Instantaneous Bethe-Salpeter equation
We present a systematic algebraic and numerical investigation of the instantaneous Beth-Salpeter equation. Emphasis is placed on confining interaction kernels of the Lorentz scalar, time component vector, and full vector-types. We explore the stability of the solutions and Regge behavior for each of these interactions, and conclude that only time component vector confinement leads to normal Regge structure and stable solutions for all quark masses
Two-body bound states & the Bethe-Salpeter equation
Pichowsky, M. [Argonne National Lab., IL (United States); Kennedy, M. [Univ. of New Hampshire, Durham, NH (United States). Physics Dept.; Strickland, M. [Duke Univ., Durham, NC (United States)
1995-01-18
The Bethe-Salpeter formalism is used to study two-body bound states within a scalar theory: two scalar fields interacting via the exchange of a third massless scalar field. The Schwinger-Dyson equation is derived using functional and diagrammatic techniques, and the Bethe-Salpeter equation is obtained in an analogous way, showing it to be a two-particle generalization of the Schwinger-Dyson equation. The authors also present a numerical method for solving the Bethe-Salpeter equation without three-dimensional reduction. The ground and first excited state masses and wavefunctions are computed within the ladder approximation and space-like form factors are calculated.
RPA equations and the instantaneous Bethe-Salpeter equation
Resag, J
1993-01-01
We give a derivation of the particle-hole RPA equations for an interacting multi-fermion system by applying the instantaneous approximation to the amputated two-fermion propagator of the system. In relativistic field theory the same approximation leads from the fermion-antifermion Bethe-Salpeter equation to the Salpeter equation. We show that RPA equations and Salpeter equation are indeed equivalent.
Glueball properties from the Bethe-Salpeter equation
For over thirty years bound states of gluons are an outstanding problem of both theoretical and experimental physics. Being predicted by Quantum-Chromodynamics their experimental confirmation is one of the foremost goals of large experimental facilities currently under construction like FAIR in Darmstadt. This thesis presents a novel approach to the theoretical determination of physical properties of bound states of two gluons, called glueballs. It uses the consistent combination of Schwinger-Dyson equations for gluons and ghosts and appropriate Bethe-Salpeter equations describing their corresponding bound-states. A rigorous derivation of both sets of equations, starting from an 2PI effective action is given as well as a general determination of appropriate decompositions of Bethe-Salpeter amplitudes to a given set of quantum numbers of a glueball. As an application example bound state masses of glueballs in a simple truncation scheme are calculated. (orig.)
Excited charmonium states from Bethe-Salpeter Equation
Šauli, Vladimír; Bicudo, P.
2012-01-01
Roč. 7, 043 (2012), s. 1-10. ISSN 1824-8039. [International Workshop on QCD Green’s Functions. Tranto, 05.09.2011-09.09.2011] R&D Projects: GA MŠk(CZ) LG11005 Institutional research plan: CEZ:AV0Z10480505 Keywords : charmonium * Bethe-Salpeter Equation Subject RIV: BE - Theoretical Physics http://pos.sissa.it/archive/conferences/136/043/QCD- TNT -II_043.pdf
Bethe-Salpeter equation for elastic nucleon-nucleon scattering
The Bethe-Salpeter equation for NN scattering with one-boson exchange is investigated for the case in which the pion-nucleon coupling is described by axial-vector theory. In contrast to the results with pseudoscalar coupling, good agreement with the experimental data can be obtained for all partial waves. Also, the deviations from the Blankenbecler-Sugar equation are not as large as they are for pseudoscalar coupling. In addition, cancellations between the direct and the crossed box graph with pseudoscalar πN coupling are investigated for the 3S1 phase shift in the framework of the variational operator Pade approximation
Light Pseudoscalar Mesons in Bethe-Salpeter Equation with Instantaneous Interaction
Lucha, Wolfgang
2015-01-01
The light pseudoscalar mesons play a twofold role: they may or have to be regarded both as low-lying bound states of the fundamental degrees of freedom of quantum chromodynamics as well as the (pseudo-) Goldstone bosons of the spontaneously broken chiral symmetries of quantum chromodynamics. We interrelate these aspects in a single quantum-field-theoretic approach relying on the Bethe-Salpeter formalism in instantaneous approximation by very simple means: the shape of the pseudoscalar-meson Bethe-Salpeter wave function dictated by chiral symmetry is used in Bethe-Salpeter equations for bound states of vanishing mass, in order to deduce analytically the interactions which govern the bound states under study. In this way, we obtain exact Bethe-Salpeter solutions for pseudoscalar mesons, in the sense of establishing the rigorous relationship between, on the one hand, the relevant interactions and, on the other hand, the Bethe-Salpeter amplitudes that characterize the bound states.
Bethe-salpeter equation from many-body perturbation theory
Sander, Tobias; Starke, Ronald; Kresse, Georg [Computational Materials Physics, University of Vienna, Sensengasse 8/12, 1090 Vienna (Austria)
2013-07-01
The Green function formalism is a powerful tool to calculate not only electronic structure within the quasi-particle (QP) picture, but it also gives access to optical absorption spectra. Starting from QP energies within the GW method, the polarizability, as central quantity, is calculated from the solution of a Bethe-Salpeter-like equation (BSE). It is usually solved within the Tamm-Dancoff Approximation (TDA) which neglects the coupling of resonant (positive frequency branch) and anti-resonant (negative frequency branch) excitations. In this work we solve the full BSE (beyond TDA) based on self-consistently calculated QP orbitals and energies for typical systems. The dielectric function is averaged over many low dimensional shifted k-meshes to obtain k-point converged results. We compare the results to recently introduced approximation to the BSE kernel. Additionally, the time-evolution ansatz is employed to calculate the polarizability, which avoids the direct solution of the BSE.
Bethe-salpeter equation from many-body perturbation theory
The Green function formalism is a powerful tool to calculate not only electronic structure within the quasi-particle (QP) picture, but it also gives access to optical absorption spectra. Starting from QP energies within the GW method, the polarizability, as central quantity, is calculated from the solution of a Bethe-Salpeter-like equation (BSE). It is usually solved within the Tamm-Dancoff Approximation (TDA) which neglects the coupling of resonant (positive frequency branch) and anti-resonant (negative frequency branch) excitations. In this work we solve the full BSE (beyond TDA) based on self-consistently calculated QP orbitals and energies for typical systems. The dielectric function is averaged over many low dimensional shifted k-meshes to obtain k-point converged results. We compare the results to recently introduced approximation to the BSE kernel. Additionally, the time-evolution ansatz is employed to calculate the polarizability, which avoids the direct solution of the BSE.
Excited charmonium states from Bethe-Salpeter equation
Sauli, Vladimir
2011-01-01
We solve the Bethe-Salpeter equation for a system of a heavy quark-antiquark pair interacting with a screened linear confining potential. First we show the spinless QFT model is inadequate and fail to describe even gross feature of the quarkonia spectrum. In order to get reliable description the spine degrees of freedom has to be considered. Within the approximation employed we reasonably reproduce known radial excitation of vector charmonium. The BSE favors relatively large string breaking scale $\\mu\\simeq 350MeV$ . Using free charm quark propagators we observe that $J/\\Psi$ is the only charmonium left bellow naive quark-antiquark threshold $2m_c$, while the all excited states are situated above this threshold. Within the numerical method we overcome obstacles related with threshold singularity and discuss the consequences of the use of free propagators for calculation of excited states above the threshold.
Two-body bound states ampersand the Bethe-Salpeter equation
The Bethe-Salpeter formalism is used to study two-body bound states within a scalar theory: two scalar fields interacting via the exchange of a third massless scalar field. The Schwinger-Dyson equation is derived using functional and diagrammatic techniques, and the Bethe-Salpeter equation is obtained in an analogous way, showing it to be a two-particle generalization of the Schwinger-Dyson equation. The authors also present a numerical method for solving the Bethe-Salpeter equation without three-dimensional reduction. The ground and first excited state masses and wavefunctions are computed within the ladder approximation and space-like form factors are calculated
Scattering solutions of Bethe-Salpeter equation in Minkowski and Euclidean spaces
Carbonell, J
2016-01-01
We shortly review different methods to obtain the scattering solutions of the Bethe-Salpeter equation in Minkowski space. We emphasize the possibility to obtain the zero energy observables in terms of the Euclidean scattering amplitude.
A systematic approach to sketch Bethe-Salpeter equation
Qin, Si-xue
2016-01-01
To study meson properties, one needs to solve the gap equation for the quark propagator and the Bethe-Salpeter (BS) equation for the meson wavefunction, self-consistently. The gluon propagator, the quark-gluon vertex, and the quark--anti-quark scattering kernel are key pieces to solve those equations. Predicted by lattice-QCD and Dyson-Schwinger analyses of QCD's gauge sector, gluons are non-perturbatively massive. In the matter sector, the modeled gluon propagator which can produce a veracious description of meson properties needs to possess a mass scale, accordingly. Solving the well-known longitudinal Ward-Green-Takahashi identities (WGTIs) and the less-known transverse counterparts together, one obtains a nontrivial solution which can shed light on the structure of the quark-gluon vertex. It is highlighted that the phenomenologically proposed anomalous chromomagnetic moment (ACM) vertex originates from the QCD Lagrangian symmetries and its strength is proportional to the magnitude of dynamical chiral symm...
Efficient implementation of core-excitation Bethe Salpeter equation calculations
Gilmore, K; Shirley, E L; Prendergast, D; Pemmaraju, C D; Kas, J J; Vila, F D; Rehr, J J
2016-01-01
We present an efficient implementation of the Bethe-Salpeter equation (BSE) method for obtaining core-level spectra including x-ray absorption (XAS), x-ray emission (XES), and both resonant and non-resonant inelastic x-ray scattering spectra (N/RIXS). Calculations are based on density functional theory (DFT) electronic structures generated either by abinit or Quantumespresso, both plane-wave basis, pseudopotential codes. This electronic structure is improved through the inclusion of a GW self energy. The projector augmented wave technique is used to evaluate transition matrix elements between core-level and band states. Final two-particle scattering states are obtained with the NIST core-level BSE solver (NBSE). We have previously reported this implementation, which we refer to as ocean (Obtaining Core Excitations from Ab initio electronic structure and NBSE) [Phys. Rev. B 83, 115106 (2011)]. Here, we present additional efficiencies that enable us to evaluate spectra for systems ten times larger than previous...
