gauss sums and Dedekind sums to study the hybrid mean value problem involving Dedekind sums and the two-term exponential sums, and give an interesting identity and asymptotic formula for it.
Determinant Sums for Undirected Hamiltonicity
Björklund, Andreas
2010-01-01
We present a Monte Carlo algorithm for Hamiltonicity detection in an $n$-vertex undirected graph running in $O^*(1.657^{n})$ time. To the best of our knowledge, this is the first superpolynomial improvement on the worst case runtime for the problem since the $O^*(2^n)$ bound established for TSP almost fifty years ago (Bellman 1962, Held and Karp 1962). It answers in part the first open problem in Woeginger's 2003 survey on exact algorithms for NP-hard problems. For bipartite graphs, we improve the bound to $O^*(1.414^{n})$ time. Both the bipartite and the general algorithm can be implemented to use space polynomial in $n$. We combine several recently resurrected ideas to get the results. Our main technical contribution is a new reduction inspired by the algebraic sieving method for $k$-Path (Koutis ICALP 2008, Williams IPL 2009). We introduce the Labeled Cycle Cover Sum in which we are set to count weighted arc labeled cycle covers over a finite field of characteristic two. We reduce Hamiltonicity to Labeled ...
Parameterized Telescoping Proves Algebraic Independence of Sums
Schneider, Carsten
2008-01-01
Usually creative telescoping is used to derive recurrences for sums. In this article we show that the non-existence of a creative telescoping solution, and more generally, of a parameterized telescoping solution, proves algebraic independence of certain types of sums. Combining this fact with summation-theory shows transcendence of whole classes of sums. Moreover, this result throws new light on the question why, e.g., Zeilberger's algorithm fails to find a recurrence with minimal order.
Some Finite Sums Involving Generalized Fibonacci and Lucas Numbers
E. Kılıç
2011-01-01
Full Text Available By considering Melham's sums (Melham, 2004, we compute various more general nonalternating sums, alternating sums, and sums that alternate according to (−12+1 involving the generalized Fibonacci and Lucas numbers.
The BFKL Pomeron calculus: Summing enhanced diagrams
Levin, E., E-mail: leving@post.tau.ac.il [Department of Particle Physics, School of Physics and Astronomy, Tel Aviv University, Tel Aviv 69978 (Israel); Departamento de Fisica, Universidad Tecnica Federico Santa Maria, and Centro Cientifico-Tecnologico de Valparaiso, Casilla 110-V, Valparaiso (Chile); Miller, J., E-mail: jeremy.miller@ist.utl.pt [Department of Particle Physics, School of Physics and Astronomy, Tel Aviv University, Tel Aviv 69978 (Israel); CENTRA, Departamento de Fisica, Instituto Superior Tecnico (IST), Av. Rovisco Pais, 1049-001 Lisboa (Portugal)
2012-07-01
The goal of this paper is to sum over a class of enhanced diagrams, and derive a new Pomeron Green function. It is found that this sum gives the Pomeron contribution to the scattering amplitude that decreases with energy. In other words, we found that the total cross section of two colourless dipoles of small but equal sizes, falls down at high energies.
The package HarmonicSums: Computer Algebra and Analytic aspects of Nested Sums
Ablinger, Jakob
2014-01-01
This paper summarizes the essential functionality of the computer algebra package HarmonicSums. On the one hand HarmonicSums can work with nested sums such as harmonic sums and their generalizations and on the other hand it can treat iterated integrals of the Poincare and Chen-type, such as harmonic polylogarithms and their generalizations. The interplay of these representations and the analytic aspects are illustrated by concrete examples.
A New Sum Analogous to Gauss Sums and Its Fourth Power Mean
Shaofeng Ru
2014-01-01
Full Text Available The main purpose of this paper is to use the analytic methods and the properties of Gauss sums to study the computational problem of one kind of new sum analogous to Gauss sums and give an interesting fourth power mean and a sharp upper bound estimate for it.
A new sum analogous to Gauss sums and its fourth power mean.
Ru, Shaofeng; Zhang, Wenpeng
2014-01-01
The main purpose of this paper is to use the analytic methods and the properties of Gauss sums to study the computational problem of one kind of new sum analogous to Gauss sums and give an interesting fourth power mean and a sharp upper bound estimate for it.
A hybrid mean value related to the Dedekind sums and Kloosterman sums
无
2010-01-01
The main purpose of this paper is using the properties of character sum and the analytic method to study a hybrid mean value problem related to the Dedekind sums and Kloosterman sums,and give some interesting mean value formulae and identities for it.
Private Decayed Sum Estimation under Continual Observation
Bolot, Jean; Muthukrishnan, S; Nikolov, Aleksandar; Taft, Nina
2011-01-01
Motivated by monitoring applications, recently, Dwork et al. initiated the study of differential privacy as data is continually updated over time. They abstracted the problem of running sums that is applicable widely, and proved upper and lower bounds on accuracy of \\epsilon - differentially private algorithms for this problem. We continue their study, but we are motivated by the reality that in many monitoring applications, recent data is more important than distant data. Thus, we study the sums problem for well known decay models of data, from window to exponential and polynomial decay. Such "decayed sums" are challenging because (a) while we want accuracy in analysis with respect to the window or decayed sum, we still want differential privacy; (b) sums within windows and decayed sums in general are not monotonic or even near-monotonic as studied in the work of Dwork et al. We present algorithms for decayed sum in each model which are \\epsilon-differentially private, and are accurate. For window and expone...
Irene Machado
2008-11-01
Full Text Available Nem sempre os temas candentes da investigação, numa determinada área do conhecimento, são colocados de maneira orgânica e organizada para o conjunto dos pesquisadores que sobre eles se debruçam. Quase nunca as edições cientícas, que se propõem a torná-los acessíveis a seus leitores, conseguem harmonizá-los sem correr os riscos de aproximações indevidas. A única forma de não incorrer em equívocos perigosos é assumir a idiossincrasia do temário diversificado que constitui o campo em questão. O leitor que ora inicia seu diálogo com este sétimo número de Galáxia não deve tomar esse preâmbulo por alerta, mas sim como tentativa de a revista manter a coerência face a seu compromisso de ser porta-voz dos temas e problemas da comunicação e da cultura pelo prisma das teorias semióticas que orientam o olhar dos vários colaboradores que encontram neste espaço uma tribuna aberta ao trânsito das diferenças. Basta um relance pelo sumário desta edição para que tal armação possa ser confirmada. Os textos que constituem o Fórum, respeitadas as singularidades, tratam de temas que são caros para as abordagens da comunicação e da semiótica na cultura. Temos o privilégio de publicar o texto inédito em português de Jakob von Uexküll em que o autor apresenta sua teoria da Umwelt, caracterizando formulações da biossemiótica sobre o signi.cado do entorno ou do espaço circundante, que são valiosas para compreender a percepção, a interação, o contexto, a informação, os códigos em ambientes de semiose. De um outro lugar - aquele modulado pela lógica da linguagem - Lucrécia Ferrara perscruta o campo conceitual que entende o design não pelo viés da operatividade, mas como processo semiótico-cognitivo. A outra ponta deste que pode ser um triálogo nos é dado pela comunicologia de Vilém Flusser. Para Michael Hanke, Flusser foi um dos grandes teóricos a investigar a importância da mídia para os
A method to compute periodic sums
Gumerov, Nail A
2013-01-01
In a number of problems in computational physics, a finite sum of kernel functions centered at $N$ particle locations located in a box in three dimensions must be extended by imposing periodic boundary conditions on box boundaries. Even though the finite sum can be efficiently computed via fast summation algorithms, such as the fast multipole method (FMM), the periodized extension is usually treated via a different algorithm, Ewald summation, accelerated via the fast Fourier transform (FFT). A different approach to compute this periodized sum just using a blackbox finite fast summation algorithm is presented in this paper. The method splits the periodized sum in to two parts. The first, comprising the contribution of all points outside a large sphere enclosing the box, and some of its neighbors, is approximated inside the box by a collection of kernel functions ("sources") placed on the surface of the sphere or using an expansion in terms of spectrally convergent local basis functions. The second part, compri...
Certain Binomial Sums with recursive coefficients
Kilic, Emrah
2010-01-01
In this short note, we establish some identities containing sums of binomials with coefficients satisfying third order linear recursive relations. As a result and in particular, we obtain general forms of earlier identities involving binomial coefficients and Fibonacci type sequences.
On Learning Ring-Sum-Expansions
Fischer, Paul; Simon, H. -U.
1992-01-01
The problem of learning ring-sum-expansions from examples is studied. Ring-sum-expansions (RSE) are representations of Boolean functions over the base {#123;small infinum, (+), 1}#125;, which reflect arithmetic operations in GF(2). k-RSE is the class of ring-sum-expansions containing only monomials...... of a 2-CNF and a 1-DNF. Finally the paper presents learning (on-line prediction) algorithms for k-RSE that are optimal with respect to the sample size (worst case mistake bound)...... of length at most k:. term-RSE is the class of ring-sum-expansions having at most I: monomials. It is shown that k-RSE, k>or=1, is learnable while k-term-RSE, k>2, is not learnable if RPnot=NP. Without using a complexity-theoretical hypothesis, it is proven that k-RSE, k>or=1, and k-term-RSE, k>or=2 cannot...
Structural relations between nested harmonic sums
Bluemlein, J.
2008-07-15
We describe the structural relations between nested harmonic sums emerging in the description of physical single scale quantities up to the 3-loop level in renormalizable gauge field theories. These are weight w=6 harmonic sums. We identify universal basic functions which allow to describe a large class of physical quantities and derive their complex analysis. For the 3-loop QCD Wilson coefficients 35 basic functions are required, whereas a subset of 15 describes the 3-loop anomalous dimensions. (orig.)
Trigonometric sums in number theory and analysis
Karatsuba, Anatoly A; Chubarikov, Vladimir N; Shishkova, Maria
2004-01-01
The book presents the theory of multiple trigonometric sums constructed by the authors. Following a unified approach, the authors obtain estimates for these sums similar to the classical I. M. Vinogradov´s estimates and use them to solve several problems in analytic number theory. They investigate trigonometric integrals, which are often encountered in physics, mathematical statistics, and analysis, and in addition they present purely arithmetic results concerning the solvability of equations in integers.
Skew quantum Murnaghan-Nakayama rule
Konvalinka, Matjaz
2011-01-01
In this paper, we extend recent results of Assaf and McNamara on skew Pieri rule and skew Murnaghan-Nakayama rule to a more general identity, which gives an elegant expansion of the product of a skew Schur function with a quantum power sum function in terms of skew Schur functions. We give two proofs, one completely bijective in the spirit of Assaf-McNamara's original proof, and one via Lam-Lauve-Sotille's skew Littlewood-Richardson rule. We end with some conjectures for skew rules for Hall-Littlewood polynomials.
Exponential sums over primes in short intervals
LIU; Jianya
2006-01-01
[1]Vinogradov,I.M.,Estimation of certain trigonometric sums with prime variables,Izv.Acad.Nauk.SSSR,1939,3:371-398.[2]Zhan,T.,On the representation of large odd integer as a sum of three almost equal primes,Acta Math.Sin.,1991,7:259-272.[3]Ren,X.M.,On exponential sums over primes and application in the Waring-Goldbach problem,Sci.China,Ser.A-Math.,2005,48(6):785-797.[4]Liu,J.Y.,Wooley,T.D.,Yu,G.,The quadratic Waring-Goldbach problem,J.Number Theory,2004,107:298-321.[5]Hua,L.K.,Some results in the additive prime number theory,Quart.J.Math.(Oxford),1938,9:68-80.[6]Liu,J.Y.,Zhan,T.,On sums of five almost equal prime squares,Acta Arith.,1996,77:369-383.[7]Bauer,C.,A note on sums of five almost equal prime squares,Arch.Math,1997,69:20-30.[8]Liu,J.Y.,Zhan,T.,Sums of five almost equal prime squares,Science in China,Ser.A,1998,41:710-722.[9]Liu,J.Y.,Zhan,T.,Hua's theorem on prime squares in short intervals,Acta Math.Sin.,2000,16:1-22.[10]Bauer,C.,Sums of five almost equal prime squares,Acta Math.Sin.,2005,21(4):833-840.[11]Lü,G.S.,Hua's Theorem with five almost equal prime variables,Chin.Ann.Math.,Ser.B,2005,26(2):291-304.[12]Vinogradov,I.M.,Elements of Number Theory,Dover Publications,1954.[13]Titchmarsh,E.C.,The Theory of the Riemann Zeta-function,2nd ed.,Oxford:Oxford University Press,1986.