Normalization and perturbation theory for tightly bound states of the spinor Bethe-Salpeter equation
L.G. Suttorp
1976-01-01
The normalisation integrals for the tightly-bound-state solutions of the spinor Bethe-Salpeter equation that have been derived recently are evaluated. Ghost states are found to appear when the continuous parameters characterising the type of fermion-boson interaction reach a critical value. Perturba
Exact solutions of the spinor Bethe-Salpeter equation for tightly bound states
L.G. Suttorp
1975-01-01
Exact solutions are obtained for the spinor Bethe-Salpeter equation that describes tightly bound states of spin-/sup 1///sub 2/ fermions with massless-boson exchange. The corresponding coupling constants form a discrete spectrum that depends continuously on the parameters characterizing the type of
Calculation of Spin Observables for Proton-Neutron Elastic Scattering in the Bethe-Salpeter Equation
Kinpara, Susumu
2016-01-01
Bethe-Salpeter equation is applied to $p$-$n$ elastic scattering. The spin observables are calculated by the M matrix similar to $p$-$p$ case. The parameters of the meson-exchange model are used with the cut-off for the pion exchange interaction. Change of the M matrix indicates breaking of the charge independence in the nucleon-nucleon system.
Stochastic integration of the Bethe-Salpeter equation for two bound fermions
A non-perturbative method using a Monte Carlo algorithm is used to integrate the Bethe-Salpeter equation in momentum space. Solutions for two scalars and two fermions with an arbitrary coupling constant are calculated for bound states in the ladder approximation. The results are compared with other numerical methods. (Author) (13 refs., 2 figs.)
Solving the inhomogeneous Bethe-Salpeter Equation in Minkowski space: the zero-energy limit
Frederico, T; Viviani, M
2015-01-01
For the first time, the inhomogeneous Bethe-Salpeter Equation for an interacting system, composed by two massive scalars exchanging a massive scalar, is numerically investigated in ladder approximation, directly in Minkowski space, by using an approach based on the Nakanishi integral representation. In this paper, the limiting case of zero-energy states is considered, extending the approach successfully applied to bound states presented in Phys. Rev. D 89, (2014) 016010, where the Nakanishi integral representation has been exploited for solving the homogeneous Bethe-Salpeter Equation. The numerical values of scattering lengths, evaluated by using two different integral equations that stem within the Nakanishi framework, are compared with the analogous quantities recently obtained, within a totally different framework. Moreover, relevant functions, like the Nakanishi weight functions and the distorted part of the zero-energy Light-front wave functions are also presented. Interestingly, a highly non trivial iss...
The connection of two-particle relativistic quantum mechanics with the Bethe-Salpeter equation
We show the formal equivalence between the wave equations of two-particle relativistic quantum mechanics, based on the manifestly covariant hamiltonian formalism with constraints, and the Bethe-Salpeter equation. This is achieved by algebraically transforming the latter so as to separate it into two independent equations which match the equations of hamiltonian relativistic quantum mechanics. The first equation determines the relative time evolution of the system, while the second one yields a three-dimensional eigenvalue equation. A connection is thus established between the Bethe-Salpeter wave function and its kernel on the one hand and the quantum mechanical wave function and interaction potential on the other. For the sector of solutions of the Bethe-Salpeter equation having non-relativistic limits, this relationship can be evaluated in perturbation theory. We also device a generalized form of the instantaneous approximation which simplifies the various expressions involved in the above relations. It also permits the evaluation of the normalization condition of the quantum mechanical wave function as a three-dimensional integral
Light composite Higgs boson from the normalized Bethe-Salpeter equation
Doff, A.(Universidade Tecnológica Federal do Paraná – UTFPR – DAFIS, Av. Monteiro Lobato Km 04, 84016-210 Ponta Grossa, PR, Brazil); Natale, A. A.; da Silva, P. S. Rodrigues
2009-01-01
Scalar composite boson masses have been computed in QCD and Technicolor theories with the help of the homogeneous Bethe-Salpeter equation (BSE), resulting in a scalar mass that is twice the dynamically generated fermion or technifermion mass ($m_{dyn}$). We show that in the case of walking (or quasi-conformal) technicolor theories, where the $m_{dyn}$ behavior with the momenta may be quite different from the one predicted by the standard operator product expansion, this result is incomplete a...
Gluon bound state and asymptotic freedom derived from the Bethe--Salpeter equation
Fukamachi, Hitoshi; Nishino, Shogo; Shinohara, Toru
2016-01-01
In this paper we study the two-body bound states for gluons and ghosts in a massive Yang-Mills theory which is obtained by generalizing the ordinary massless Yang-Mills theory in a manifestly Lorentz covariant gauge. First, we give a systematic derivation of the coupled Bethe-Salpeter equations for gluons and ghosts by using the Cornwall-Jackiw-Tomboulis effective action of the composite operators within the framework of the path integral quantization. Then, we obtain the numerical solutions for the Bethe-Salpeter amplitude representing the simultaneous bound states of gluons and ghosts by solving the homogeneous Bethe-Salpeter equation in the ladder approximation. We study how the inclusion of ghosts affects the two-gluon bound states in the cases of the standing and running gauge coupling constant. Moreover, we show explicitly that the approximate solutions obtained for the gluon-gluon amplitude are consistent with the ultraviolet asymptotic freedom signaled by the negative $\\beta$ function.
Symmetry preserving truncations of the gap and Bethe-Salpeter equations
Binosi, Daniele; Chang, Lei; Papavassiliou, Joannis; Qin, Si-Xue; Roberts, Craig D.
2016-05-01
Ward-Green-Takahashi (WGT) identities play a crucial role in hadron physics, e.g. imposing stringent relationships between the kernels of the one- and two-body problems, which must be preserved in any veracious treatment of mesons as bound states. In this connection, one may view the dressed gluon-quark vertex, Γμa , as fundamental. We use a novel representation of Γμa , in terms of the gluon-quark scattering matrix, to develop a method capable of elucidating the unique quark-antiquark Bethe-Salpeter kernel, K , that is symmetry consistent with a given quark gap equation. A strength of the scheme is its ability to expose and capitalize on graphic symmetries within the kernels. This is displayed in an analysis that reveals the origin of H -diagrams in K , which are two-particle-irreducible contributions, generated as two-loop diagrams involving the three-gluon vertex, that cannot be absorbed as a dressing of Γμa in a Bethe-Salpeter kernel nor expressed as a member of the class of crossed-box diagrams. Thus, there are no general circumstances under which the WGT identities essential for a valid description of mesons can be preserved by a Bethe-Salpeter kernel obtained simply by dressing both gluon-quark vertices in a ladderlike truncation; and, moreover, adding any number of similarly dressed crossed-box diagrams cannot improve the situation.
Symmetry preserving truncations of the gap and Bethe-Salpeter equations
Binosi, Daniele; Chang, Lei; Papavassiliou, Joannis; Qin, Si-Xue; Roberts, Craig D.
2016-05-01
Ward-Green-Takahashi (WGT) identities play a crucial role in hadron physics, e.g. imposing stringent relationships between the kernels of the one-and two-body problems, which must be preserved in any veracious treatment of mesons as bound states. In this connection, one may view the dressed gluon-quark vertex, Gamma(alpha)(mu), as fundamental. We use a novel representation of Gamma(alpha)(mu), in terms of the gluon-quark scattering matrix, to develop a method capable of elucidating the unique quark-antiquark Bethe-Salpeter kernel, K, that is symmetry consistent with a given quark gap equation. A strength of the scheme is its ability to expose and capitalize on graphic symmetries within the kernels. This is displayed in an analysis that reveals the origin of H-diagrams in K, which are two-particle-irreducible contributions, generated as two-loop diagrams involving the three-gluon vertex, that cannot be absorbed as a dressing of Gamma(alpha)(mu) in a Bethe-Salpeter kernel nor expressed as a member of the class of crossed-box diagrams. Thus, there are no general circumstances under which the WGT identities essential for a valid description of mesons can be preserved by a Bethe-Salpeter kernel obtained simply by dressing both gluon-quark vertices in a ladderlike truncation; and, moreover, adding any number of similarly dressed crossed-box diagrams cannot improve the situation.
Advances in solving the two-fermion homogeneous Bethe-Salpeter equation in Minkowski space
de Paula, W; Salmè, G; Viviani, M
2016-01-01
Actual solutions of the Bethe-Salpeter equation for a two-fermion bound system are becoming available directly in Minkowski space, by virtue of a novel technique, based on the so-called Nakanishi integral representation of the Bethe-Salpeter amplitude and improved by expressing the relevant momenta through light-front components, i.e. $k^\\pm=k^0 \\pm k^3$. We solve a crucial problem that widens the applicability of the method to real situations by providing an analytically exact treatment of the singularities plaguing the two-fermion problem in Minkowski space, irrespective of the complexity of the irreducible Bethe-Salpeter kernel. This paves the way for feasible numerical investigations of relativistic composite systems, with any spin degrees of freedom. We present a thorough comparison with existing numerical results, evaluated in both Minkowski and Euclidean space, fully corroborating our analytical treatment, as well as fresh light-front amplitudes illustrating the potentiality of non perturbative calcula...
Solution to Bethe-Salpeter equation via Mellin-Barnes transform
Allendes, Pedro [Concepcion Univ. (Chile). Dept. de Fisica; Kniehl, Bernd [Hamburg Univ. (Germany). 2. Inst. fuer Theoretische Physik; Kondrashuk, Igor; Rojas Medar, Marko [Univ. del Bio-Bio, Chillan (Chile). Dept. de Ciencias Basicas; Notte Cuello, Eduardo A. [Univ. de La Serena (Chile). Facultad de Ciencias
2012-06-15
We consider Mellin-Barnes transform of triangle ladder-like scalar diagram in d=4 dimensions. It is shown how multi-fold MB transform of the momentum integral corresponding to any number of rungs is reduced to two-fold MB transform. For this purpose we use Belokurov-Usyukina reduction method for four-dimensional scalar integrals in the position space. The result is represented in terms of Euler {psi}-function and its derivatives. We derive new formulas for MB two-fold integration in the complex planes of two complex variables. We demonstrate that these formulas solve Bethe-Salpeter equation. We comment on further applications of solution to Bethe-Salpeter equation for vertices in N=4 supersymmetric Yang-Mills theory. We show that the recursive property of MB transforms observed in the present work for that kind of diagrams has nothing to do with quantum field theory, theory of integral transforms, or with theory of polylogarithms in general, but has an origin in a simple recursive property for smooth functions which can be shown by using basic methods of mathematical analysis.
Ground State Mass Spectrum for Scalar Diquarks with Bethe-Salpeter Equation
WANG Zhi-Gang; WAN Shao-Long; YANG Wei-Min
2007-01-01
In this article,we study the structures of the pseudoscalar mesons π,K and the scalar diquarks Ua,Da,Sa in the framework of the coupled rainbow Schwinger-Dyson equation and ladder Bethe-Salpeter equation with the confining effective potential.The u,d,s quarks have small current masses,and the renormalization is very large,the mass poles in the timelike region are absent which implements confinement naturally.The Bethe-Salpeter wavefunctions of the pseudoscalar mesons π,K,and the scalar diquarks Ua,Da,Sa have the same type (Gaussian type) momentum dependence,center around zero momentum and extend to the energy scale about q2 = 1 GeV2,which happens to be the energy scale for the chiral symmetry breaking,the strong interactions in the infrared region result in bound (or quasi-bound) states.The numerical results for the masses and decay constants of the π and K mesons can reproduce the experimental values,and the ground state masses of the scalar diquarks Ua,Da,Sa are consistent with the existing theoretical calculations.We suggest a new Lagrangian which may explain the uncertainty of the masses of the scalar diquarks.
Symmetry preserving truncations of the gap and Bethe-Salpeter equations
Binosi, Daniele; Papavassiliou, Joannis; Qin, Si-Xue; Roberts, Craig D
2016-01-01
Ward-Green-Takahashi (WGT) identities play a crucial role in hadron physics, e.g. imposing stringent relationships between the kernels of the one- and two-body problems, which must be preserved in any veracious treatment of mesons as bound-states. In this connection, one may view the dressed gluon-quark vertex, $\\Gamma_\\mu^a$, as fundamental. We use a novel representation of $\\Gamma_\\mu^a$, in terms of the gluon-quark scattering matrix, to develop a method capable of elucidating the unique quark-antiquark Bethe-Salpeter kernel, $K$, that is symmetry-consistent with a given quark gap equation. A strength of the scheme is its ability to expose and capitalise on graphic symmetries within the kernels. This is displayed in an analysis that reveals the origin of $H$-diagrams in $K$, which are two-particle-irreducible contributions, generated as two-loop diagrams involving the three-gluon vertex, that cannot be absorbed as a dressing of $\\Gamma_\\mu^a$ in a Bethe-Salpeter kernel nor expressed as a member of the class...
Intriguin solutions of Bethe-Salpeter equation for radially excited pseudoscalar charmonia
Sauli, Vladimir
2012-01-01
When generalizing recent various quantum mechanical models of heavy quarkonia to Quantum Filed theoretical approach based on Bethe-Salpeter equation one is faced to the solutions that do not exist in nonrelativistic limit. Mainly, there is unexpected doubling of the spectrum when comparing to the experimentally known spectrum as well as the ones obtained from the solution of the Schroedinger equation. These additional states are not apriory unphysical as both of them have the same symmetry. Our study strongly suggests that these solutions appear due to the sensitivity of BSE to the details of the analytical form of the constituents quark and antiquark propagators, more specifically they are consequence of using unconfining free propagators. To show this explicitly we develop and describe the efficient method of the numerical solution for quarkonium BSE and numerically solve it for the case of pseudoscalar charmonia. For the bare propagators of constituents we are able to find BSE solution for arbitrarily high...
The Bethe-Salpeter equation is solved in closed form with the help of a four dimensional separable 'potential'. For possible applications to three-nucleon investigations the authors have fitted all nucleon-nucleon S-wave phase shifts in a sufficient way by this method; in addition they also present an example for a P-wave. (Auth.)
Gadjiev, S A
2001-01-01
Scattering amplitude of fermions and bosons in the ladder approximation at high energies is investigated. For the imaginary part of the scattering amplitude the set of Bethe-Salpeter type integral equations is constructed. Solutions of this set in the Regge asymptotic form are found. The impact of mass parameters on the behavior of the amplitude at high energies is studied.
Bethe-Salpeter equation for non-self conjugate mesons in a power-law potential
We develop an approach to the solution of the spinless Bethe-Salpeter equation for the different-mass case. Although the calculations are developed for spin-zero particles in any arbitrary spherically symmetric potential, the non-Coulombic effective power-law potential is used as a kernel to produce the spin-averaged bound states of the non-self-conjugate mesons. The analytical formulae are also applicable to the self-conjugate mesons in the equal-mass case. The flavor-independent case is investigated in this work. The calculations are carried out to the third-order correction of the energy series. Results are consistent with those obtained before. (author). 14 refs, 1 tab
Many-body-QED perturbation theory: Connection to the two-electron Bethe-Salpeter equation
Lindgren, I.; Salomonson, S.; Hedendahl, D.
2005-03-01
The connection between many-body perturbation theory (MBPT) and quantum electrodynamics (QED) is reviewed for systems of two fermions in an external field. The treatment is mainly based on the recently developed covariant-evolution-operator method for QED calculations (I. Lindgren, S. Salomonson, and B. Asen. Phys. Rep. 389, 161 (2004)), which is quite similar in structure to MBPT. At the same time, this procedure is closely related to the S-matrix and Green's-function formalisms and can therefore serve as a bridge connecting various approaches. It is demonstrated that the MBPT-QED scheme, when carried to all orders, leads to a Schrodinger-like equation, equivalent to the Bethe-Salpeter (BS) equation. A Bloch equation in commutator form that can be used for an "extended" or quasi-degenerate model space is derived. This is a multi-state equation that has the same relation to the single-state BS equation as the standard Bloch equation has to the ordinary Schrodinger equation. It can be used to generate a perturbation expansion compatible with the BS equation even in the case of a quasi-degenerate model space.
无
2005-01-01
The interaction kernel in the Bethe-Salpeter equation for quark-antiquark bound states is derived newly from QCD in the case where the quark and the antiquark are of different flavors. The technique of the derivation is the usage of the irreducible decomposition of the Green's functions involved in the Bethe-Salpeter equation satisfied by the quark-antiquark four-point Green's function. The interaction kernel derived is given a closed and explicit expression which shows a specific structure of the kernel since the kernel is represented in terms of the quark, antiquark and gluon propagators and some kinds of quark, antiquark and/or gluon three, four, five and six-point vertices. Therefore,the expression of the kernel is not only convenient for perturbative calculations, but also suitable for nonperturbative investigations.
Solving the inhomogeneous Bethe-Salpeter equation in Minkowski space: the zero-energy limit
Frederico, Tobias; Salmè, Giovanni; Viviani, Michele
2015-08-01
The inhomogeneous Bethe-Salpeter equation for an interacting system, composed of two massive scalars exchanging a massive scalar, is numerically investigated in the ladder approximation directly in Minkowski space, by using for the first time in the continuum an approach based on the Nakanishi integral representation. In this paper, the limiting case of zero-energy states is considered, thus extending an approach that has already been successfully applied to bound states. The numerical values of scattering lengths, are calculated for several values of the Yukawa coupling constant, by using two different integral equations that stem from the Nakanishi framework. Those low-energy observables are compared with (1) the analogous quantities recently obtained in literature, within a totally different framework, and (2) the non-relativistic evaluations, to illustrate the relevance of a nonperturbative, genuine field theoretical treatment in Minkowski space, even in the low-energy regime. Moreover, dynamical functions, like the Nakanishi weight functions and the distorted part of the zero-energy light-front wave functions are also presented. Interestingly, a highly non-trivial issue related to the abrupt change in the width of the support of the Nakanishi weight function, when the zero-energy limit is approached, is elucidated, ensuring a sound basis to the forthcoming evaluation of phase shifts.
Solving the inhomogeneous Bethe-Salpeter equation in Minkowski space: the zero-energy limit
Frederico, Tobias [Instituto Tecnologico de Aeronautica, DCTA, Dept. de Fisica, Sao Paulo (Brazil); Salme, Giovanni [Istituto Nazionale di Fisica Nucleare, Sezione di Roma, Roma (Italy); Viviani, Michele [Istituto Nazionale di Fisica Nucleare, Sezione di Pisa, Pisa (Italy)
2015-08-15
The inhomogeneous Bethe-Salpeter equation for an interacting system, composed of two massive scalars exchanging a massive scalar, is numerically investigated in the ladder approximation directly in Minkowski space, by using for the first time in the continuum an approach based on the Nakanishi integral representation. In this paper, the limiting case of zero-energy states is considered, thus extending an approach that has already been successfully applied to bound states. The numerical values of scattering lengths, are calculated for several values of the Yukawa coupling constant, by using two different integral equations that stem from the Nakanishi framework. Those low-energy observables are compared with (1) the analogous quantities recently obtained in literature, within a totally different framework, and (2) the non-relativistic evaluations, to illustrate the relevance of a nonperturbative, genuine field theoretical treatment in Minkowski space, even in the low-energy regime. Moreover, dynamical functions, like the Nakanishi weight functions and the distorted part of the zero-energy light-front wave functions are also presented. Interestingly, a highly non-trivial issue related to the abrupt change in the width of the support of the Nakanishi weight function, when the zero-energy limit is approached, is elucidated, ensuring a sound basis to the forthcoming evaluation of phase shifts. (orig.)
Radiative decay widths are calculated for the radiative decay processes observed experimentally in the charmonium system. The model uses a Bethe-Salpeter equation with a static kernel and harmonic oscillator potentials to model the c-anti c system. Each decay width is calculated for 21 different choices of the c-quark mass. The potential used was a linear combination of a vector coupled and a scalar coupled harmonic oscillator potential. The quark mass and the scalar to vector coupling ratio were determined by trying to fit simultaneously the psi'(3685) - psi(3095) mass difference, the psi(3095) → e+ + e-decay width and the 3P/sub J/ mass splittings. A single choice of the quark mass and scalar to vector coupling ratio could not simultaneously fit all these constraints. The best fit to these constraints occurred when the quark mass was 5.5 and the scalar to vector coupling ratio parameter was -0.16. The decay width calculations are shown graphically for values of the quark mass from 0.00 to 16 GeV. The decay widths were calculated two different ways: (1) using the matrix elements of the quark momentum; (2) using the matrix elements of the quark position. Most of the published calculations use method (2). The widths computed by methods (1) and (2) are quite different for all masses and all transitions implying that the usual method (2) give incorrect results, and the fits with experimental data are fortuitous
Hadronic Observables from Dyson-Schwinger and Bethe-Salpeter equations
Sanchis-Alepuz, Helios
2015-01-01
In these proceedings we present a mini-review on the topic of the Dyson-Schwinger/Bethe-Salpeter approach to the study of relativistic bound-states in physics. In particular, we present a self-contained discussion of their derivation, as well as their truncation such that important symmetries are maintained.