Randomly Stopped Sums: Models and Psychological Applications
Michael eSmithson
2014-11-01
Full Text Available This paper describes an approach to modeling the sums of a continuous random variable over a number of measurement occasions when the number of occasions also is a random variable. A typical example is summing the amounts of time spent attending to pieces of information in an information search task leading to a decision to obtain the total time taken to decide. Although there is a large literature on randomly stopped sums in financial statistics, it is largely absent from psychology. The paper begins with the standard modeling approaches used in financial statistics, and then extends them in two ways. First, the randomly stopped sums are modeled as ``life distributions'' such as the gamma or log-normal distribution. A simulation study investigates Type I error rate accuracy and power for gamma and log-normal versions of this model. Second, a Bayesian hierarchical approach is used for constructing an appropriate general linear model of the sums. Model diagnostics are discussed, and three illustrations are presented from real datasets.
An Entropy-Weighted Sum over Non-Perturbative Vacua
Gregori, Andrea
2007-01-01
We discuss how, in a Universe restricted to the causal region connected to the observer, General Relativity implies the quantum nature of physical phenomena and directly leads to a string theory scenario, whose dynamics is ruled by a functional that weights all configurations according to their entropy. The most favoured configurations are those of minimal entropy. Along this class of vacua a four-dimensional space-time is automatically selected; when, at large volume, a description of space-time in terms of classical geometry can be recovered, the entropy-weighted sum reduces to the ordinary Feynman's path integral. What arises is a highly predictive scenario, phenomenologically compatible with the experimental observations and measurements, in which everything is determined in terms of the fundamental constants and the age of the Universe, with no room for freely-adjustable parameters. We discuss how this leads to the known spectrum of particles and interactions. Besides the computation of masses and coupli...
Dowker, J S
2015-01-01
The finite sums of powers of cosecs occur in numerous situations, both physical and mathematical, examples being the Casimir effect, Renyi entropy, Verlinde's formula and Dedekind sums. I here present some further discussion which consists mainly of a reprise of early work by H.M.Jeffery in 1862-64 which has fallen by the wayside and whose results are being reproduced up to the present day. The motivation is partly historical justice and partly that, because of the continuing appearance of the sums, his particular methods deserve re--exposure. For example, simple trigonometric generating functions are found and these have a field theoretic, Green function significance and I make a few comments in the topic of R\\'enyi entropies.
Fundamentals of sum-frequency spectroscopy
Shen, Y R
2016-01-01
The first book on the topic, and written by the founder of the technique, this comprehensive resource provides a detailed overview of sum-frequency spectroscopy, its fundamental principles, and the wide range of applications for surfaces, interfaces, and bulk. Beginning with an overview of the historical context, and introductions to the basic theory of nonlinear optics and surface sum-frequency generation, topics covered include discussion of different experimental arrangements adopted by researchers, notes on proper data analysis, an up-to-date survey commenting on the wide range of successful applications of the tool, and a valuable insight into current unsolved problems and potential areas to be explored in the future. With the addition of chapter appendices that offer the opportunity for more in-depth theoretical discussion, this is an essential resource that integrates all aspects of the subject and is ideal for anyone using, or interested in using, sum-frequency spectroscopy.
Concentration inequalities for sums and martingales
Bercu, Bernard; Rio, Emmanuel
2015-01-01
The purpose of this book is to provide an overview of historical and recent results on concentration inequalities for sums of independent random variables and for martingales. The first chapter is devoted to classical asymptotic results in probability such as the strong law of large numbers and the central limit theorem. Our goal is to show that it is really interesting to make use of concentration inequalities for sums and martingales. The second chapter deals with classical concentration inequalities for sums of independent random variables such as the famous Hoeffding, Bennett, Bernstein and Talagrand inequalities. Further results and improvements are also provided such as the missing factors in those inequalities. The third chapter concerns concentration inequalities for martingales such as Azuma-Hoeffding, Freedman and De la Pena inequalities. Several extensions are also provided. The fourth chapter is devoted to applications of concentration inequalities in probability and statistics.
Least square regularized regression in sum space.
Xu, Yong-Li; Chen, Di-Rong; Li, Han-Xiong; Liu, Lu
2013-04-01
This paper proposes a least square regularized regression algorithm in sum space of reproducing kernel Hilbert spaces (RKHSs) for nonflat function approximation, and obtains the solution of the algorithm by solving a system of linear equations. This algorithm can approximate the low- and high-frequency component of the target function with large and small scale kernels, respectively. The convergence and learning rate are analyzed. We measure the complexity of the sum space by its covering number and demonstrate that the covering number can be bounded by the product of the covering numbers of basic RKHSs. For sum space of RKHSs with Gaussian kernels, by choosing appropriate parameters, we tradeoff the sample error and regularization error, and obtain a polynomial learning rate, which is better than that in any single RKHS. The utility of this method is illustrated with two simulated data sets and five real-life databases.
Irreducible polynomials with prescribed sums of coefficients
Tuxanidy, Aleksandr; Wang, Qiang
2016-01-01
Let $q$ be a power of a prime, let $\\mathbb{F}_q$ be the finite field with $q$ elements and let $n \\geq 2$. For a polynomial $h(x) \\in \\mathbb{F}_q[x]$ of degree $n \\in \\mathbb{N}$ and a subset $W \\subseteq [0,n] := \\{0, 1, \\ldots, n\\}$, we define the sum-of-digits function $$S_W(h) = \\sum_{w \\in W}[x^{w}] h(x)$$ to be the sum of all the coefficients of $x^w$ in $h(x)$ with $w \\in W$. In the case when $q = 2$, we prove, except for a few genuine exceptions, that for any $c \\in \\mathbb{F}_2$ an...
Almost Sure Central Limit Theory for Self-Normalized Products of Sums of Partial Sums
Qunying Wu
2012-01-01
Full Text Available Let X,X1,X2,… be a sequence of independent and identically distributed random variables in the domain of attraction of a normal law. An almost sure limit theorem for the self-normalized products of sums of partial sums is established.
Summing threshold logs in a parton shower
Nagy, Zoltan
2016-01-01
When parton distributions are falling steeply as the momentum fractions of the partons increases, there are effects that occur at each order in $\\alpha_s$ that combine to affect hard scattering cross sections and need to be summed. We show how to accomplish this in a leading approximation in the context of a parton shower Monte Carlo event generator.
Form Sums of Nonnegative Selfadjoint Operators
Hassi, S.; Sandovici, A.; Snoo, H.S.V. de; Winkler, Henrik; Sandovici, 27740
2006-01-01
The sum of two unbounded nonnegative selfadjoint operators is a nonnegative operator which is not necessarily densely defined. In general its selfadjoint extensions exist in the sense of linear relations (multivalued operators). One of its nonnegative selfadjoint extensions is constructed via the fo
The Ronkin number of an exponential sum
Silipo, James
2011-01-01
We give an intrinsic estimate of the number of connected components of the complementary set to the amoeba of an exponential sum with real spectrum improving the result of Forsberg, Passare and Tsikh in the polynomial case and that of Ronkin in the exponential one.
Summing threshold logs in a parton shower
Nagy, Zoltan [Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany); Soper, Davison E. [Oregon Univ., Eugene, OR (United States). Inst. of Theoretical Science
2016-05-15
When parton distributions are falling steeply as the momentum fractions of the partons increases, there are effects that occur at each order in α{sub s} that combine to affect hard scattering cross sections and need to be summed. We show how to accomplish this in a leading approximation in the context of a parton shower Monte Carlo event generator.
Sum and product in dynamic epistemic logic
Van Ditmarsch, H. P.; Ruan, J.; Verbrugge, R.
2008-01-01
The Sum-and-Product riddle was first published in the reference H. Freudenthal (1969, Nieuw Archief voor Wiskunde 3, 152) [6]. We provide an overview on the history of the dissemination of this riddle through the academic and puzzle-math community. This includes some references to precursors of the
On the Computation of Correctly Rounded Sums
Kornerup, Peter; Lefevre, Vincent; Louvet, Nicolas;
2012-01-01
algorithm introduced by Knuth is minimal, both in terms of number of operations and depth of the dependency graph. We investigate the possible use of another algorithm, Dekker's Fast2Sum algorithm, in radix-10 arithmetic. We give methods for computing, in radix 10, the floating-point number nearest...
Sums of Integer Squares: A New Look.
Sastry, K. R. S.; Pranesachar, C. R.; Venkatachala, B. J.
1998-01-01
Focuses on the study of the sum of two integer squares, neither of which is zero square. Develops some new interesting and nonstandard ideas that can be put to use in number theory class, mathematics club meetings, or popular lectures. (ASK)
Fibonacci Identities via the Determinant Sum Property
Spivey, Michael
2006-01-01
We use the sum property for determinants of matrices to give a three-stage proof of an identity involving Fibonacci numbers. Cassini's and d'Ocagne's Fibonacci identities are obtained at the ends of stages one and two, respectively. Catalan's Fibonacci identity is also a special case.
Demonstration of a Quantum Nondemolition Sum Gate
Yoshikawa, J.; Miwa, Y.; Huck, Alexander;
2008-01-01
The sum gate is the canonical two-mode gate for universal quantum computation based on continuous quantum variables. It represents the natural analogue to a qubit C-NOT gate. In addition, the continuous-variable gate describes a quantum nondemolition (QND) interaction between the quadrature compo...
Decompounding random sums: A nonparametric approach
Hansen, Martin Bøgsted; Pitts, Susan M.
review a number of applications and consider the nonlinear inverse problem of inferring the cumulative distribution function of the components in the random sum. We review the existing literature on non-parametric approaches to the problem. The models amenable to the analysis are generalized considerably...
Large- quantum chromodynamics and harmonic sums
Eduardo De Rafael
2012-06-01
In the large- limit of QCD, two-point functions of local operators become harmonic sums. I review some properties which follow from this fact and which are relevant for phenomenological applications. This has led us to consider a class of analytic number theory functions as toy models of large- QCD which also is discussed.
Zero-Sum Problems with Subgroup Weights
S D Adhikari; A A Ambily; B Sury
2010-06-01
In this note, we generalize some theorems on zero-sums with weights from [1], [4] and [5] in two directions. In particular, we consider $\\mathbb{Z}^d_p$ for a general and subgroups of $Z^∗_p$ as weights.
On the sum of generalized Fibonacci sequence
Chong, Chin-Yoon; Ho, C. K.
2014-06-01
We consider the generalized Fibonacci sequence {Un defined by U0 = 0, U1 = 1, and Un+2 = pUn+1+qUn for all n∈Z0+ and p, q∈Z+. In this paper, we derived various sums of the generalized Fibonacci sequence from their recursive relations.
On Learning Ring-Sum-Expansions
Fischer, Paul; Simon, H. -U.
1992-01-01
The problem of learning ring-sum-expansions from examples is studied. Ring-sum-expansions (RSE) are representations of Boolean functions over the base {#123;small infinum, (+), 1}#125;, which reflect arithmetic operations in GF(2). k-RSE is the class of ring-sum-expansions containing only monomials...... of length at most k:. term-RSE is the class of ring-sum-expansions having at most I: monomials. It is shown that k-RSE, k>or=1, is learnable while k-term-RSE, k>2, is not learnable if RPnot=NP. Without using a complexity-theoretical hypothesis, it is proven that k-RSE, k>or=1, and k-term-RSE, k>or=2 cannot...... be learned from positive (negative) examples alone. However, if the restriction that the hypothesis which is output by the learning algorithm is also a k-RSE is suspended, then k-RSE is learnable from positive (negative) examples only. Moreover, it is proved that 2-term-RSE is learnable by a conjunction...