Mass of Y(3940) in Bethe-Salpeter equation for quarks
Chen, Xiaozhao [Shandong University of Science and Technology, Department of Foundational Courses, Taian (China); Lue, Xiaofu [Sichuan University, Department of Physics, Chengdu (China); The Chinese Academy of Sciences, Institute of Theoretical Physics, Beijing (China); CCAST (World Laboratory), Beijing (China)
2015-03-01
The general form of the Bethe-Salpeter wave functions for the bound states composed of two vector fields of arbitrary spin and definite parity is corrected. Using the revised general formalism, we investigate the observed Y(3940) state, which is considered as a molecule state consisting of D{sup *0} anti D{sup *0}. Though the attractive potential between D{sup *0} and anti D{sup *0} including one light meson (σ, π, ω, ρ) exchange is considered, we find that in our approach the contribution from one-π exchange is equal to zero and consider SU(3) symmetry breaking. The obtained mass of Y(3940) is consistent with the experimental value. (orig.)
Gaind, Vaibhav
Fluorescence resonance energy transfer (FRET) has found many applications in in vitro imaging as an indicator of molecular activity. However, till now, in vivo FRET imaging has been restricted to near-surface multiphoton microscopy. Optical diffusion tomography (ODT) is an emerging tool for deep tissue imaging. In this work, FRET was incorporated in an ODT framework, thereby allowing FRET to be applied in deep tissue imaging. Using simulations and tissue phantom and small animal imaging experiments, the possibility of imaging molecular activity on the nanometer scale using macroscopic measurements is demonstrated. The diffusion equation model is limited to regions of high scatter and low absorption. The Bethe-Salpeter equation has been used extensively to explain various scattering phenomena and is more fundamental than the Boltzmann transport equation. In this work, the Bethe-Salpeter equation has been investigated for modeling photon transport in the non-diffusive regime.
Bruneval, Fabien; Hamed, Samia M.; Neaton, Jeffrey B.
2015-01-01
The predictive power of the ab initio Bethe-Salpeter equation (BSE) approach, rigorously based on many-body Green's function theory but incorporating information from density functional theory, has already been demonstrated for the optical gaps and spectra of solid-state systems. Interest in photoactive hybrid organic/inorganic systems has recently increased, and so has the use of the BSE for computing neutral excitations of organic molecules. However, no systematic benchmarks of the BSE for ...
In this article, we investigate the structures of the pseudoscalar mesons (π, K, D, Ds, B and Bs) in the framework of the coupled rainbow Schwinger-Dyson equation and ladder Bethe-Salpeter equation with the confining effective potential (infrared modified flat bottom potential). The Schwinger-Dyson functions for the u, d and s quarks are greatly renormalized at small momentum region and the curves are steep at about q2=1 GeV2 which indicates an explicitly dynamical symmetry breaking. The Euclidean time Fourier transformed quark propagators have no mass poles in the time-like region which naturally implements confinement. As for the c and b quarks, the current masses are very large, the renormalization are more tender, however, mass poles in the time-like region are also absent. The Bethe-Salpeter wavefunctions for those mesons have the same type (Gaussian type) momentum dependence and center around small momentum which indicate that the bound states exist in the infrared region. The decay constants for those pseudoscalar mesons are compatible with the values of experimental extractions and theoretical calculations, such as lattice simulations and QCD sum rules
Gamma Matrix Expansion of the Bethe-Salpeter Equation for Nucleon-Nucleon System
Kinpara, Susumu
2016-01-01
For the coefficients of the amplitude a set of simultaneous equations is derived in momentum space. By the auxiliary conditions they are equivalent to nonrelativistic equations and suitable for the investigation of two-nucleon system.
Meson states from the Bethe-Salpeter equation: successes and challenges
Full text: Dyson-Schwinger equations provide a nonperturbative continuum approach to QCD. The infinite coupled system of integral equations is truncated in a symmetry preserving manner to allow for both proof of exact results as well as sophisticated model calculations to illustrate these results and to perform qualitative as well as quantitative studies of hadronic observables. Over the past years a lot of investigations have used the so-called rainbow-ladder truncation. I will report the successes and ongoing progress within this truncation and demonstrate the need for a 'step beyond' with the help of examples taken from meson physics. (author)
Gomes, Adriano Doff Sotta [Universidade Tecnologica Federal do Parana (UTFPR), Pato Branco, PR (Brazil)
2011-07-01
Full text: Scalar composite boson masses have been computed in QCD and Technicolor theories with the help of the homogeneous Bethe-Salpeter equation (BSE), resulting in a scalar mass that is twice the dynamically generated fermion or technifermion mass (m{sub dyn}). In the A. Doff, A. A. Natale and P. S. Rodrigues da Silva, Phys. Rev. D 80, 055005 (2009) we study the effect of the normalization condition on the determination of scalar boson masses in dynamically broken gauge theories and verify that the normalization condition does not modify the value of the scalar boson mass when its wave function has the asymptotic behavior exactly as predicted by the OPE. However in walking (or quasi-conformal) gauge theories the asymptotic behavior of fermionic self-energies and the wave function of scalar bound states are dominated by higher order interactions and are characterized by a much harder decrease with the momentum, therefore, in this case, we show that the normalization condition of the BSE do constrain the scalar masses. In this work we apply some results obtained in the cited reference to the model described in A. Doff, Phys. Rev. D 81, 117702 (2010), in particular we compute the Higgs boson masses generated in the model assuming the effects of mixing in the wave function of scalar bound states due to the U(1){sub x} interaction of U' and D' techniquarks. (author)
The predictive power of the ab initio Bethe-Salpeter equation (BSE) approach, rigorously based on many-body Green’s function theory but incorporating information from density functional theory, has already been demonstrated for the optical gaps and spectra of solid-state systems. Interest in photoactive hybrid organic/inorganic systems has recently increased and so has the use of the BSE for computing neutral excitations of organic molecules. However, no systematic benchmarks of the BSE for neutral electronic excitations of organic molecules exist. Here, we study the performance of the BSE for the 28 small molecules in Thiel’s widely used time-dependent density functional theory benchmark set [Schreiber et al., J. Chem. Phys. 128, 134110 (2008)]. We observe that the BSE produces results that depend critically on the mean-field starting point employed in the perturbative approach. We find that this starting point dependence is mainly introduced through the quasiparticle energies obtained at the intermediate GW step and that with a judicious choice of starting mean-field, singlet excitation energies obtained from BSE are in excellent quantitative agreement with higher-level wavefunction methods. The quality of the triplet excitations is slightly less satisfactory
Regge behaviour within the Bethe-Salpeter approach
Kubrak, Stanislav; Williams, Richard
2014-01-01
We present a calculation of the spectrum of light and heavy quark bound states in the rainbow-ladder truncation of Dyson-Schwinger/Bethe-Salpeter equations. By extending the formalism include the case of total angular momentum J=3, we are able to explore Regge trajectories and make prediction of tensor bound states for light and heavy quarkonia.
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 Ds and D*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.
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.
Malik, G P
2016-01-01
Given the Debye temperature of an elemental superconductor (SC) and its Tc, BCS theory enables one to predict the value of its gap 0 at T = 0, or vice versa. This monograph shows that non-elemental SCs can be similarly dealt with via the generalized BCS equations (GBCSEs) which, given any two parameters of the set {Tc, 10, 20 > 10}, enable one to predict the third. Also given herein are new equations for the critical magnetic field and critical current density of an elemental and a non-elemental SC — equations that are derived directly from those that govern pairing in them. The monograph includes topics that are usually not covered in any one text on superconductivity, e.g., BCS-BEC crossover physics, the long-standing puzzle posed by SrTiO3, and heavy-fermion superconductors — all of which are still imperfectly understood and therefore continue to avidly engage theoreticians. It suggests that addressing the Tcs, s and other properties (e.g., number densities of charge carriers) of high-Tc SCs via GBCSE...
Bethe-Salpeter bound-state structure in Minkowski space
Gutierrez, C.; Gigante, V.; Frederico, T.; Salmè, G.; Viviani, M.; Tomio, Lauro
2016-08-01
The quantitative investigation of the scalar Bethe-Salpeter equation in Minkowski space, within the ladder-approximation framework, is extended to include the excited states. This study has been carried out for an interacting system composed by two massive bosons exchanging a massive scalar, by adopting (i) the Nakanishi integral representation of the Bethe-Salpeter amplitude, and (ii) the formally exact projection onto the null plane. Our analysis, on one hand, confirms the reliability of the method already applied to the ground state and, on the other one, extends the investigation from the valence distribution in momentum space to the corresponding quantity in the impact-parameter space, pointing out some relevant features, like (i) the equivalence between Minkowski and Euclidean transverse-momentum amplitudes, and (ii) the leading exponential fall-off of the valence wave function in the impact-parameter space.
Bethe-Salpeter bound-state structure in Minkowski space
Gutierrez, C; Frederico, T; Salmè, G; Viviani, M; Tomio, Lauro
2016-01-01
The quantitative investigation of the scalar Bethe-Salpeter equation in Minkowski space, within the ladder-approximation framework, is extended to include the excited states. This study has been carried out for an interacting system composed by two massive bosons exchanging a massive scalar, by adopting (i) the Nakanishi integral representation of the Bethe-Salpeter amplitude, and (ii) the formally exact projection onto the null plane. Our analysis, on one hand, confirms the reliability of the method already applied to the ground state and, on the other one, extends the investigation from the valence distribution in momentum space to the corresponding quantity in the impact-parameter space, pointing out some relevant features, like (i) the equivalence between Minkowski and Euclidean transverse-momentum amplitudes, and (ii) the leading exponential fall-off of the valence wave function in the impact-parameter space.
Zhang, L; Weng, M -H
2016-01-01
The matrix element of the weak transition {\\Lambda}_b\\rightarrow{\\Lambda}_c can be expressed in terms of six form factors. {\\Lambda}_Q(Q = b;c) can be regarded as composed of a heavy quark Q(Q = b;c) and a diquark which is made up of the remaining two light quarks. In this picture, we express these six form factors in terms of Bethe-Salpeter wave functions to second order in the 1/m_Q expansion. With the kernel containing both the scalar confinement and the one-gluon-exchange terms we calculate the form factors and the decay widths of the semileptonic decay {\\Lambda}_b\\rightarrow{\\Lambda}_clv as well as nonleptonic decays {\\Lambda}_b\\rightarrow{\\Lambda}_cP(V) numerically. We also add QCD corrections since they are comparable with 1/m_Q corrections.
Tetraquark bound states in a Bethe-Salpeter approach
Heupel, Walter; Eichmann, Gernot; Fischer, Christian S.
2012-01-01
We determine the mass of tetraquark bound states from a coupled system of covariant Bethe-Salpeter equations. Similar in spirit to the quark-diquark model of the nucleon, we approximate the full four-body equation for the tetraquark by a coupled set of two-body equations with meson and diquark constituents. These are calculated from their quark and gluon substructure using a phenomenologically well-established quark-gluon interaction. For the lightest scalar tetraquark we find a mass of the o...
Spectra of heavy mesons in the Bethe-Salpeter approach
Fischer, Christian S.; Kubrak, Stanislav; Williams, Richard [Justus-Liebig-Universitaet Giessen, Institut fuer Theoretische Physik, Giessen (Germany)
2015-01-01
We present a calculation of the spectrum of charmonia, bottomonia and B{sub c}-meson states with ''ordinary'' and exotic quantum numbers. We discuss the merits and limitations of a rainbow-ladder truncation of Dyson-Schwinger and Bethe-Salpeter equations and explore the effects of different shapes of the effective running coupling on ground and excited states in channels with quantum numbers J ≤ 3. We furthermore discuss the status of the X(3872) as a potential (excited) quark-antiquark state and give predictions for the masses of charmonia and bottomonia in the tensor channels with J= 2, 3. (orig.)
Direct Bethe-Salpeter solutions in Minkowski space
Carbonell, J
2016-01-01
We review a method to directly solve the Bethe-Salpeter equation in Minkowski space, both for bound and scattering states. It is based on a proper treatment of the many singularities which appear in the kernel and propagators. The off-mass shell scattering amplitude for spinless particles interacting by a one boson exchange was computed for the first time. Using our Minkowski space solutions for the initial (bound) and final (scattering) states, we calculate elastic and transition (bound to scattering state) electromagnetic form factors. The conservation of the transition electromagnetic current J.q=0, verified numerically, confirms the validity of our solutions.
π- and K-meson Bethe-Salpeter amplitudes
Independent of assumptions about the form of the quark-quark scattering kernel K, we derive the explicit relation between the flavor-nonsinglet pseudoscalar-meson Bethe-Salpeter amplitude ΓH and the dressed-quark propagator in the chiral limit. In addition to a term proportional to γ5, ΓH necessarily contains qualitatively and quantitatively important terms proportional to γ5γ·P and γ5γ·kk·P, where P is the total momentum of the bound state. The axial-vector vertex contains a bound state pole described by ΓH, whose residue is the leptonic decay constant for the bound state. The pseudoscalar vertex also contains such a bound state pole and, in the chiral limit, the residue of this pole is related to the vacuum quark condensate. The axial-vector Ward-Takahashi identity relates these pole residues, with the Gell-Mann endash Oakes endash Renner relation a corollary of this identity. The dominant ultraviolet asymptotic behavior of the scalar functions in the meson Bethe-Salpeter amplitude is fully determined by the behavior of the chiral limit quark mass function, and is characteristic of the QCD renormalization group. The rainbow-ladder Ansatz for K, with a simple model for the dressed-quark-quark interaction, is used to illustrate and elucidate these general results. The model preserves the one-loop renormalization group structure of QCD. The numerical studies also provide a means of exploring procedures for solving the Bethe-Salpeter equation without a three-dimensional reduction. copyright 1997 The American Physical Society
Tetra quark bound states in a Bethe-Salpeter approach
Heupel, Walter; Eichmann, Gernot [Institut fuer Theoretische Physik, Justus-Liebig-Universitaet Giessen, D-35392 Giessen (Germany); Fischer, Christian S., E-mail: christian.fischer@theo.physik.uni-giessen.de [Institut fuer Theoretische Physik, Justus-Liebig-Universitaet Giessen, D-35392 Giessen (Germany); GSI Helmholtzzentrum fuer Schwerionenforschung GmbH, Planckstr. 1, D-64291 Darmstadt (Germany)
2012-12-05
We determine the mass of tetraquark bound states from a coupled system of covariant Bethe-Salpeter equations. Similar in spirit to the quark-diquark model of the nucleon, we approximate the full four-body equation for the tetraquark by a coupled set of two-body equations with meson and diquark constituents. These are calculated from their quark and gluon substructure using a phenomenologically well-established quark-gluon interaction. For the lightest scalar tetraquark we find a mass of the order of 400 MeV and a wave function dominated by the pion-pion constituents. Both results are in agreement with a meson molecule picture for the f{sub 0}(600). Our results furthermore suggest the presence of a potentially narrow all-charm tetraquark in the mass region 5-6 GeV.
Tetraquark bound states in a Bethe-Salpeter approach
Heupel, Walter; Fischer, Christian S
2012-01-01
We determine the mass of tetraquark bound states from a coupled system of covariant Bethe-Salpeter equations. Similar in spirit to the quark-diquark model of the nucleon, we approximate the full four-body equation for the tetraquark by a coupled set of two-body equations with meson and diquark constituents. These are calculated from their quark and gluon substructure using a phenomenologically well-established quark-gluon interaction. For the lightest scalar tetraquark we find a mass of the order of 400 MeV and a wave function dominated by the pion-pion constituents. Both results are in agreement with a meson molecule picture for the f_0(600). Our results furthermore suggest the presence of a potentially narrow all-charm tetraquark in the mass region 5-6 GeV.
Tetraquark bound states in a Bethe-Salpeter approach
Heupel, Walter; Eichmann, Gernot; Fischer, Christian S.
2012-12-01
We determine the mass of tetraquark bound states from a coupled system of covariant Bethe-Salpeter equations. Similar in spirit to the quark-diquark model of the nucleon, we approximate the full four-body equation for the tetraquark by a coupled set of two-body equations with meson and diquark constituents. These are calculated from their quark and gluon substructure using a phenomenologically well-established quark-gluon interaction. For the lightest scalar tetraquark we find a mass of the order of 400 MeV and a wave function dominated by the pion-pion constituents. Both results are in agreement with a meson molecule picture for the f0 (600). Our results furthermore suggest the presence of a potentially narrow all-charm tetraquark in the mass region 5-6 GeV.
Tetra quark bound states in a Bethe-Salpeter approach
We determine the mass of tetraquark bound states from a coupled system of covariant Bethe-Salpeter equations. Similar in spirit to the quark-diquark model of the nucleon, we approximate the full four-body equation for the tetraquark by a coupled set of two-body equations with meson and diquark constituents. These are calculated from their quark and gluon substructure using a phenomenologically well-established quark-gluon interaction. For the lightest scalar tetraquark we find a mass of the order of 400 MeV and a wave function dominated by the pion-pion constituents. Both results are in agreement with a meson molecule picture for the f0(600). Our results furthermore suggest the presence of a potentially narrow all-charm tetraquark in the mass region 5-6 GeV.
We proposed the algorithm for umerical solving a boundary value problem for two-quark bound states described by the Salpeter equation with potential V0r2-αs/r which is coupled integro-differential equations depending on physical parameters m0 and αs. In this algorithm an iteration scheme of the continuous analogy of Newton's method, with corresponding choice of the iteration parameter, is realized. It is shown that using the continuation over parameter (m0, αs) method allows one to extend considerably a region of convergence of the iteration method. The solutions of the Salpeter equation for set of parameters m0 and αs are obtained, which reproduce the results are available (when m0=αs=0). 17 refs.; 1 fig.; 2 tabs
Relativistic three-nucleon calculations within the Bethe-Salpeter approach
Bondarenko, S G; Yurev, S A
2015-01-01
The relativistic properties of the three-nucleon system are investigated using the Faddeev equations within the Bethe-Salpeter approach. The nucleon-nucleon interaction is chosen in a separable form. The Gauss quadrature method is used to calculate the integrals. The system of the integral equations are solving by iterations method. The binding energy and the partial-wave amplitudes (1S 0 and 3S 1) of the triton are found.
Relativistic Three-Nucleon Calculations within the Bethe-Salpeter Approach
Bondarenko S.G.
2016-01-01
Full Text Available The relativistic properties of the three-nucleon system are investigated using the Faddeev equations within the Bethe-Salpeter approach. The nucleon-nucleon interaction is chosen in a separable form. The Gauss quadrature method is used to calculate the integrals. The system of the integral equations is solved by an iterative method. The binding energy and the partial-wave amplitudes (1S0 and 3S1 of the triton are found.
Instantaneous Bethe-Salpeter View of Goldstone-Type Pseudoscalar Mesons
Lucha, Wolfgang
2016-01-01
Describing the lightest pseudoscalar mesons as bound states of quark and antiquark within the framework of an instantaneous Bethe-Salpeter formalism constructed such as to retain (in contrast to Salpeter's equation) as much information on the relativistic effects provided by the full quark propagator as conceivable allows for a surprisingly simple implementation of their near masslessness mandatory for their interpretability as pseudo-Goldstone bosons related to the spontaneous breaking of the chiral symmetries of quantum chromodynamics.
Peculiarities in the Structure of Two-Particle States within the Bethe-Salpeter Approach
Dorkin, S. M.; Semikh, S. S.; Beyer, M.; Kaptari, L. P.
2006-01-01
The two-fermion bound system is an attractive subject of atomic and sub-atomic physics. Despite these systems are rather simple the study of two-particle bound states is challenging and still remains a source of progress in quantum theory. Here we present a new method of solving the Bethe Salpeter equations for the bound states of spinor particles by using the expansion of the vertex functions over the complete set of four-dimensional hyperspherical harmonics. Within this method the BS equati...
Physical properties of the pion in the covariant Bethe-Salpeter formalism
Some problems concerned with normalization of wave functions, which are obtained from the general method for the Lorentz-covariant Bethe-Salpeter equation of the Goldstone boson developed in our previous work, are discussed in connection with the axial Ward-Takahashi identity. Physical properties of the pion, including the π0→γγ amplitude, are calculated in QCD-motivated models with the general method. Both the chiral limit and the effect of explicit chiral-symmetry breaking by the bare quark mass are considered. A quite good agreement with experimental data is obtained with these models
Delta and Omega electromagnetic form factors in a Dyson-Schwinger/Bethe-Salpeter approach
Diana Nicmorus, Gernot Eichmann, Reinhard Alkofer
2010-12-01
We investigate the electromagnetic form factors of the Delta and the Omega baryons within the Poincare-covariant framework of Dyson-Schwinger and Bethe-Salpeter equations. The three-quark core contributions of the form factors are evaluated by employing a quark-diquark approximation. We use a consistent setup for the quark-gluon dressing, the quark-quark bound-state kernel and the quark-photon interaction. Our predictions for the multipole form factors are compatible with available experimental data and quark-model estimates. The current-quark mass evolution of the static electromagnetic properties agrees with results provided by lattice calculations.