The Distribution of Sum of Random Sums%随机和的和的分布
王开永; 戚文文
2012-01-01
对于两个独立的随机和，利用概率论的方法讨论它们的和的分布问题，可以得出独立的随机和的和仍然为随机和的结论．另外具体给出复合Poisson分布和、复合二项分布和、复合负二项分布和，以及复合几何分布和的分布．’%For two independent random sums, the distribution of the sum of these two random sums is investigated and a general result that the sum of two independent random sums is still a random sum is presented, which shows the relation between the two distributions. Using this result, the distributions of the sums of some common compound distributions are given which include the compound Poisson distribution, binomial distribution, generalized binomial distribution, and geometric distribution.
A New Generalization of Hardy-Berndt Sums
Muhammet Cihat Dağli; Mümün Can
2013-05-01
In this paper, we construct a new generalization of Hardy–Berndt sums which are explicit extensions of Hardy–Berndt sums. We express these sums in terms of Dedekind sums $s_r(h,k:x,y|)$ with ==0 and obtain corresponding reciprocity formulas.
The information content of rules and rule sets and its application
HU Dan; LI HongXing; YU XianChuan
2008-01-01
The information content of rules is categorized into inner mutual information content and outer impartation information content. Actually, the conventional objective interestingness measures based on information theory are all inner mutual informarion, which represent the confidence of rules and the mutual information between the antecedent and consequent. Moreover, almost all of these measures lose sight of the outer impartation information, which is conveyed to the user and help the user to make decisions. We put forward the viewpoint that the outer impartation information content of rules and rule sets can be represented by the relations from input universe to output universe. By binary relations, the interaction of rules in a rule set can be easily represented by operators: union and intersection. Based on the entropy of relations, the outer impartation information content of rules and rule sets are well measured. Then, the conditional information content of rules and rule sets, the independence of rules and rule sets and the inconsistent knowledge of rule sets are defined and measured. The properties of these new measures are discussed and some interesting results are proven, such as the information content of a rule set may be bigger than the sum of the information content of rules in the rule set, and the conditional information content of rules may be negative. At last, the applications of these new measures are discussed. The new method for the appraisement of .rule mining algorithm, and two rule pruning algorithms, λ-choice and RPCIC, are put forward. These new methods and algorithms havepredominance in satisfying the need of more efficient decision information.
Theorems of Forming and Summing of Natural Numbers and Their Application
2013-01-01
This paper presents the way to form other set of natural numbers from a given set of natural numbers and formulae to determine the sum of resulting numbers. The other set of natural numbers can be formed either by arranging a given natural numbers in specific order that is by using the principles of permutation rule or by using the principle of product rule provided that a given set of natural numbers should contain equal number of digits. The major areas of study to carry out this particular...
Strong sum distance in fuzzy graphs.
Tom, Mini; Sunitha, Muraleedharan Shetty
2015-01-01
In this paper the idea of strong sum distance which is a metric, in a fuzzy graph is introduced. Based on this metric the concepts of eccentricity, radius, diameter, center and self centered fuzzy graphs are studied. Some properties of eccentric nodes, peripheral nodes and central nodes are obtained. A characterisation of self centered complete fuzzy graph is obtained and conditions under which a fuzzy cycle is self centered are established. We have proved that based on this metric, an eccentric node of a fuzzy tree G is a fuzzy end node of G and a node is an eccentric node of a fuzzy tree if and only if it is a peripheral node of G and the center of a fuzzy tree consists of either one or two neighboring nodes. The concepts of boundary nodes and interior nodes in a fuzzy graph based on strong sum distance are introduced. Some properties of boundary nodes, interior nodes and complete nodes are studied.
Transition Mean Values of Shifted Convolution Sums
Petrow, Ian
2011-01-01
Let f be a classical holomorphic cusp form for SL_2(Z) of weight k which is a normalized eigenfunction for the Hecke algebra, and let \\lambda(n) be its eigenvalues. In this paper we study "shifted convolution sums" of the eigenvalues \\lambda(n) after averaging over many shifts h and obtain asymptotic estimates. The result is somewhat surprising: one encounters a transition region depending on the ratio of the square of the length of the average over h to the length of the shifted convolution sum. The phenomenon is similar to that encountered by Conrey, Farmer and Soundararajan in their 2000 paper Transition Mean Values of Real Characters, and the connection of both results to Eisenstein series and multiple Dirichlet series is discussed.
Maximum Segment Sum, Monadically (distilled tutorial
Jeremy Gibbons
2011-09-01
Full Text Available The maximum segment sum problem is to compute, given a list of integers, the largest of the sums of the contiguous segments of that list. This problem specification maps directly onto a cubic-time algorithm; however, there is a very elegant linear-time solution too. The problem is a classic exercise in the mathematics of program construction, illustrating important principles such as calculational development, pointfree reasoning, algebraic structure, and datatype-genericity. Here, we take a sideways look at the datatype-generic version of the problem in terms of monadic functional programming, instead of the traditional relational approach; the presentation is tutorial in style, and leavened with exercises for the reader.
Geometric optimization and sums of algebraic functions
Vigneron, Antoine E.
2014-01-01
We present a new optimization technique that yields the first FPTAS for several geometric problems. These problems reduce to optimizing a sum of nonnegative, constant description complexity algebraic functions. We first give an FPTAS for optimizing such a sum of algebraic functions, and then we apply it to several geometric optimization problems. We obtain the first FPTAS for two fundamental geometric shape-matching problems in fixed dimension: maximizing the volume of overlap of two polyhedra under rigid motions and minimizing their symmetric difference. We obtain the first FPTAS for other problems in fixed dimension, such as computing an optimal ray in a weighted subdivision, finding the largest axially symmetric subset of a polyhedron, and computing minimum-area hulls.
Disjoint sum forms in reliability theory
B. Anrig
2014-01-01
Full Text Available The structure function f of a binary monotone system is assumed to be known and given in a disjunctive normal form, i.e. as the logical union of products of the indicator variables of the states of its subsystems. Based on this representation of f, an improved Abraham algorithm is proposed for generating the disjoint sum form of f. This form is the base for subsequent numerical reliability calculations. The approach is generalized to multivalued systems. Examples are discussed.
Variance of partial sums of stationary sequences
Deligiannidis, George
2012-01-01
Let $X_1, X_2,...$ be a centred sequence of weakly stationary random variables with spectral measure $F$ and partial sums $S_n = X_1 +...+ X_n$, and let $G(x) = \\int_{-x}^x F(\\rd x)$. We show that $\\var(S_n)$ is regularly varying of index $\\gamma$ at infinity, if and only if $G(x)$ is regularly varying of index $2-\\gamma$ at the origin ($0<\\gamma<2$).
Sequences, Bent Functions and Jacobsthal sums
Helleseth, Tor
2010-01-01
The $p$-ary function $f(x)$ mapping $\\mathrm{GF}(p^{4k})$ to $\\mathrm{GF}(p)$ and given by $f(x)={\\rm Tr}_{4k}\\big(ax^d+bx^2\\big)$ with $a,b\\in\\mathrm{GF}(p^{4k})$ and $d=p^{3k}+p^{2k}-p^k+1$ is studied with the respect to its exponential sum. In the case when either $a^{p^k(p^k+1)}\
Gao's Conjecture on Zero-Sum Sequences
B Sury; R Thangadurai
2002-08-01
In this paper, we shall address three closely-related conjectures due to van Emde Boas, W D Gao and Kemnitz on zero-sum problems on $\\mathbf{Z}_p \\oplus \\mathbf{Z}_p$. We prove a number of results including a proof of the conjecture of Gao for the prime = 7 (Theorem 3.1). The conjecture of Kemnitz is also proved (Propositions 4.6, 4.9, 4.10) for many classes of sequences.
A 2-categorical state sum model
Baratin, Aristide; Freidel, Laurent
2015-01-01
It has long been argued that higher categories provide the proper algebraic structure underlying state sum invariants of 4-manifolds. This idea has been refined recently, by proposing to use 2-groups and their representations as specific examples of 2-categories. The challenge has been to make these proposals fully explicit. Here, we give a concrete realization of this program. Building upon our earlier work with Baez and Wise on the representation theory of 2-groups, we construct a four-dimensional state sum model based on a categorified version of the Euclidean group. We define and explicitly compute the simplex weights, which may be viewed a categorified analogue of Racah-Wigner 6j-symbols. These weights solve a hexagon equation that encodes the formal invariance of the state sum under the Pachner moves of the triangulation. This result unravels the combinatorial formulation of the Feynman amplitudes of quantum field theory on flat spacetime proposed in A. Baratin and L. Freidel [Classical Quantum Gravity 24, 2027-2060 (2007)] which was shown to lead after gauge-fixing to Korepanov's invariant of 4-manifolds.
A 2-categorical state sum model
Baratin, Aristide
2014-01-01
It has long been argued that higher categories provide the proper algebraic structure underlying state sum invariants of 4-manifolds. This idea has been refined recently, by proposing to use 2-groups and their representations as specific examples of 2-categories. The challenge has been to make these proposals fully explicit. Here we give a concrete realization of this program. Building upon our earlier work with Baez and Wise on the representation theory of 2-groups, we construct a four-dimensional state sum model based on a categorified version of the Euclidean group. We define and explicitly compute the simplex weights, which may be viewed a categorified analogue of Racah-Wigner 6$j$-symbols. These weights solve an hexagon equation that encodes the formal invariance of the state sum under the Pachner moves of the triangulation. This result unravels the combinatorial formulation of the Feynman amplitudes of quantum field theory on flat spacetime proposed in [1], which was shown to lead after gauge-fixing to ...
A 2-categorical state sum model
Baratin, Aristide, E-mail: abaratin@uwaterloo.ca [Department of Applied Mathematics, University of Waterloo, 200 University Ave W, Waterloo, Ontario N2L 3G1 (Canada); Freidel, Laurent, E-mail: lfreidel@perimeterinstitute.ca [Perimeter Institute for Theoretical Physics, 31 Caroline Str. N, Waterloo, Ontario N2L 2Y5 (Canada)
2015-01-15
It has long been argued that higher categories provide the proper algebraic structure underlying state sum invariants of 4-manifolds. This idea has been refined recently, by proposing to use 2-groups and their representations as specific examples of 2-categories. The challenge has been to make these proposals fully explicit. Here, we give a concrete realization of this program. Building upon our earlier work with Baez and Wise on the representation theory of 2-groups, we construct a four-dimensional state sum model based on a categorified version of the Euclidean group. We define and explicitly compute the simplex weights, which may be viewed a categorified analogue of Racah-Wigner 6j-symbols. These weights solve a hexagon equation that encodes the formal invariance of the state sum under the Pachner moves of the triangulation. This result unravels the combinatorial formulation of the Feynman amplitudes of quantum field theory on flat spacetime proposed in A. Baratin and L. Freidel [Classical Quantum Gravity 24, 2027–2060 (2007)] which was shown to lead after gauge-fixing to Korepanov’s invariant of 4-manifolds.
Onorato, P.
2011-01-01
An introduction to quantum mechanics based on the sum-over-paths (SOP) method originated by Richard P. Feynman and developed by E. F. Taylor and coworkers is presented. The Einstein-Brillouin-Keller (EBK) semiclassical quantization rules are obtained following the SOP approach for bounded systems, and a general approach to the calculation of…
Generalizations of some Zero Sum Theorems
M N Chintamani; B K Moriya
2012-02-01
Given an abelian group of order , and a finite non-empty subset of integers, the Davenport constant of with weight , denoted by $D_A(G)$, is defined to be the least positive integer such that, for every sequence $(x_1,\\ldots,x_t)$ with $x_i\\in G$, there exists a non-empty subsequence $(x_{j_1},\\ldots,x_{j_l})$ and $a_i\\in A$ such that $\\sum^l_{i=1}a_ix_{j_i}=0$. Similarly, for an abelian group of order $n,E_A(G)$ is defined to be the least positive integer such that every sequence over of length contains a subsequence $(x_{j_1},\\ldots,x_{j_n})$ such that $\\sum^n_{i=1}a_ix_{j_i}=0$, for some $a_i\\in A$. When is of order , one considers to be a non-empty subset of $\\{1,\\ldots,n-1\\}$. If is the cyclic group $\\mathbb{Z}/n\\mathbb{Z}$, we denote $E_A(G)$ and $D_A(G)$ by $E_A(n)$ and $D_A(n)$ respectively. In this note, we extend some results of Adhikari et al(Integers 8(2008) Article A52) and determine bounds for $D_{R_n}(n)$ and $E_{R_n}(n)$, where $R_n=\\{x^2:x\\in(\\mathbb{Z}/n\\mathbb{Z})^∗\\}$. We follow some lines of argument from Adhikari et al(Integers 8 (2008) Article A52) and use a recent result of Yuan and Zeng (European J. Combinatorics 31 (2010) 677–680), a theorem due to Chowla (Proc. Indian Acad. Sci. (Math. Sci.) 2 (1935) 242–243) and Kneser’s theorem (Math. Z.58(1953) 459–484;66(1956) 88–110;61(1955) 429–434).
Some Zero-Sum Constants with Weights
S D Adhikari; R Balasubramanian; F Pappalardi; P Rath
2008-05-01
For an abelian group , the Davenport constant () is defined to be the smallest natural number such that any sequence of elements in has a non-empty subsequence whose sum is zero (the identity element). Motivated by some recent developments around the notion of Davenport constant with weights, we study them in some basic cases. We also define a new combinatorial invariant related to $(\\mathbb{Z}/n\\mathbb{Z})^d$, more in the spirit of some constants considered by Harborth and others and obtain its exact value in the case of $(\\mathbb{Z}/n\\mathbb{Z})^2$ where is an odd integer.
Exponential sums over primes in short intervals
LIU Jianya; L(U) Guangshi; ZHAN Tao
2006-01-01
In this paper we establish one new estimate on exponential sums over primes in short intervals. As an application of this result, we sharpen Hua's result by proving that each sufficiently large integer N congruent to 5 modulo 24 can be written as N = p21 +p22 +p23 +p24 +p25, with |pj - √N/5| ≤ U = N1/2-1/20+ε,where pj are primes. This result is as good as what one can obtain from the generalized Riemann hypothesis.
Clique Cover Width and Clique Sum
Shahrokhi, Farhad
2015-01-01
For a clique cover $C$ in the undirected graph $G$, the clique cover graph of $C$ is the graph obtained by contracting the vertices of each clique in $C$ into a single vertex. The clique cover width of G, denoted by $CCW(G)$, is the minimum value of the bandwidth of all clique cover graphs of $G$. When $G$ is the clique sum of $G_1$ and $G_2$, we prove that $CCW(G) \\le 3/2(CCW(G_1) + CCW(G_2))$.
Sum-of-squares clustering on networks
Carrizosa Emilio
2011-01-01
Full Text Available Finding p prototypes by minimizing the sum of the squared distances from a set of points to its closest prototype is a well-studied problem in clustering, data analysis and continuous location. In this note, this very same problem is addressed assuming, for the first time, that the space of possible prototype locations is a network. We develop some interesting properties of such clustering problem. We also show that optimal cluster prototypes are not necessary located at vertices of the network.
Sums of two-dimensional spectral triples
Christensen, Erik; Ivan, Cristina
2007-01-01
construct a sum of two dimensional modules which reflects some aspects of the topological dimensions of the compact metric space, but this will only give the metric back approximately. At the end we make an explicit computation of the last module for the unit interval in. The metric is recovered exactly......, the Dixmier trace induces a multiple of the Lebesgue integral but the growth of the number of eigenvalues is different from the one found for the standard differential operator on the unit interval....
Dedekind zeta-functions and Dedekind sums
陆洪文; 焦荣政; 纪春岗
2002-01-01
In this paper we use Dedekind zeta functions of two real quadratic number fields at -1 to denote Dedekind sums of high rank. Our formula is different from that of Siegel's. As an application, we get a polynomial representation of ζK(-1): ζK(-1) =1/45(26n3-41n±9), n ≡±2(mod 5), where K=Q( q),prime q=4n2+1, and the class number of quadratic number field K2=Q(q) is 1.
Partial Row-Sums of Pascal's Triangle
Ollerton, Richard L.
2007-01-01
Identities for many and varied combinations of binomial coefficients abound. Indeed, because of the wide range of interrelationships it is possible that a great deal of mathematical effort has been wasted in proving essentially equivalent formulae. As well as proving identities these methods can be used to rule out closed form solutions (at least…
Sum-SINR/sum-capacity optimal multisignature spread-spectrum steganography
Wei, Lili; Pados, Dimitris A.; Batalama, Stella N.; Medley, Michael J.
2008-04-01
For any given digital host image or audio file (or group of hosts) and any (block) transform domain of interest, we find an orthogonal set of signatures that achieves maximum sum-signal-to-interference-plus-noise ratio (sum- SINR) spread-spectrum message embedding for any fixed embedding amplitude values. We also find the sumcapacity optimal amplitude allocation scheme for any given total distortion budget under the assumption of (colored) Gaussian transform-domain host data. The practical implication of the results is sum-SINR, sumcapacity optimal multiuser/multisignature spread-spectrum data hiding in the same medium. Theoretically, the findings establish optimality of the recently presented Gkizeli-Pados-Medley multisignature eigen-design algorithm.
Evans, Philip; Wolf, Bob
2005-01-01
Corporate leaders seeking to boost growth, learning, and innovation may find the answer in a surprising place: the Linux open-source software community. Linux is developed by an essentially volunteer, self-organizing community of thousands of programmers. Most leaders would sell their grandmothers for workforces that collaborate as efficiently, frictionlessly, and creatively as the self-styled Linux hackers. But Linux is software, and software is hardly a model for mainstream business. The authors have, nonetheless, found surprising parallels between the anarchistic, caffeinated, hirsute world of Linux hackers and the disciplined, tea-sipping, clean-cut world of Toyota engineering. Specifically, Toyota and Linux operate by rules that blend the self-organizing advantages of markets with the low transaction costs of hierarchies. In place of markets' cash and contracts and hierarchies' authority are rules about how individuals and groups work together (with rigorous discipline); how they communicate (widely and with granularity); and how leaders guide them toward a common goal (through example). Those rules, augmented by simple communication technologies and a lack of legal barriers to sharing information, create rich common knowledge, the ability to organize teams modularly, extraordinary motivation, and high levels of trust, which radically lowers transaction costs. Low transaction costs, in turn, make it profitable for organizations to perform more and smaller transactions--and so increase the pace and flexibility typical of high-performance organizations. Once the system achieves critical mass, it feeds on itself. The larger the system, the more broadly shared the knowledge, language, and work style. The greater individuals' reputational capital, the louder the applause and the stronger the motivation. The success of Linux is evidence of the power of that virtuous circle. Toyota's success is evidence that it is also powerful in conventional companies.
The Infinite Sum of Reciprocal of the Fibonacci Numbers
Guo Jie ZHANG
2011-01-01
In this paper,we consider infinite sums of the reciprocals of the Fibonacci numbers.Then applying the floor function to the reciprocals of this sums,we obtain a new identity involving the Fibonacci numbers.
Christensen, Jørgen Riber
2011-01-01
Thomas Arne’s The Masque of Alfred (1740) with a libretto by James Thomson and David Mallet was written and performed in the historical context of George II’s reign where a kind of constitutional monarchy based on the Bill of Rights from 1689 was granting civil rights to the early bourgeoisie...... of the Proms, and this article considers it as a global real-time media event. “Rule, Britannia!” is placed in the contexts of political history, cultural history and experience economy....
Interpreting the Four Types of Sums of Squares in SPSS.
Tanguma, Jesus; Speed, F. M.
This paper analyzes three possible research designs using each of the four types of sums of squares in the Statistical Package for the Social Sciences (SPSS). When the design is balanced (i.e., each cell has the same number of observations), all of the SPSS types of sums of squares yield equivalent results (testable hypotheses and sums of squares)…
27 CFR 24.148 - Penal sums of bonds.
2010-04-01
... 27 Alcohol, Tobacco Products and Firearms 1 2010-04-01 2010-04-01 false Penal sums of bonds. 24.148 Section 24.148 Alcohol, Tobacco Products and Firearms ALCOHOL AND TOBACCO TAX AND TRADE BUREAU... Penal sums of bonds. The penal sums of bonds prescribed in this part are as follows: Bond Basis...
22 CFR 19.13-1 - Lump-sum credit.
2010-04-01
... 22 Foreign Relations 1 2010-04-01 2010-04-01 false Lump-sum credit. 19.13-1 Section 19.13-1... THE FOREIGN SERVICE RETIREMENT AND DISABILITY SYSTEM § 19.13-1 Lump-sum credit. “Lump-sum credit” is the compulsory and special contributions to a participant's or former participant's credit in the Fund...
42 CFR 411.46 - Lump-sum payments.
2010-10-01
... Covered Under Workers' Compensation § 411.46 Lump-sum payments. (a) Lump-sum commutation of future benefits. If a lump-sum compensation award stipulates that the amount paid is intended to compensate the... payment of workers' compensation benefits, medical expenses incurred after the date of the settlement are...
Logical consistency and sum-constrained linear models
van Perlo -ten Kleij, Frederieke; Steerneman, A.G.M.; Koning, Ruud H.
2006-01-01
A topic that has received quite some attention in the seventies and eighties is logical consistency of sum-constrained linear models. Loosely defined, a sum-constrained model is logically consistent if the restrictions on the parameters and explanatory variables are such that the sum constraint is a
尉志武; 周蕊; 刘芸
2002-01-01
A solubility-related rule, nonzero solubility rule, is introduced in this paper. It is complementary to the existing rules such as the "like dissolves like" rule and can be understood on the basis of classical chemical thermodynamics.
Character sums for primitive root densities
Lenstra, H W; Stevenhagen, P
2011-01-01
It follows from the work of Artin and Hooley that, under assumption of the generalized Riemann hypothesis, the density of the set of primes $q$ for which a given non-zero rational number $r$ is a primitive root modulo $q$ can be written as an infinite product $\\prod_p \\delta_p$ of local factors $\\delta_p$ reflecting the degree of the splitting field of $X^p-r$ at the primes $p$, multiplied by a somewhat complicated factor that corrects for the `entanglement' of these splitting fields. We show how the correction factors arising in Artin's original primitive root problem and some of its generalizations can be interpreted as character sums describing the nature of the entanglement. The resulting description in terms of local contributions is so transparent that it greatly facilitates explicit computations, and naturally leads to non-vanishing criteria for the correction factors.
On Zero Sum Subsequences of Restricted Size
B K Moriya
2010-09-01
Let be a finite abelian group with $\\exp(G)=e$. Let $s(G)$ be the minimal integer with the property that any sequence of elements in contains an -term subsequence with sum zero. Let , and be positive integers and ≥ 3. Furthermore, $(C^r_m)=a_r(m-1)+1$, for some constant $a_r$ depending on and is a fixed positive integer such that $$n≥\\frac{m^r(c(r)m-a_r(m-1)+m-3)(m-1)-(m+1)+(m+1)(a_r+1)}{m(m+1)(a_r+1)}$$ and $s(C^r_n)=(a_r+1)(n-1)+1$. In the above lower bound on $n,c(r)$ is the Alon-Dubiner constant. Then $s(C^r_{nm})=(a_r+1)(nm-1)+1$.
Scattering and; Delay, Scale, and Sum Migration
Lehman, S K
2011-07-06
How do we see? What is the mechanism? Consider standing in an open field on a clear sunny day. In the field are a yellow dog and a blue ball. From a wave-based remote sensing point of view the sun is a source of radiation. It is a broadband electromagnetic source which, for the purposes of this introduction, only the visible spectrum is considered (approximately 390 to 750 nanometers or 400 to 769 TeraHertz). The source emits an incident field into the known background environment which, for this example, is free space. The incident field propagates until it strikes an object or target, either the yellow dog or the blue ball. The interaction of the incident field with an object results in a scattered field. The scattered field arises from a mis-match between the background refractive index, considered to be unity, and the scattering object refractive index ('yellow' for the case of the dog, and 'blue' for the ball). This is also known as an impedance mis-match. The scattering objects are referred to as secondary sources of radiation, that radiation being the scattered field which propagates until it is measured by the two receivers known as 'eyes'. The eyes focus the measured scattered field to form images which are processed by the 'wetware' of the brain for detection, identification, and localization. When time series representations of the measured scattered field are available, the image forming focusing process can be mathematically modeled by delayed, scaled, and summed migration. This concept of optical propagation, scattering, and focusing have one-to-one equivalents in the acoustic realm. This document is intended to present the basic concepts of scalar scattering and migration used in wide band wave-based remote sensing and imaging. The terms beamforming and (delayed, scaled, and summed) migration are used interchangeably but are to be distinguished from the narrow band (frequency domain) beamforming to determine
Sum of Bernoulli Mixtures: Beyond Conditional Independence
Taehan Bae
2014-01-01
Full Text Available We consider the distribution of the sum of Bernoulli mixtures under a general dependence structure. The level of dependence is measured in terms of a limiting conditional correlation between two of the Bernoulli random variables. The conditioning event is that the mixing random variable is larger than a threshold and the limit is with respect to the threshold tending to one. The large-sample distribution of the empirical frequency and its use in approximating the risk measures, value at risk and conditional tail expectation, are presented for a new class of models which we call double mixtures. Several illustrative examples with a Beta mixing distribution, are given. As well, some data from the area of credit risk are fit with the models, and comparisons are made between the new models and also the classical Beta-binomial model.