Covariant Bethe-Salpeter wave functions for heavy hadrons
In recent years the dynamics of heavy mesons and baryons has considerably simplified by the development of the so-called heavy quark effective theory (HQET). A covariant formulation of heavy meson and heavy baryon decays in the leading order of the HQET is presented. The method is based on a Bethe-Salpeter formulation in the limit of the heavy quark mass going to infinity. 15 refs, 4 figs
GW and Bethe-Salpeter study of small water clusters
Blase, Xavier, E-mail: xavier.blase@neel.cnrs.fr; Boulanger, Paul [CNRS, Institut NEEL, F-38042 Grenoble (France); Bruneval, Fabien [CEA, DEN, Service de Recherches de Métallurgie Physique, F-91191 Gif-sur-Yvette (France); Fernandez-Serra, Marivi [Department of Physics and Astronomy, Stony Brook University, Stony Brook, New York 11794-3800 (United States); Institute for Advanced Computational Sciences, Stony Brook University, Stony Brook, New York 11794-3800 (United States); Duchemin, Ivan [INAC, SP2M/L-Sim, CEA/UJF Cedex 09, 38054 Grenoble (France)
2016-01-21
We study within the GW and Bethe-Salpeter many-body perturbation theories the electronic and optical properties of small (H{sub 2}O){sub n} water clusters (n = 1-6). Comparison with high-level CCSD(T) Coupled-Cluster at the Single Double (Triple) levels and ADC(3) Green’s function third order algebraic diagrammatic construction calculations indicates that the standard non-self-consistent G{sub 0}W{sub 0}@PBE or G{sub 0}W{sub 0}@PBE0 approaches significantly underestimate the ionization energy by about 1.1 eV and 0.5 eV, respectively. Consequently, the related Bethe-Salpeter lowest optical excitations are found to be located much too low in energy when building transitions from a non-self-consistent G{sub 0}W{sub 0} description of the quasiparticle spectrum. Simple self-consistent schemes, with update of the eigenvalues only, are shown to provide a weak dependence on the Kohn-Sham starting point and a much better agreement with reference calculations. The present findings rationalize the theory to experiment possible discrepancies observed in previous G{sub 0}W{sub 0} and Bethe-Salpeter studies of bulk water. The increase of the optical gap with increasing cluster size is consistent with the evolution from gas to dense ice or water phases and results from an enhanced screening of the electron-hole interaction.
The tensor analyzing power T20 in deuteron break-up reactions within the Bethe-Salpeter formalism
The deuteron tensor analyzing power T20 in the deuteron break-up reaction Dp → pX is calculated within a relativistic approach based on the Bethe-Salpeter equation with a realistic meson-exchange potential. Our results on T20 and the cross section are compared with experimental data and non-relativistic calculations and with the outcome of a relativization procedure of the deuteron wave function. (orig.)
In this paper the general structure of leptonic decay constants of vector mesons is evaluated in the framework of Bethe-Salpeter Equation under Covariant Instantaneous Ansatz (CIA) with a modified structure of the Hqq-bar vertex function Γ which is generalized to include Dirac covariants other than the leading Dirac covariant γμ within its structure. The numerical values of fv in this CIA framework are calculated. (author)
$\\pi$ and K-meson Bethe-Salpeter Amplitudes
Maris, P
1997-01-01
Independent of assumptions about the form of the quark-quark scattering kernel, K, we derive the explicit relation between the flavour-nonsinglet pseudoscalar meson Bethe-Salpeter amplitude, Gamma_H, and the dressed-quark propagator in the chiral limit. In addition to a term proportional to gamma_5, Gamma_H necessarily contains qualitatively and quantitatively important terms proportional to gamma_5 gamma.P and gamma_5 gamma.k k.P, where P is the total momentum of the bound state. The axial-vector vertex contains a bound state pole described by Gamma_H, whose residue is the leptonic decay constant for the bound state. The pseudoscalar vertex also contains such a bound state pole and, in the chiral limit, the residue of this pole is related to the vacuum quark condensate. The axial-vector Ward-Takahashi identity relates these pole residues; with the Gell-Mann--Oakes--Renner relation a corollary of this identity. The dominant ultraviolet asymptotic behaviour of the scalar functions in the meson Bethe-Salpeter a...
Maggio, Emanuele; Kresse, Georg
2016-06-01
The correlation energy of the homogeneous electron gas is evaluated by solving the Bethe-Salpeter equation (BSE) beyond the Tamm-Dancoff approximation for the electronic polarization propagator. The BSE is expected to improve on the random-phase approximation, owing to the inclusion of exchange diagrams. For instance, since the BSE reduces in second order to Møller-Plesset perturbation theory, it is self-interaction free in second order. Results for the correlation energy are compared with quantum Monte Carlo benchmarks and excellent agreement is observed. For low densities, however, we find imaginary eigenmodes in the polarization propagator. To avoid the occurrence of imaginary eigenmodes, an approximation to the BSE kernel is proposed that allows us to completely remove this issue in the low-electron-density region. We refer to this approximation as the random-phase approximation with screened exchange (RPAsX). We show that this approximation even slightly improves upon the standard BSE kernel.
Theory of x-ray absorption: a Bethe-Salpeter approach
Shirley, Eric L.
2002-03-01
First-principles calculations of x-ray absorption spectra of solids is a well-established field. The best known and most used treatments are probably those based on real-space multiple-scattering theory. Such Green's Function approaches are particular useful for incorporating electron damping effects (self-energy effects) that broaden spectral features at high electron kinetic energy. Near-edge structure can also be treated, and it can also be treated in super-cell calculations. In this talk, I will present results obtained using an alternative, reciprocal-space approach based on solving the Bethe-Salpeter equation, which is related to the Bethe-Salpeter method used to treat valence excitation signatures in optical absorption spectra. This amounts to solving the coupling equations of motion for the electron-core hole pair that is produced by x-ray absorption. Mutual localization of the electron and core hole in real space is realized by permitting the electron to exist as a wave-packet of Bloch states peaked near the core hole, governed by the excitation process and ensuing electron core-hole attraction. Because this approach permits state-of-the-art electron band structure calculations to be used to evaluate the electron wave function, this approach is particularly well suited for detailed near-edge structure. In presenting the approach and results obtained, particular attention is focused on (1) the role of the electron-hole interaction, (2) the need to deal with core-hole screening accurately, (3) the evaluation of accurate transition matrix elements between core states and Bloch states, and (4) computational-time scaling issues. This work has been done in collaboration with J.A. Soininen, J.J. Rehr, E.K. Chang, and others. This work was supported in part by the U.S. Deparment of Energy (DOE) Grant DE-FG03-97ER45623 and facilitated by the DOE Computational Materials Science Network (CMSN).
Janus-Facedness of the Pion: Analytic Instantaneous Bethe-Salpeter Models
Lucha, Wolfgang
2016-01-01
Inversion enables the construction of interaction potentials underlying - under fortunate circumstances even analytic - instantaneous Bethe-Salpeter descriptions of all lightest pseudoscalar mesons as quark-antiquark bound states of Goldstone-boson nature.
All-electron Bethe-Salpeter calculations for shallow-core x-ray absorption near-edge structures
Olovsson, W.; Tanaka, I.; Mizoguchi, T.; Puschnig, P.; Ambrosch-Draxl, C.
2009-01-01
X-ray absorption near-edge structure spectra are calculated by fully solving the electron/core-hole Bethe-Salpeter equation (BSE) in an all-electron framework. We study transitions from shallow core states, including the Mg L2,3 edge in MgO, the Li K edge in the Li halides LiF, LiCl, LiBr, and LiI, as well as Li2O. We illustrate the advantage of the many-body approach over a core-hole supercell calculation. Both schemes lead to strongly bound excitons, but the nonlocal treatment of the electr...
Bondarenko, S G; Rogochaya, E P
2011-01-01
The electrodisintegration of the deuteron is considered within a relativistic model of nucleon-nucleon interaction based on the Bethe-Salpeter approach with a separable interaction kernel. The exclusive cross section is calculated within the impulse approximation under various kinematic conditions. Final state interactions between the outgoing nucleons are taken into account. The comparison of nonrelativistic and relativistic calculations is presented. Partial-wave states of the neutron-proton pair with total angular momentum $J=0,1$ are considered.
Exclusive electrodisintegration of the deuteron in the Bethe-Salpeter approach
An exclusive process of the deuteron electrodisintegration is analyzed in the framework of the Bethe-Salpeter formalism with a phenomenological Graz II rank-three separable interaction. The approximations made are the neglect of final-state interaction, two-body exchange currents, negative-energy components of the bound-state vertex function and the scattering T matrix. The comparison of the relativistic calculations of the exclusive cross section in the laboratory system with the experimental data is presented within different kinematic conditions
On the electrodisintegration of the deuteron in the Bethe-Salpeter formalism
Bondarenko, S G; Goy, A A; Rogochaya, E P
2006-01-01
The (ed -> enp) process in the frame of the Bethe-Salpeter approach with a separable kernel of the Nucleon-Nucleon (NN) interaction was considered. This conception keeps the covariance of description of the process. Special attention was devoted to a contribution of the D-states of the deuteron in the cross section of the electrodisintegration. It was shown that the spectator particle (neutron) plays an important role. The factorization of a cross section of this reaction in the impulse approximation was checked by analytical and numerical calculations.
Puschnig, Peter; Ambrosch-Draxl, Claudia
2007-03-01
The solution of the Bethe-Salpeter equation (BSE) has turned out to be the method of choice for the ab-initio calculation of optical properties of semiconductors and insulators which is capable of correctly accounting for excitonic effects. Commonly, however, the coupling between the resonant and anti-resonant excitations is neglected, referred to as the Tamm-Dancoff approximation (TDA). This is well justified in many cases, in particular, for the working horses of theoretical solid state physics, such as bulk Si and GaAs. Here, we report on a first-principles investigation of the optical properties of organic semiconductors which are highly anisotropic systems. We find that the TDA no longer holds in such low-dimensional systems, where the exciton binding energies are no longer small compared to the band gaps. Going beyond the TDA leads to an increase of the exciton binding energy in the order of several tenths of an eV thereby considerably improving the agreement with experiment.