Exponential Approximations Using Fourier Series Partial Sums
Banerjee, Nana S.; Geer, James F.
1997-01-01
The problem of accurately reconstructing a piece-wise smooth, 2(pi)-periodic function f and its first few derivatives, given only a truncated Fourier series representation of f, is studied and solved. The reconstruction process is divided into two steps. In the first step, the first 2N + 1 Fourier coefficients of f are used to approximate the locations and magnitudes of the discontinuities in f and its first M derivatives. This is accomplished by first finding initial estimates of these quantities based on certain properties of Gibbs phenomenon, and then refining these estimates by fitting the asymptotic form of the Fourier coefficients to the given coefficients using a least-squares approach. It is conjectured that the locations of the singularities are approximated to within O(N(sup -M-2), and the associated jump of the k(sup th) derivative of f is approximated to within O(N(sup -M-l+k), as N approaches infinity, and the method is robust. These estimates are then used with a class of singular basis functions, which have certain 'built-in' singularities, to construct a new sequence of approximations to f. Each of these new approximations is the sum of a piecewise smooth function and a new Fourier series partial sum. When N is proportional to M, it is shown that these new approximations, and their derivatives, converge exponentially in the maximum norm to f, and its corresponding derivatives, except in the union of a finite number of small open intervals containing the points of singularity of f. The total measure of these intervals decreases exponentially to zero as M approaches infinity. The technique is illustrated with several examples.
On solving equations of algebraic sum of equal powers
WANG Xinghua; YANG Shijun
2006-01-01
It is well known that a system of equations of sum of equal powers can be converted to an algebraic equation of higher degree via Newton's identities. This is the Viete-Newton theorem. This work reports the generalizations of the Viete-Newton theorem to a system of equations of algebraic sum of equal powers. By exploiting some facts from algebra and combinatorics,it is shown that a system of equations of algebraic sum of equal powers can be converted in a closed form to two algebraic equations, whose degree sum equals the number of unknowns of the system of equations of algebraic sum of equal powers.
Definition and Properties of Direct Sum Decomposition of Groups1
Nakasho Kazuhisa
2015-03-01
Full Text Available In this article, direct sum decomposition of group is mainly discussed. In the second section, support of element of direct product group is defined and its properties are formalized. It is formalized here that an element of direct product group belongs to its direct sum if and only if support of the element is finite. In the third section, product map and sum map are prepared. In the fourth section, internal and external direct sum are defined. In the last section, an equivalent form of internal direct sum is proved. We referred to [23], [22], [8] and [18] in the formalization.
Equivalent Expressions of Direct Sum Decomposition of Groups1
Nakasho Kazuhisa
2015-03-01
Full Text Available In this article, the equivalent expressions of the direct sum decomposition of groups are mainly discussed. In the first section, we formalize the fact that the internal direct sum decomposition can be defined as normal subgroups and some of their properties. In the second section, we formalize an equivalent form of internal direct sum of commutative groups. In the last section, we formalize that the external direct sum leads an internal direct sum. We referred to [19], [18] [8] and [14] in the formalization.
$N_c$-counting rules and the axial vector coupling constant of the constituent quark
Broniowski, W; Steiner, A
1993-01-01
Instead of using a simple reggeon-exchange model, we provide a model-independent estimate of high-energy contribution to the Adler-Weisberger sum-rule. Results and conclusions of the paper remain unchanged.
Large convexly independent subsets of Minkowski sums
Swanepoel, Konrad J
2010-01-01
Let $E_d(n)$ be the maximum number of pairs that can be selected from a set of $n$ points in $R^d$ such that the midpoints of these pairs are convexly independent. We show that $E_2(n)\\geq \\Omega(n\\sqrt{\\log n})$, which answers a question of Eisenbrand, Pach, Rothvo\\ss, and Sopher (2008) on large convexly independent subsets in Minkowski sums of finite planar sets, as well as a question of Halman, Onn, and Rothblum (2007). We also show that $\\lfloor\\frac{1}{3}n^2\\rfloor\\leq E_3(n)\\leq \\frac{3}{8}n^2+O(n^{3/2})$. Let $W_d(n)$ be the maximum number of pairwise nonparallel unit distance pairs in a set of $n$ points in some $d$-dimensional strictly convex normed space. We show that $W_2(n)=\\Theta(E_2(n))$ and for $d\\geq 3$ that $W_d(n)\\sim\\frac12\\left(1-\\frac{1}{a(d)}\\right)n^2$, where $a(d)\\in N$ is related to strictly antipodal families. In fact we show that the same asymptotics hold without the requirement that the unit distance pairs form pairwise nonparallel segments, and also if diameter pairs are considere...
Level-1 Jets and Sums Trigger Performance
CMS Collaboration
2016-01-01
After the first long shutdown, the LHC has restarted at a centre-of-mass energy of 13 TeV. The LHC is expected to achieve an instantaneous luminosity larger than $10^{34} \\rm{cm}^{-2} \\rm{s}^{-1}$ and an average number of pile-up interactions of at least 40. The CMS Level-1 trigger architecture has undergone a full upgrade in order to maintain and improve the trigger performance under these new conditions. It will allow CMS to keep the trigger rate under control and to avoid a significant increase in trigger thresholds that would have a negative impact on the CMS physics programme. First studies of the performance of the calorimeter trigger upgrade for jets and energy sums are shown. Details of the algorithms and commissioning may be found in CMS-DP-2015-051 and the CMS Technical Design Report for the Level-1 Trigger upgrade: CERN-LHCC-2013-011, CMS-TDR-12 (2013)
Resonance sum rules from large $N_C$ and partial wave dispersive analysis
Guo, Zhi-Hui
2008-01-01
Combining large $N_C$ techniques and partial wave dispersion theory to analyze the $\\pi\\pi$ scattering, without relying on any explicit resonance lagrangian, some interesting results are derived: (a) a general KSRF relation including the scalar meson contribution; (b) a new relation between resonance couplings, with which we have made an intensive analysis in several specific models; (c) low energy constants in chiral perturbation theory related with $\\pi\\pi$ scattering in terms of the mass and decay width of resonances.
Sum Rule Constraints and the Quality of Approximate Kubo-Transformed Correlation Functions.
Hernández de la Peña, Lisandro
2016-02-11
In this work, a general protocol for evaluating the quality of approximate Kubo correlation functions of nontrivial systems in many dimensions is discussed. We first note that the generalized deconvolution of the Kubo transformed correlation function onto a time correlation function at a given value τ in imaginary time, such that 0 function and whose iterative extension allows us to link derivatives of different order in the corresponding correlation functions. We focus on the case when τ = βℏ/2, for which all deconvolution kernels become real valued functions and their asymptotic behavior at long times exhibits a polynomial divergence. It is then shown that thermally symmetrized static averages, and the averages of the corresponding time derivatives, are ideally suited to investigate the quality of approximate Kubo correlation functions at successively larger (and up to arbitrarily long) times. This overall strategy is illustrated analytically for a harmonic system and numerically for a multidimensional double-well potential and a Lennard-Jones fluid. The analysis includes an assessment of RPMD position autocorrelation results as a function of the number of dimensions in a double-well potential and of the RPMD velocity autocorrelation function of liquid neon at 30 K.
SPECTRAL-WEIGHT TRANSFER - BREAKDOWN OF LOW-ENERGY-SCALE SUM-RULES IN CORRELATED SYSTEMS
MEINDERS, MBJ; ESKES, H; SAWATZKY, GA
1993-01-01
In this paper we study the spectral-weight transfer from the high- to the low-energy scale by means of exact diagonalization of finite clusters for the Mott-Hubbard and charge-transfer model. We find that the spectral-weight transfer is very sensitive to the hybridization strength as well as to the
Modeling the hyperpolarizability dispersion with the Thomas-Kuhn sum rules
De Mey, Kurt; Perez-Moreno, Javier; Clays, Koen
2011-10-01
The continued interest in molecules that possess large quadratic nonlinear optical (NLO) properties has motivated considerable interplay between molecular synthesis and theory. The screening of viable candidates for NLO applications has been a tedious work, much helped by the advent of the hyper-Rayleigh scattering (HRS) technique. The downside of this technique is the low efficiency, which usually means that measurements have to be performed at wavelengths that are close to the molecular resonances, in the visible area. This means generally that one has to extrapolate the results from HRS characterization to the longer wavelengths that are useful for applications. Such extrapolation is far from trivial and the classic 2-level model can only be used for the most straightforward single charge-transfer chromophores. An alternative is the TKSSOS technique, which uses a few input-hyperpolarizabilities and UV-Vis absorption data to calculate the entire hyperpolarizability spectrum. We have applied this TKS-SOS technique on a set of porphyrines to calculate the hyperpolarizability dispersion. We have also built a tunable HRS set up, capable of determining hyperpolarizabilities in the near infrared (up to 1600 nm). This has allowed us to directly confirm the results predicted in the application region. Due to the very sharp transitions in the hyperpolarizability dispersion, the calculation is subjected to a very precise calibration with respect to the input-hyperpolarizabilities, resulting in very accurate predictions for long wavelength hyperpolarizabilities. Our results not only underscribe the aforementioned technique, but also confirm the use of porphyrines as powerful moieties in NLO applications.
Dielectric function of dense plasmas, their stopping power, and sum rules.
Arkhipov, Yu V; Ashikbayeva, A B; Askaruly, A; Davletov, A E; Tkachenko, I M
2014-11-01
Mathematical, particularly, asymptotic properties of the random-phase approximation, Mermin approximation, and extended Mermin-type approximation of the coupled plasma dielectric function are analyzed within the method of moments. These models are generalized for two-component plasmas. Some drawbacks and advantages of the above models are pointed out. The two-component plasma stopping power is shown to be enhanced with respect to that of the electron fluid.
Renormalons and multiloop estimates in scalar correlators, Higgs decay and quark-mass sum rule
Broadhurst, D J; Maxwell, C J
2001-01-01
The single renormalon-chain contribution to the correlator of scalar currents in QCD is calculated in the $\\bar{MS}$-scheme in the limit of a large $N_f$. We find that in the factorial growth of the coefficients due to renormalons takes over almost immediately in the euclidean region. The essential differences between the large-order growth of coefficients in the scalar case, and in the vector case are analysed.In the timelike region a stabilization of the perturbative series for the imaginary part, with $n$-loop behaviour $S_n/[\\log(s/\\Lambda^2)]^{n-1}$, where $S_n$ is essentially constant for $n\\le{6}$, is observed. Only for $n\\ge{7}$ does one discern the factorial growth and alternations of sign. Our all-orders results are used to scrutinize the performance of multiloop estimates, within the ``naive nonabelianization'' procedure, and the effective charges approach. The asymptotic behaviour of perturbative coefficients, in both large-$N_f$ and large-$N_c$ limits, is analysed. A contour-improved resummation ...
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.
Three nucleon forces in nuclear matter in the QCD sum rules
Drukarev, E G; Sadovnikova, V A
2016-01-01
We calculate the single-particle nucleon characteristics in symmetric nuclear matter with inclusion of the 3N interactions. The contribution of the 3N forces to the nucleon self energies are expressed in terms of the nonlocal scalar condensate (d=3) and of the configuration of the two four-quark condensates (d=6) in which two diquark operators act on two different nucleons of the matter. The most important part of the contribution of the four-quark condensate is calculated in a model-independent way. We employed a relativistic quark model of nucleon for calculation of the rest part. The density dependence of the vector and scalar nucleon self energies and of the single-particle potential energy are obtained.
The subsequence weight distribution of summed maximum length digital sequences
Weathers, G. D.; Graf, E. R.; Wallace, G. R.
1974-01-01
An attempt is made to develop mathematical formulas to provide the basis for the design of pseudorandom signals intended for applications requiring accurate knowledge of the statistics of the signals. The analysis approach involves calculating the first five central moments of the weight distribution of subsequences of hybrid-sum sequences. The hybrid-sum sequence is formed from the modulo-two sum of k maximum length sequences and is an extension of the sum sequences formed from two maximum length sequences that Gilson (1966) evaluated. The weight distribution of the subsequences serves as an approximation to the filtering process. The basic reason for the analysis of hybrid-sum sequences is to establish a large group of sequences with good statistical properties. It is shown that this can be accomplished much more efficiently using the hybrid-sum approach rather than forming the group strictly from maximum length sequences.
Central Binomial Sums, Multiple Clausen Values and Zeta Values
Borwein, J M; Kamnitzer, J
2000-01-01
We find and prove relationships between Riemann zeta values and central binomial sums. We also investigate alternating binomial sums (also called Ap\\'ery sums). The study of non-alternating sums leads to an investigation of different types of sums which we call multiple Clausen values. The study of alternating sums leads to a tower of experimental results involving polylogarithms in the golden ratio. In the non-alternating case, there is a strong connection to polylogarithms of the sixth root of unity, encountered in the 3-loop Feynman diagrams of {\\tt hep-th/9803091} and subsequently in hep-ph/9910223, hep-ph/9910224, cond-mat/9911452 and hep-th/0004010.
Twisted exponential sums of polynomials in one variable
无
2010-01-01
The twisted T-adic exponential sums associated to a polynomial in one variable are studied.An explicit arithmetic polygon in terms of the highest two exponents of the polynomial is proved to be a lower bound of the Newton polygon of the C-function of the twisted T-adic exponential sums.This bound gives lower bounds for the Newton polygon of the L-function of twisted p-power order exponential sums.
27 CFR 25.93 - Penal sum of bond.
2010-04-01
... 27 Alcohol, Tobacco Products and Firearms 1 2010-04-01 2010-04-01 false Penal sum of bond. 25.93... OF THE TREASURY LIQUORS BEER Bonds and Consents of Surety § 25.93 Penal sum of bond. (a)(1) Brewers....164(c)(2), the penal sum of the brewers bond must be equal to 10 percent of the maximum amount of...
Exponential convergence rates for weighted sums in noncommutative probability space
Choi, Byoung Jin; Ji, Un Cig
2016-11-01
We study exponential convergence rates for weighted sums of successive independent random variables in a noncommutative probability space of which the weights are in a von Neumann algebra. Then we prove a noncommutative extension of the result for the exponential convergence rate by Baum, Katz and Read. As applications, we first study a large deviation type inequality for weighted sums in a noncommutative probability space, and secondly we study exponential convergence rates for weighted free additive convolution sums of probability measures.
PROBABILITY INEQUALITIES FOR SUMS OF INDEPENDENT UNBOUNDED RANDOM VARIABLES
张涤新; 王志诚
2001-01-01
The tail probability inequalities for the sum of independent unbounded random variables on a probability space ( Ω , T, P) were studied and a new method was proposed to treat the sum of independent unbounded random variables by truncating the original probability space (Ω, T, P ). The probability exponential inequalities for sums of independent unbounded random variables were given. As applications of the results, some interesting examples were given. The examples show that the method proposed in the paper and the results of the paper are quite useful in the study of the large sample properties of the sums of independent unbounded random variables.
Nahm sums, stability and the colored Jones polynomial
Garoufalidis, Stavros
2011-01-01
Nahm sums are $q$-series of a special hypergeometric type that appear in character formulas in Conformal Field Theory, and give rise to elements ot the Bloch group, and have interesting modularity properties. In our paper, we show how Nahm sums arise natural in Quantum Knot Theory, namely we prove the stability of the coefficients of an alternating link and present a Nahm sum formula for the resulting power series, defined in terms of a reduced, downward diagram of an alternating link. The Nahm sum formula comes with a computer implementation, illustrated in numerous examples of proven or conjectural identities among $q$-series.
On minimum sum representations for weighted voting games
Kurz, Sascha
2011-01-01
A proposal in a weighted voting game is accepted if the sum of the (non-negative) weights of the "yea" voters is at least as large as a given quota. Several authors have considered representations of weighted voting games with minimum sum, where the weights and the quota are restricted to be integers. Freixas and Molinero have classified all weighted voting games without a unique minimum sum representation for up to 8 voters. Here we exhaustively classify all weighted voting games consisting of 9 voters which do not admit a unique minimum sum integer weight representation.
On unit root formulas for toric exponential sums
Adolphson, Alan
2010-01-01
Starting from a classical generating series for Bessel functions due to Schlomilch, we use Dwork's relative dual theory to broadly generalize unit-root results of Dwork on Kloosterman sums and Sperber on hyperkloosterman sums. In particular, we express the (unique) p-adic unit root of an arbitrary exponential sum on the torus in terms of special values of the p-adic analytic continuation of a ratio of A-hypergeometric functions. In contrast with the earlier works, we use noncohomological methods and obtain results that are valid for arbitrary exponential sums without any hypothesis of nondegeneracy.
A note on the moments of Kloosterman sums
Xi, Ping
2011-01-01
In this note, we deduce an asymptotic formula for even power moments of Kloosterman sums based on the important work of N. M. Katz on Kloosterman sheaves. In a similar manner, we can also obtain an upper bound for odd power moments. Moreover, we shall give an asymptotic formula for odd power moments of absolute Kloosterman sums.
Partial sums of arithmetical functions with absolutely convergent Ramanujan expansions
BISWAJYOTI SAHA
2016-08-01
For an arithmetical function $f$ with absolutely convergent Ramanujan expansion, we derive an asymptotic formula for the $\\sum_{n\\leq N}$ f(n)$ with explicit error term. As a corollary we obtain new results about sum-of-divisors functions and Jordan’s totient functions.
Almost Sure Central Limit Theorems for Heavily Trimmed Sums
Fang WANG; Shi Hong CHENG
2004-01-01
We obtain an almost sure central limit theorem (ASCLT) for heavily trimmed sums. We also prove a function-typed ASCLT under the same conditions that assure measurable functions to satisfy the ASCLT for the partial sums of i.i.d. random variables with EX1 = 0, EX12 = 1.
On Sum--Connectivity Index of Bicyclic Graphs
Du, Zhibin
2009-01-01
We determine the minimum sum--connectivity index of bicyclic graphs with $n$ vertices and matching number $m$, where $2\\le m\\le \\lfloor\\frac{n}{2}\\rfloor$, the minimum and the second minimum, as well as the maximum and the second maximum sum--connectivity indices of bicyclic graphs with $n\\ge 5$ vertices. The extremal graphs are characterized.
Analytic and algorithmic aspects of generalized harmonic sums and polylogarithms
Ablinger, Jakob; Schneider, Carsten [Johannes Kepler Univ., Linz (Austria). Research Inst. for Symbolic Computation; Bluemlein, Johannes [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany)
2013-01-15
In recent three-loop calculations of massive Feynman integrals within Quantum Chromodynamics (QCD) and, e.g., in recent combinatorial problems the so-called generalized harmonic sums (in short S-sums) arise. They are characterized by rational (or real) numerator weights also different from {+-}1. In this article we explore the algorithmic and analytic properties of these sums systematically. We work out the Mellin and inverse Mellin transform which connects the sums under consideration with the associated Poincare iterated integrals, also called generalized harmonic polylogarithms. In this regard, we obtain explicit analytic continuations by means of asymptotic expansions of the S-sums which started to occur frequently in current QCD calculations. In addition, we derive algebraic and structural relations, like differentiation w.r.t. the external summation index and different multi-argument relations, for the compactification of S-sum expressions. Finally, we calculate algebraic relations for infinite S-sums, or equivalently for generalized harmonic polylogarithms evaluated at special values. The corresponding algorithms and relations are encoded in the computer algebra package HarmonicSums.
Chain hexagonal cacti with the extremal eccentric distance sum.
Qu, Hui; Yu, Guihai
2014-01-01
Eccentric distance sum (EDS), which can predict biological and physical properties, is a topological index based on the eccentricity of a graph. In this paper we characterize the chain hexagonal cactus with the minimal and the maximal eccentric distance sum among all chain hexagonal cacti of length n, respectively. Moreover, we present exact formulas for EDS of two types of hexagonal cacti.
Finding Sums for an Infinite Class of Alternating Series
Chen, Zhibo; Wei, Sheng; Xiao, Xuerong
2012-01-01
Calculus II students know that many alternating series are convergent by the Alternating Series Test. However, they know few alternating series (except geometric series and some trivial ones) for which they can find the sum. In this article, we present a method that enables the students to find sums for infinitely many alternating series in the…
College Sports: The Mystery of the Zero-Sum Game
Getz, Malcolm; Siegfried, John J.
2012-01-01
In recent years, when a university may earn well over $10 million per year from fees for sports-broadcast rights, half of the teams still lose. Collegiate athletic competition is a zero sum game: The number of winners equals the number of losers. So why do universities spend growing sums of scarce resources on an activity when the odds of winning…
A Note on the Sum of Correlated Gamma Random Variables
Paris, Jose F
2011-01-01
The sum of correlated gamma random variables appears in the analysis of many wireless communications systems, e.g. in systems under Nakagami-m fading. In this Letter we obtain exact expressions for the probability density function (PDF) and the cumulative distribution function (CDF) of the sum of arbitrarily correlated gamma variables in terms of certain Lauricella functions.
Integrals of $K$ and $E$ from Lattice Sums
J. G. WAN; Zucker, I. J.
2014-01-01
We give closed form evaluations for many families of integrals, whose integrands contain algebraic functions of the complete elliptic integrals $K$ and $E$. Our methods exploit the rich structures connecting complete elliptic integrals, Jacobi theta functions, lattice sums, and Eisenstein series. Various examples are given, and along the way new (including 10-dimensional) lattice sum evaluations are produced.
Generating matrix and sums of Fibonacci and Pell sequences
Ho, C. K.; Woon, H. S.; Chong, Chin-Yoon
2014-07-01
In this paper, we study the Fibonacci sequence and Pell sequence and developed generating matrices for them. First we proved two results on the even sum of the Fibonacci sequence and the Pell sequence, using the generating matrix approach. We then deduce the odd sums, some identities and recursive formulas for these two sequences.
GRASP with Path Relinking for the SumCut Problem
Jesús Sánchez-Oro
2012-01-01
Full Text Available This paper proposes a GRASP algorithm combined with Path Relinking to solve the SumCut minimization problem. In the SumCut problem one is given a graph with n nodes and must label the nodes in a way that each node receives a unique label from the set{1,2,…,n}, in order to minimize the sum cut of the generated solution. The SumCut problem is really important in archeology (in seriation tasks and in genetics, helping in the Human Genome Project. This problem is equivalent to the Profile problem, because a solution for SumCut is reversal solution for Profile problem. Experimental results show that the GRASP and Path Relinking methods presented outperform in terms of average percentage deviation the results from the State of the Art using shorter CPU time.
Harmonic sums, polylogarithms, special numbers, and their generalizations
Ablinger, Jakob [Johannes Kepler Univ., Linz (Austria). Research Inst. for Symbolic Computation; Bluemlein, Johannes [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany)
2013-04-15
In these introductory lectures we discuss classes of presently known nested sums, associated iterated integrals, and special constants which hierarchically appear in the evaluation of massless and massive Feynman diagrams at higher loops. These quantities are elements of stuffle and shuffle algebras implying algebraic relations being widely independent of the special quantities considered. They are supplemented by structural relations. The generalizations are given in terms of generalized harmonic sums, (generalized) cyclotomic sums, and sums containing in addition binomial and inverse-binomial weights. To all these quantities iterated integrals and special numbers are associated. We also discuss the analytic continuation of nested sums of different kind to complex values of the external summation bound N.