Efficient on-the-fly interpolation technique for Bethe-Salpeter calculations of optical spectra
Gillet, Yannick; Giantomassi, Matteo; Gonze, Xavier
2016-06-01
The Bethe-Salpeter formalism represents the most accurate method available nowadays for computing neutral excitation energies and optical spectra of crystalline systems from first principles. Bethe-Salpeter calculations yield very good agreement with experiment but are notoriously difficult to converge with respect to the sampling of the electronic wavevectors. Well-converged spectra therefore require significant computational and memory resources, even by today's standards. These bottlenecks hinder the investigation of systems of great technological interest. They are also barriers to the study of derived quantities like piezoreflectance, thermoreflectance or resonant Raman intensities. We present a new methodology that decreases the workload needed to reach a given accuracy. It is based on a double-grid on-the-fly interpolation within the Brillouin zone, combined with the Lanczos algorithm. It achieves significant speed-up and reduction of memory requirements. The technique is benchmarked in terms of accuracy on silicon, gallium arsenide and lithium fluoride. The scaling of the performance of the method as a function of the Brillouin Zone point density is much better than a conventional implementation. We also compare our method with other similar techniques proposed in the literature.
Separable Kernel of Nucleon-Nucleon Interaction in the Bethe-Salpeter Approach for J=0,1
Bondarenko, S G; Hamamoto, N; Hosaka, Y; Manabe, Y; Toki, H
2003-01-01
The solution for the nucleon-nucleon T matrix in the framework of the covariant Bethe-Salpeter approach for a two spin-one-half particle system with a separable kernel of interaction is analyzed. The explicit analytical connection between parameters of the separable kernel and low energy scattering parameters, deuteron binding energy and phase shifts is established.Covariant separable kernels for positive-energy partial channels with total angular momentum J=0 (1S0+, 3P0+) and J=1 (3S1+-3D1+, 1P1+, 3P1+) are constructed by using obtained relations.
Hadron-hadron interactions from imaginary-time Nambu-Bethe-Salpeter wave function on the lattice
Imaginary-time Nambu-Bethe-Salpeter (NBS) wave function is introduced to extend our previous approach for hadron-hadron interactions on the lattice. Scattering states of hadrons with different energies encoded in the NBS wave function are utilized to extract non-local hadron-hadron potential. “The ground state saturation”, which is commonly used in lattice QCD but is hard to be achieved for multi-baryons, is not required. We demonstrate that the present method works efficiently for the nucleon-nucleon interaction (the potential and the phase shift) in the 1S0 channel.
Hadron-hadron interactions from imaginary-time Nambu-Bethe-Salpeter wave function on the lattice
Ishii, Noriyoshi, E-mail: ishii@ribf.riken.jp [Kobe Branch, Center for Computational Sciences, University of Tsukuba, in RIKEN Advanced Institute for Computational Science (AICS), Portisland, Kobe 650-0047 (Japan); Aoki, Sinya [Graduate School of Pure and Applied Physics, University of Tsukuba, Tsukuba, Ibaraki 305-8571 (Japan); Center for Computational Sciences, University of Tsukuba, Tsukuba, Ibaraki 305-8577 (Japan); Doi, Takumi [Theoretical Research Division, Nishina Center, RIKEN, Wako 351-0198 (Japan); Hatsuda, Tetsuo [Theoretical Research Division, Nishina Center, RIKEN, Wako 351-0198 (Japan); Department of Physics, University of Tokyo, Tokyo 113-0033 (Japan); Ikeda, Yoichi [Department of Physics, Tokyo Institute of Technology, Meguro, Tokyo 152-8551 (Japan); Inoue, Takashi [Nihon University, College of Bioresource Sciences, Fujisawa 252-0880 (Japan); Murano, Keiko [Theoretical Research Division, Nishina Center, RIKEN, Wako 351-0198 (Japan); Nemura, Hidekatsu; Sasaki, Kenji [Center for Computational Sciences, University of Tsukuba, Tsukuba, Ibaraki 305-8577 (Japan)
2012-06-12
Imaginary-time Nambu-Bethe-Salpeter (NBS) wave function is introduced to extend our previous approach for hadron-hadron interactions on the lattice. Scattering states of hadrons with different energies encoded in the NBS wave function are utilized to extract non-local hadron-hadron potential. 'The ground state saturation', which is commonly used in lattice QCD but is hard to be achieved for multi-baryons, is not required. We demonstrate that the present method works efficiently for the nucleon-nucleon interaction (the potential and the phase shift) in the {sup 1}S{sub 0} channel.
Hadron-Hadron Interactions from Imaginary-time Nambu-Bethe-Salpeter Wave Function on the Lattice
Ishii, Noriyoshi; Doi, Takumi; Hatsuda, Tetsuo; Ikeda, Yoichi; Inoue, Takashi; Murano, Keiko; Nemura, Hidekatsu; Sasaki, Kenji
2012-01-01
Imaginary-time Nambu-Bethe-Salpeter (NBS) wave function is introduced to extend our previous approach for hadron-hadron interactions on the lattice. Scattering states of hadrons with different energies encoded in the NBS wave-function are utilized to extract non-local hadron-hadron potential. "The ground state saturation", which is commonly used in lattice QCD but is hard to be achieved for multi-baryons, is not required. We demonstrate that the present method works efficiently for the nucleon-nucleon interaction (the potential and the phase shift) in the 1S_0 channel.
Radozycki, Tomasz [Cardinal Stefan Wyszynski University, Faculty of Mathematics and Natural Sciences, College of Sciences, Warsaw (Poland)
2015-09-15
The Lorentz transformation properties of the equal-time bound-state Bethe-Salpeter amplitude in the two-dimensional massless quantum electrodynamics (the so-called Schwinger model) are considered. It is shown that while boosting a bound state (a 'meson') this amplitude is subject to approximate Lorentz contraction. The effect is exact for large separations of constituent particles ('quarks'), while for small distances the deviation is more significant. For this phenomenon to appear, the full function, i.e. with the inclusion of all instanton contributions, has to be considered. The amplitude in each separate topological sector does not exhibit such properties. (orig.)
Rebolini, Elisa
2015-01-01
We present a range-separated linear-response time-dependent density-functional theory (TDDFT) which combines a density-functional approximation for the short-range response kernel and a frequency-dependent second-order Bethe-Salpeter approximation for the long-range response kernel. This approach goes beyond the adiabatic approximation usually used in linear-response TDDFT and aims at improving the accuracy of calculations of electronic excitation energies of molecular systems. A detailed derivation of the frequency-dependent second-order Bethe-Salpeter correlation kernel is given using many-body Green-function theory. Preliminary tests of this range-separated TDDFT method are presented for the calculation of excitation energies of four small molecules: N2, CO2, H2CO, and C2H4. The results suggest that the addition of the long-range second-order Bethe-Salpeter correlation kernel overall slightly improves the excitation energies.
Vinson, J.; Rehr, J. J.
2012-11-01
We present ab initio Bethe-Salpeter equation (BSE) calculations of the L2,3 edges of several insulating and metallic compounds containing Ca, V, Fe, Co, Ni, and Cu, spanning a range of 3d-electron occupations. Our approach includes the key ingredients of a unified treatment of both extended states and atomic multiplet effects, i.e., Bloch states, self-consistent crystal potentials, ground-state magnetism, GW self-energy corrections, spin-orbit terms, and Coulomb interactions between the L2 and L3 levels. The method is implemented in the ocean package, which uses plane-wave pseudopotential wave functions as a basis, a projector-augmented-wave construction for the transition matrix elements, and a resolvent formalism for the BSE calculation. The results are in near quantitative agreement with experiment, including both fine structure at the edges and the nonstatistical L3/L2 ratios observed for these systems. Approximations such as time-dependent density-functional theory are shown to be less accurate.
Bethe-Salpeter calculation of optical-absorption spectra of In2O3 and Ga2O3
Varley, Joel B.; Schleife, André
2015-02-01
Transparent conducting oxides keep attracting strong scientific interest not only due to their promising potential for ‘transparent electronics’ applications but also due to their intriguing optical absorption characteristics. Materials such as In2O3 and Ga2O3 have complicated unit cells and, consequently, are interesting systems for studying the physics of excitons and anisotropy of optical absorption. Since currently no experimental data is available, for instance, for their dielectric functions across a large photon-energy range, we employ modern first-principles computational approaches based on many-body perturbation theory to provide theoretical-spectroscopy results. Using the Bethe-Salpeter framework, we compute dielectric functions and we compare to spectra computed without excitonic effects. We find that the electron-hole interaction strongly modifies the spectra and we discuss the anisotropy of optical absorption that we find for Ga2O3 in relation to existing theoretical and experimental data.
The Strong Decays of Orbitally Excited $B^{*}_{sJ}$ Mesons by Improved Bethe-Salpeter Method
Wang, Zhi-Hui; Wang, Guo-Li; Fu, Hui-Feng; Jiang, Yue
2012-01-01
We calculate the masses and the strong decays of orbitally excited states $B_{s0}$, $B'_{s1}$, $B_{s1}$ and $B_{s2}$ by the improved Bethe-Salpeter method. The predicted masses of $B_{s0}$ and $B'_{s1}$ are $M_{B_{s0}}=5.723\\pm0.280 {\\rm GeV}$, $M_{B'_{s1}}=5.774\\pm0.330 {\\rm GeV}$. We calculate the isospin symmetry violating decay processes $B_{s0}\\to B_s \\pi$ and $B'_{s1}\\to B_s^* \\pi$ through $\\pi^0-\\eta$ mixing and get small widths. Considering the uncertainties of the masses, for $B_{s0}...
Intriguing solutions of the Bethe-Salpeter equation for radially excited pseudoscalar charmonia
Šauli, Vladimír
2014-01-01
Roč. 90, č. 1 (2014), 016005. ISSN 1550-7998 Institutional support: RVO:61389005 Keywords : quantum chromodynamics * confinement * quarks * gluons Subject RIV: BE - Theoretical Physics Impact factor: 4.643, year: 2014
Many-body-QED perturbation theory: Connection to the Bethe-Salpeter equation
Lindgren, Ingvar
2005-01-01
The connection between many-body theory (MBPT)--in perturbative and non-perturbative form--and quantum-electrodynamics (QED) is reviewed for systems of two fermions in an external field. The treatment is mainly based upon the recently developed covariant-evolution-operator method for QED calculations [Lindgren et al. Phys. Rep. 389, 161 (2004)], which has a structure quite akin to that of many-body perturbation theory. At the same time this procedure is closely connected to the S-matrix and t...