Harmonic Sums, Polylogarithms, Special Numbers, and their Generalizations
Ablinger, Jakob
2013-01-01
In these introductory lectures we discuss classes of presently known nested sums, associated iterated integrals, and special constants which hierarchically appear in the evaluation of massless and massive Feynman diagrams at higher loops. These quantities are elements of stuffle and shuffle algebras implying algebraic relations being widely independent of the special quantities considered. They are supplemented by structural relations. The generalizations are given in terms of generalized harmonic sums, (generalized) cyclotomic sums, and sums containing in addition binomial and inverse-binomial weights. To all these quantities iterated integrals and special numbers are associated. We also discuss the analytic continuation of nested sums of different kind to complex values of the external summation bound N.
Evaluation of the multi-sums for large scale problems
Bluemlein, J.; Hasselhuhn, A. [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany); Schneider, C. [Johannes Kepler Univ., Linz (Austria). Research Inst. for Symbolic Computation
2012-02-15
A big class of Feynman integrals, in particular, the coefficients of their Laurent series expansion w.r.t. the dimension parameter {epsilon} can be transformed to multi-sums over hypergeometric terms and harmonic sums. In this article, we present a general summation method based on difference fields that simplifies these multi--sums by transforming them from inside to outside to representations in terms of indefinite nested sums and products. In particular, we present techniques that assist in the task to simplify huge expressions of such multi-sums in a completely automatic fashion. The ideas are illustrated on new calculations coming from 3-loop topologies of gluonic massive operator matrix elements containing two fermion lines, which contribute to the transition matrix elements in the variable flavor scheme. (orig.)
Lim, Kim-Hui,; Har, Wai-Mun
2008-01-01
The lack of academic and thinking culture is getting more worried and becomes a major challenge to our academia society this 21st century. Few directions that move academia from "cogito ergo sum" to "consumo ergo sum" are actually leading us to "the end of academia". Those directions are: (1) the death of dialectic;…
Romer C. Castillo
2015-11-01
Full Text Available Factoriangular numbers resulted from adding corresponding factorials and triangular numbers. If Ftn is the nth factoriangular number, n! is the factorial of n and Tn is the nth triangular number, then Ftn = n! + Tn. In this study, interesting results on the representations of factoriangular number as sum of two triangular numbers and as sum of two squares are presented.
Harmonic sums and polylogarithms generated by cyclotomic polynomials
Ablinger, Jakob; Schneider, Carsten [Johannes Kepler Univ., Linz (Austria). Research Inst. for Symbolic Computation; Bluemlein, Johannes [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany)
2011-05-15
The computation of Feynman integrals in massive higher order perturbative calculations in renormalizable Quantum Field Theories requires extensions of multiply nested harmonic sums, which can be generated as real representations by Mellin transforms of Poincare-iterated integrals including denominators of higher cyclotomic polynomials. We derive the cyclotomic harmonic polylogarithms and harmonic sums and study their algebraic and structural relations. The analytic continuation of cyclotomic harmonic sums to complex values of N is performed using analytic representations. We also consider special values of the cyclotomic harmonic polylogarithms at argument x=1, resp., for the cyclotomic harmonic sums at N{yields}{infinity}, which are related to colored multiple zeta values, deriving various of their relations, based on the stuffle and shuffle algebras and three multiple argument relations. We also consider infinite generalized nested harmonic sums at roots of unity which are related to the infinite cyclotomic harmonic sums. Basis representations are derived for weight w=1,2 sums up to cyclotomy l=20. (orig.)
Minkowski sum of HV-polytopes in Rn
Delos, Vincent
2014-01-01
Minkowski sums cover a wide range of applications in many different fields like algebra, morphing, robotics, mechanical CAD/CAM systems ... This paper deals with sums of polytopes in a n dimensional space provided that both H-representation and V-representation are available i.e. the polytopes are described by both their half-spaces and vertices. The first method uses the polytope normal fans and relies on the ability to intersect dual polyhedral cones. Then we introduce another way of considering Minkowski sums of polytopes based on the primal polyhedral cones attached to each vertex.
Evolution of sum-chirp in polarization multiplexed communication system
Wang Jing; Wang Zhen-Li
2004-01-01
The evolution of sum-chirp for an initially chirped Gaussian pulse is studied in the polarization multiplexed communication system, with fibre attenuation considered. The sum-chirp is found to have the character of saturation.Its value appears different along the two different polarization axes, determined by the incidence polarization angle. We also find that sum-chirp is dominated by the initial chirp at a short distance, and by the cross-phase modulation effect at long distance. And it is influenced apparently by a wavevector mismatch parameter below 10 ps/km. Further, its saturation results from the effective distance determined by fibre attenuation.
Sums of magnetic eigenvalues are maximal on rotationally symmetric domains
Laugesen, Richard S; Roy, Arindam
2011-01-01
The sum of the first n energy levels of the planar Laplacian with constant magnetic field of given total flux is shown to be maximal among triangles for the equilateral triangle, under normalization of the ratio (moment of inertia)/(area)^3 on the domain. The result holds for both Dirichlet and Neumann boundary conditions, with an analogue for Robin (or de Gennes) boundary conditions too. The square similarly maximizes the eigenvalue sum among parallelograms, and the disk maximizes among ellipses. More generally, a domain with rotational symmetry will maximize the magnetic eigenvalue sum among all linear images of that domain. These results are new even for the ground state energy (n=1).
The Nonlinearity of Sum and Product for Boolean Functions
Huang Jinglian
2016-01-01
Full Text Available In this paper, we study the relationship between the nonlinearity of Boolean function and the nonlinearity of the sum and product of Boolean function, while derivative and e-derivative are used to study the problem further. We obtain that the sum of two functions’ nonlinearity is not less than the nonlinearity of the sum of two functions. The relationship between the nonlinearity of function and the nonlinearity of the sum and product of two functions are also obtained. Furthermore, we also get the relationship between the nonlinearity of the product of functions, and the derivative and e-derivative of function. Moreover, we also deduced some important applications on the basis of the above work.
The Sum and Difference of Two Lognormal Random Variables
C. F. Lo
2012-01-01
Full Text Available We have presented a new unified approach to model the dynamics of both the sum and difference of two correlated lognormal stochastic variables. By the Lie-Trotter operator splitting method, both the sum and difference are shown to follow a shifted lognormal stochastic process, and approximate probability distributions are determined in closed form. Illustrative numerical examples are presented to demonstrate the validity and accuracy of these approximate distributions. In terms of the approximate probability distributions, we have also obtained an analytical series expansion of the exact solutions, which can allow us to improve the approximation in a systematic manner. Moreover, we believe that this new approach can be extended to study both (1 the algebraic sum of N lognormals, and (2 the sum and difference of other correlated stochastic processes, for example, two correlated CEV processes, two correlated CIR processes, and two correlated lognormal processes with mean-reversion.
Limiting Behavior of Weighted Sums of NOD Random Variables
De Hua QIU; Ping Yan CHEN
2011-01-01
The strong laws of large numbers and laws of the single logarithm for weighted sums of NOD random variables are established.The results presented generalize the corresponding results of Chen and Gan [5]in independent sequence case.
Sublinear Time Approximate Sum via Uniform Random Sampling
Fu, Bin; Peng, Zhiyong
2012-01-01
We investigate the approximation for computing the sum $a_1+...+a_n$ with an input of a list of nonnegative elements $a_1,..., a_n$. If all elements are in the range $[0,1]$, there is a randomized algorithm that can compute an $(1+\\epsilon)$-approximation for the sum problem in time ${O({n(\\log\\log n)\\over\\sum_{i=1}^n a_i})}$, where $\\epsilon$ is a constant in $(0,1)$. Our randomized algorithm is based on the uniform random sampling, which selects one element with equal probability from the input list each time. We also prove a lower bound $\\Omega({n\\over \\sum_{i=1}^n a_i})$, which almost matches the upper bound, for this problem.
Induction and Analogy in a Problem of Finite Sums
Zielinski, Ryan
2016-01-01
What is a general expression for the sum of the first n integers, each raised to the mth power, where m is a positive integer? Answering this question will be the aim of the paper....We will take the unorthodox approach of presenting the material from the point of view of someone who is trying to solve the problem himself. Keywords: analogy, Johann Faulhaber, finite sums, heuristics, inductive reasoning, number theory, George Polya, problem solving, teaching of mathematics
Unidirectional ring-laser operation using sum-frequency mixing
Tidemand-Lichtenberg, Peter; Cheng, Haynes Pak Hay; Pedersen, Christian
2010-01-01
A technique enforcing unidirectional operation of ring lasers is proposed and demonstrated. The approach relies on sum-frequency mixing between a single-pass laser and one of the two counterpropagating intracavity fields of the ring laser. Sum-frequency mixing introduces a parametric loss for the...... where lossless second-order nonlinear materials are available. Numerical modeling and experimental demonstration of parametric-induced unidirectional operation of a diode-pumped solid-state 1342 nm cw ring laser are presented....
The quantum Ising model: finite sums and hyperbolic functions
Damski, Bogdan
2015-10-01
We derive exact closed-form expressions for several sums leading to hyperbolic functions and discuss their applicability for studies of finite-size Ising spin chains. We show how they immediately lead to closed-form expressions for both fidelity susceptibility characterizing the quantum critical point and the coefficients of the counterdiabatic Hamiltonian enabling arbitrarily quick adiabatic driving of the system. Our results generalize and extend the sums presented in the popular Gradshteyn and Ryzhik Table of Integrals, Series, and Products.
The quantum Ising model: finite sums and hyperbolic functions
Bogdan Damski
2015-01-01
We derive exact closed-form expressions for several sums leading to hyperbolic functions and discuss their applicability for studies of finite-size Ising spin chains. We show how they immediately lead to closed-form expressions for both fidelity susceptibility characterizing the quantum critical point and the coefficients of the counterdiabatic Hamiltonian enabling arbitrarily quick adiabatic driving of the system. Our results generalize and extend the sums presented in the popular Gradshteyn...
A Hybrid Continuous Max-Sum Algorithm for Decentralised Coordination
Voice, Thomas; Stranders, Ruben; Rogers, Alex; Jennings, Nick
2010-01-01
Recent advances in decentralised coordination of multiple agents have led to the proposal of the max-sum algorithm for solving distributed constraint optimisation problems (DCOPs). The max-sum algorithm is fully decentralised, converges to optimality for problems with acyclic constraint graphs and otherwise performs well in empirical studies. However, it requires agents to have discrete state spaces, which are of practical size to conduct repeated searches over. In contrast, there are decentr...
Complete Convergence for Weighted Sums of WOD Random Variables
ZHANG Ying; ZHANG Yu; SHEN Ai-ting
2016-01-01
In this article, we study the complete convergence for weighted sums of widely orthant dependent random variables. By using the exponential probability inequality, we establish a complete convergence result for weighted sums of widely orthant dependent ran-dom variables under mild conditions of weights and moments. The result obtained in the paper generalizes the corresponding ones for independent random variables and negatively dependent random variables.
Upper bounds on a two-term exponential sum
Todd; Cochrane
2001-01-01
［1］Davenport, H. , Heibronn, H., On an exponential sum, Proc. Lond. Math. Soc., 1936, 41(2): 449-453.［2］Hua, L. K., On exponential sums, Sci. Record (Peking) (N.S.), 1957, 1: 1-4.［3］Vaughan, R. C. , The Hardy-Littlewood Method, 2nd ed. , Cambridge Tracts in Math. , Cambridge: Cambridge Univ. Press, 1997, 125.［4］Weil, A., On some exponential sums, Proc. Nat. Acad. Sci. USA, 1948, 34: 204-207.［5］Cochrane, T., Zheng, Z., Pure and mixed exponential sums, Acta Arith. , 1999, 91(3): 249-278.［6］Chalk, J. H. H., On Hua's estimate for exponential sums, Mathematika, 1987, 34: 115-123.［7］Loh, W. K. A. , Hua's Lemma, Bull. Australian Math. Soc., 1994, 50(3): 451-458.［8］Ding, P., An improvement to Chalk's estimation of exponential sums, Acta Arith. , 1991, 59(2): 149-155.
Filiz KANBAY
2005-01-01
We consider the Bonnet ruled surfaces which admit only one non-trivial isometry that preserves the principal curvatures. We determine the Bonnet ruled surfaces whose generators and orthogonal trajectories form a special net called an A-net.
Cosmological diagrammatic rules
Giddings, Steven B
2010-01-01
A simple set of diagrammatic rules is formulated for perturbative evaluation of ``in-in" correlators, as is needed in cosmology and other nonequilibrium problems. These rules are both intuitive, and efficient for calculational purposes.
Cosmological diagrammatic rules
Giddings, Steven B. [Department of Physics, University of California, Santa Barbara, CA 93106 (United States); Sloth, Martin S., E-mail: giddings@physics.ucsb.edu, E-mail: sloth@cern.ch [CERN, Physics Department, Theory Unit, CH-1211 Geneva 23 (Switzerland)
2010-07-01
A simple set of diagrammatic rules is formulated for perturbative evaluation of ''in-in'' correlators, as is needed in cosmology and other nonequilibrium problems. These rules are both intuitive, and efficient for calculational purposes.
Phonological reduplication in sign language: rules rule
Iris eBerent
2014-06-01
Full Text Available Productivity—the hallmark of linguistic competence—is typically attributed to algebraic rules that support broad generalizations. Past research on spoken language has documented such generalizations in both adults and infants. But whether algebraic rules form part of the linguistic competence of signers remains unknown. To address this question, here we gauge the generalization afforded by American Sign Language (ASL. As a case study, we examine reduplication (X→XX—a rule that, inter alia, generates ASL nouns from verbs. If signers encode this rule, then they should freely extend it to novel syllables, including ones with features that are unattested in ASL. And since reduplicated disyllables are preferred in ASL, such rule should favor novel reduplicated signs. Novel reduplicated signs should thus be preferred to nonreduplicative controls (in rating, and consequently, such stimuli should also be harder to classify as nonsigns (in the lexical decision task. The results of four experiments support this prediction. These findings suggest that the phonological knowledge of signers includes powerful algebraic rules. The convergence between these conclusions and previous evidence for phonological rules in spoken language suggests that the architecture of the phonological mind is partly amodal.
Rokosz, Francis M.
1981-01-01
Standard sports rules can be altered to improve the game for intramural participants. These changes may improve players' attitudes, simplify rules for officials, and add safety features to a game. Specific rule modifications are given for volleyball, football, softball, floor hockey, basketball, and soccer. (JN)
Keiding, Hans; Peleg, Bezalel
2006-01-01
is binary if it is rationalized by an acyclic binary relation. The foregoing result motivates our definition of a binary effectivity rule as the effectivity rule of some binary SCR. A binary SCR is regular if it satisfies unanimity, monotonicity, and independence of infeasible alternatives. A binary...... effectivity rule is regular if it is the effectivity rule of some regular binary SCR. We characterize completely the family of regular binary effectivity rules. Quite surprisingly, intrinsically defined von Neumann-Morgenstern solutions play an important role in this characterization...
Safety Commission
2008-01-01
The revision of CERN Safety rules is in progress and the following new Safety rules have been issued on 15-04-2008: Safety Procedure SP-R1 Establishing, Updating and Publishing CERN Safety rules: http://cern.ch/safety-rules/SP-R1.htm; Safety Regulation SR-S Smoking at CERN: http://cern.ch/safety-rules/SR-S.htm; Safety Regulation SR-M Mechanical Equipment: http://cern.ch/safety-rules/SR-M.htm; General Safety Instruction GSI-M1 Standard Lifting Equipment: http://cern.ch/safety-rules/GSI-M1.htm; General Safety Instruction GSI-M2 Standard Pressure Equipment: http://cern.ch/safety-rules/GSI-M2.htm; General Safety Instruction GSI-M3 Special Mechanical Equipment: http://cern.ch/safety-rules/GSI-M3.htm. These documents apply to all persons under the Director General’s authority. All Safety rules are available at the web page: http://www.cern.ch/safety-rules The Safety Commission
Dardzinska, Agnieszka
2013-01-01
We are surrounded by data, numerical, categorical and otherwise, which must to be analyzed and processed to convert it into information that instructs, answers or aids understanding and decision making. Data analysts in many disciplines such as business, education or medicine, are frequently asked to analyze new data sets which are often composed of numerous tables possessing different properties. They try to find completely new correlations between attributes and show new possibilities for users. Action rules mining discusses some of data mining and knowledge discovery principles and then describe representative concepts, methods and algorithms connected with action. The author introduces the formal definition of action rule, notion of a simple association action rule and a representative action rule, the cost of association action rule, and gives a strategy how to construct simple association action rules of a lowest cost. A new approach for generating action rules from datasets with numerical attributes...
Transition Strength Sums and Quantum Chaos in Shell Model States
Kota, V K B; Kar, K; Gómez, J M G; Retamosa, J
2000-01-01
For the embedded Gaussian orthogonal ensemble (EGOE) of random matrices, the strength sums generated by a transition operator acting on an eigenstate vary with the excitation energy as the ratio of two Gaussians. This general result is compared to exact shell model calculations, with realistic interactions, of spherical orbit occupancies and Gamow-Teller strength sums in some $(ds)$ and $(fp)$ shell examples. In order to confirm that EGOE operates in the chaotic domain of the shell model spectrum, calculations are carried out using two different interpolating hamiltonians generating order-chaos transitions. Good agreement is obtained in the chaotic domain of the spectrum, and strong deviations are observed as nuclear motion approaches a regular regime (transition strength sums appear to follow the Dyson's $\\Delta_3$ statistic). More importantly, they shed new light on the newly emerging understanding that in the chaotic domain of isolated finite interacting many particle systems smoothed densities (they inclu...
Skew Schur Functions of Sums of Fat Staircases
Morin, Matthew
2010-01-01
We define a fat staircase to be a Ferrers diagram corresponding to a partition of the form $(n^{\\alpha_n}, {n-1}^{\\alpha_{n-1}},..., 1^{\\alpha_1})$, where $\\alpha = (\\alpha_1,...,\\alpha_n)$ is a composition, or the $180^\\circ$ rotation of such a diagram. If a diagram's skew Schur function is a linear combination of Schur functions of fat staircases, we call the diagram a sum of fat staircases. We prove a Schur-positivity result that is obtained each time we augment a sum of fat staircases with a skew diagram. We also determine conditions on which diagrams can be sums of fat staircases, including necessary and sufficient conditions in the special case when the diagram is a fat staircase skew a single row or column.
A supercharacter table decomposition via power-sum symmetric functions
Bergeron, Nantel
2011-01-01
We give an $AB$-factorization of the supercharacter table of the group of $n\\times n$ unipotent upper triangular matrices over $\\FF_q$, where $A$ is a lower-triangular matrix with entries in $\\ZZ[q]$ and $B$ is a unipotent upper-triangular matrix with entries in $\\ZZ[q^{-1}]$. To this end we introduce a $q$ deformation of a new power-sum basis of the Hopf algebra of symmetric functions in noncommutative variables. The factorization is obtain from the transition matrices between the supercharacter basis, the $q$-power-sum basis and the superclass basis. This is similar to the decomposition of the character table of the symmetric group $S_n$ given by the transition matrices between Schur functions, monomials and power-sums. We deduce some combinatorial results associated to this decomposition. In particular we compute the determinant of the supercharacter table.
Sums of hermitian squares and the BMV conjecture
Klep, Igor
2007-01-01
Recently Lieb and Seiringer showed that the Bessis-Moussa-Villani conjecture from quantum physics can be restated in the following purely algebraic way: The sum of all words in two positive semidefinite matrices where the number of each of the two letters is fixed is always a matrix with nonnegative trace. We show that this statement holds if the words are of length at most 13. This has previously been known only up to length 7. In our proof, we establish a connection to sums of hermitian squares of polynomials in noncommuting variables and to semidefinite programming. As a by-product we obtain an example of a real polynomial in two noncommuting variables having nonnegative trace on all symmetric matrices of the same size, yet not being a sum of hermitian squares and commutators.
Fermionic Sum Representations for Conformal Field Theory Characters
Kedem, R; McCoy, B M; Melzer, E
1993-01-01
We present sum representations for all characters of the unitary Virasoro minimal models. They can be viewed as fermionic companions of the Rocha-Caridi sum representations, the latter related to the (bosonic) Feigin-Fuchs-Felder construction. We also give fermionic representations for certain characters of the general $(G^{(1)})_k \\times (G^{(1)})_l \\over (G^{(1)})_{k+l}}$ coset conformal field theories, the non-unitary minimal models ${\\cal M}(p,p+2)$ and ${\\cal M}(p,kp+1)$, the $N$=2 superconformal series, and the $\\ZZ_N$-parafermion theories, and relate the $q\\to 1$ behaviour of all these fermionic sum representations to the thermodynamic Bethe Ansatz.
Limit theorems for multi-indexed sums of random variables
Klesov, Oleg
2014-01-01
Presenting the first unified treatment of limit theorems for multiple sums of independent random variables, this volume fills an important gap in the field. Several new results are introduced, even in the classical setting, as well as some new approaches that are simpler than those already established in the literature. In particular, new proofs of the strong law of large numbers and the Hajek-Renyi inequality are detailed. Applications of the described theory include Gibbs fields, spin glasses, polymer models, image analysis and random shapes. Limit theorems form the backbone of probability theory and statistical theory alike. The theory of multiple sums of random variables is a direct generalization of the classical study of limit theorems, whose importance and wide application in science is unquestionable. However, to date, the subject of multiple sums has only been treated in journals. The results described in this book will be of interest to advanced undergraduates, graduate students and researchers who ...
Ramanujan sums via generalized Möbius functions and applications
Vichian Laohakosol
2006-01-01
Full Text Available A generalized Ramanujan sum (GRS is defined by replacing the usual Möbius function in the classical Ramanujan sum with the Souriau-Hsu-Möbius function. After collecting basic properties of a GRS, mostly containing existing ones, seven aspects of a GRS are studied. The first shows that the unique representation of even functions with respect to GRSs is possible. The second is a derivation of the mean value of a GRS. The third establishes analogues of the remarkable Ramanujan's formulae connecting divisor functions with Ramanujan sums. The fourth gives a formula for the inverse of a GRS. The fifth is an analysis showing when a reciprocity law exists. The sixth treats the problem of dependence. Finally, some characterizations of completely multiplicative function using GRSs are obtained and a connection of a GRS with the number of solutions of certain congruences is indicated.
A new dipole-free sum-over-states expression for the second hyperpolarizability
Pérez-Moreno, Javier; Clays, Koen; Kuzyk, Mark G.
2008-02-01
The generalized Thomas-Kuhn sum rules are used to eliminate the explicit dependence on dipolar terms in the traditional sum-over-states (SOS) expression for the second hyperpolarizability to derive a new, yet equivalent, SOS expression. This new dipole-free expression may be better suited to study the second hyperpolarizability of nondipolar systems such as quadrupolar, octupolar, and dodecapolar structures. The two expressions lead to the same fundamental limits of the off-resonance second hyperpolarizability; and when applied to a particle in a box and a clipped harmonic oscillator, have the same frequency dependence. We propose that the new dipole-free equation, when used in conjunction with the standard SOS expression, can be used to develop a three-state model of the dispersion of the third-order susceptibility that can be applied to molecules in cases where normally many more states would have been required. Furthermore, a comparison between the two expressions can be used as a convergence test of molecular orbital calculations when applied to the second hyperpolarizability.
Sum of Roots Characterization for H2 Control Performance Limitations
Hara, Shinji; Kanno, Masaaki
This paper provides new expressions of H2 control performance limits achievable by feedback for SISO continuous-time systems. The result for the regulation problem is expressed in a simple manner in terms of two sums of roots obtained from the plant and the associated polynomial spectral factorization. We show that it can connect the two existing solutions, namely the Riccati solution and the analytical expression with an integral form. The similar result for the tracking problem is also derived using the reciprocal transform. Finally parametric optimization making use of the derived expression by means of symbolic computation is demonstrated to confirm the validity of the sum of roots characterization.