Bethe-Salpeter wave functions of $\\eta_c(2S)$ and $\\psi(2S)$ states from full lattice QCD
Nochi, Kazuki; Sasaki, Shoichi
2016-01-01
We discuss the internal structure of radially excited charmonium mesons based on the equal-time and Coulomb gauge Bethe-Salpeter (BS) amplitudes, which are obtained in lattice QCD. Our simulations are performed with a relativistic heavy-quark action for the charm quark on the 2+1 flavor PACS-CS gauge configurations at the lightest pion mass, $M_{\\pi}=156(7)$ MeV. The variational method is applied to the study of optimal charmonium operator for ground and first excited states of $S$-wave charmonia. We successfully calculate the BS wave functions of $\\eta_c(2S)$ and $\\psi(2S)$ states, as well as $\\eta_c(1S)$ and $J/\\psi$ states, and then estimate the root-mean-square radii of both the $1S$ and $2S$ charmonium states. We also examine whether a series of the BS wave functions from the ground state to excited states can be described by a single set of the spin-independent and spin-dependent interquark potentials with a unique quark mass. It is found that the quark kinetic mass and, both the central and spin-spin c...
The Strong Decays of Orbitally Excited $B^{*}_{sJ}$ Mesons by Improved Bethe-Salpeter Method
Wang, Zhi-Hui; Fu, Hui-Feng; Jiang, Yue
2012-01-01
We calculate the masses and the strong decays of orbitally excited states $B_{s0}$, $B'_{s1}$, $B_{s1}$ and $B_{s2}$ by the improved Bethe-Salpeter method. The predicted masses of $B_{s0}$ and $B'_{s1}$ are $M_{B_{s0}}=5.723\\pm0.280 {\\rm GeV}$, $M_{B'_{s1}}=5.774\\pm0.330 {\\rm GeV}$. We calculate the isospin symmetry violating decay processes $B_{s0}\\to B_s \\pi$ and $B'_{s1}\\to B_s^* \\pi$ through $\\pi^0-\\eta$ mixing and get small widths. Considering the uncertainties of the masses, for $B_{s0}$ and $B'_{s1}$, we also calculate the OZI allowed decay channels: $B_{s0}\\to B\\bar K$ and $B'_{s1}\\to B^*\\bar K$. For $B_{s1}$ and $B_{s2}$, the OZI allowed decay channels $B_{s1}\\to B^{*}\\bar K$, $B_{s2}\\to B\\bar K$ and $B_{s2}\\to B^{*}\\bar K$ are studied. In all the decay channels, the reduction formula, PCAC relation and low energy theorem are used to estimate the decay widths. We also obtain the strong coupling constants $G_{B_{s0}B_s\\pi}$, $G_{B_{s0}B\\bar K}$, $G_{B'_{s1}B_s^*\\pi}$, $F_{B'_{s1}B_s^*\\pi}$, $G_{B'_{s1...
Boulanger, Paul; Chibani, Siwar; Le Guennic, Boris; Duchemin, Ivan; Blase, Xavier; Jacquemin, Denis
2014-10-14
We propose to use a blend of methodologies to tackle a challenging case for quantum approaches: the simulation of the optical properties of asymmetric fluoroborate derivatives. Indeed, these dyes, which present a low-lying excited-state exhibiting a cyanine-like nature, are treated not only with the Time-Dependent Density Functional Theory (TD-DFT) method to determine both the structures and vibrational patterns but also with the Bethe-Salpeter approach to compute both the vertical absorption and emission energies. This combination allows us to obtain 0-0 energies with a significantly improved accuracy compared to the "raw" TD-DFT estimates. We also discuss the impact of various declinations of the Polarizable Continuum Model (linear-response, corrected linear-response, and state-specific models) on the obtained accuracy. PMID:26588148
Accurate calculation of the x-ray absorption spectrum of water via the GW/Bethe-Salpeter equation
Gilmore, Keith; Vinson, John; Kas, Josh; Vila, Fernando; Rehr, John
2014-03-01
We calculate x-ray absorption spectra (XAS) of water within the OCEAN code, which combines plane-wave, pseudopotential electronic structure, PAW transition elements, GW self-energy corrections, and the NIST BSE solver. Due to the computational demands of this approach, our initial XAS calculations were limited to 17 molecule super cells. This lead to unphysical, size dependent effects in the calculated spectra. To treat larger systems, we extended the OCEAN interface to support well-parallelized codes such as QuantumESPRESSO. We also implemented an efficient interpolation scheme of Shirley. We applied this large-scale GW/BSE approach to 64 molecule unit cell structures of water obtained from classical DFT/MD and PIMD simulations. In concurrence with previous work, we find the calculated spectrum both qualitatively and quantitatively reproduces the experimental features. The agreement implies that structures based on PIMD, which are similar to the traditional distorted tetrahedral view, are consistent with experimental observations. Supported by the DOE CMCSN through DOE award DE-SC0005180 (Princeton University) and in part by DOE Grant No. DE-FG03-97ER45623 (JJR) with computer support from NERSC.
Towards a model of pion generalized parton distributions from Dyson-Schwinger equations
Moutarde, H. [CEA, Centre de Saclay, IRFU/Service de Physique Nucléaire, F-91191 Gif-sur-Yvette (France)
2015-04-10
We compute the pion quark Generalized Parton Distribution H{sup q} and Double Distributions F{sup q} and G{sup q} in a coupled Bethe-Salpeter and Dyson-Schwinger approach. We use simple algebraic expressions inspired by the numerical resolution of Dyson-Schwinger and Bethe-Salpeter equations. We explicitly check the support and polynomiality properties, and the behavior under charge conjugation or time invariance of our model. We derive analytic expressions for the pion Double Distributions and Generalized Parton Distribution at vanishing pion momentum transfer at a low scale. Our model compares very well to experimental pion form factor or parton distribution function data.
Yan, Jun; Jacobsen, Karsten W.; Thygesen, Kristian S.
2012-01-01
through the BSE using the statically screened interaction evaluated in the random phase approximation. For a representative set of semiconductors and insulators we find excellent agreement with experiments for the dielectric functions, onset of absorption, and lowest excitonic features. For the two......-dimensional systems of graphene and hexagonal boron-nitride (h-BN) we find good agreement with previous many-body calculations. For the graphene/h-BN interface we find that the fundamental and optical gaps of the h-BN layer are reduced by 2.0 and 0.7 eV, respectively, compared to freestanding h-BN. This reduction...
Enhanced transferability for Bethe-Salpeter Calculations
Shirley, Eric L.
2015-03-01
We have systematized projector-augmented-wave methods to reliably augment plane-wave/pseudopotential Bloch functions in atomic core regions for purposes of performing screening calculations, evaluating transition matrix elements, and evaluating Slater integrals in the condensed matter environment. This has improved the accuracy of core-hole screening, adherence to sum rules, and control of the strength of absorption features. This also ensures that transition matrix elements and concomitant core excitation spectra are reliable over significant energy ranges. To accomplish this, we improve the quality of the pseudopotentials (which become harder), extending norm conservation, and increasing the number of ``valence electrons.'' We present results for both insulators and metals, and for both core and valence excitations. Comparison to experimental data is a key part of this work. We also emphasize what approximations remain to be tackled in the treatment of electronic excitation spectra, many of which are more difficult to treat than what is within the scope of this work.
Electromagnetic Currents and the Blankenbecler-Sugar Equation
Coester, F
1993-01-01
The effective electromagnetic current density for a two-nucleon system that is described by the Blankenbecler-Sugar equation is derived. In addition to the single nucleon currents there are exchange currents of two different origins. The first is the exchange current that is required to compensate for the violation of the continuity equation in the impulse approximation. The second is an exchange current, which arises in the quasipotential reduction from the Bethe-Salpeter equation, and which represents effects of suppressed degrees of freedom. Explicit general expressions are given for both of these exchange currents. The results are applicable to both elastic and inelastic processes.
Electromagnetic currents and the Blankenbecler-Sugar equation
The effective electromagnetic current density for a two-nucleon system that is described by the Blankenbecler-Sugar equation is derived. In addition to the single nucleon currents there are exchange currents of two different origins. The first is the exchange current that is required to compensate for the violation of the continuity equation in the impulse approximation. The second is an exchange current, which arises in the quasipotential reduction from the Bethe-Salpeter equation and which represents effects of suppressed degrees of freedom. Explicit general expressions are given for both of these exchange currents. The results are applicable to both elastic and inelastic processes. 26 refs
Electromagnetic interactions for the two-body spectator equations
Adam, J; Gross, F; Gross, Franz
1998-01-01
This paper presents a new non-associative algebra which is used to (i) show how the spectator (or Gross) two-body equations and electromagnetic currents can be formally derived from the Bethe-Salpeter equation and currents if both are treated to all orders, (ii) obtain explicit expressions for the Gross two-body electromagnetic currents valid to any order, and (iii) prove that the currents so derived are exactly gauge invariant when truncated consistently to any finite order. In addition to presenting these new results, this work complements and extends previous treatments based largely on the analysis of sums of Feynman diagrams.
SU(N)-QCD2 meson equation in next-to-leading order
We compute the 1/N corrections to the meson equation in the regular cut-off scheme. We illustrate that although the quark and gluon self energy and vertex corrections do not vanish explicitly as in the singular cut-off scheme, their contributions to the meson Bethe-Salpeter equation get cancelled within the whole set of contributing diagrams. We also argue that 0(1/N) corrections to the meson equation remove the massless boson from the spectrum in accordance with the Coleman theorem. (author)
Hadronic bound states in SU(2) from Dyson-Schwinger equations
Vujinovic, Milan [Karl-Franzens-Universitaet Graz, Institut fuer Physik, Graz (Austria); Williams, Richard [Justus-Liebig-Universitaet Giessen, Institut fuer Theoretische Physik, Giessen (Germany)
2015-03-01
By using the Dyson-Schwinger/Bethe-Salpeter formalism in Euclidean spacetime, we calculate the ground state spectrum of J ≤ 1 hadrons in an SU(2) gauge theory with two fundamental fermions. We show that the rainbow-ladder truncation, commonly employed in QCD studies, is unsuitable for a description of an SU(2) theory. This we remedy by truncating at the level of the quark-gluon vertex Dyson-Schwinger equation in a diagrammatic expansion. Results obtained within this novel approach show good agreement with lattice studies. These findings emphasize the need to use techniques more sophisticated than rainbow-ladder when investigating generic strongly interacting gauge theories. (orig.)
From Bethe-Salpeter Wave Functions to Generalised Parton Distributions
Mezrag, C; Rodriguez-Quintero, J
2016-01-01
We review recent works on the modelling of Generalised Parton Distributions within the Dyson-Schwinger formalism. We highlight how covariant computations, using the impulse approximation, allows one to fulfil most of the theoretical constraints of the GPDs. Specific attention is brought to chiral properties and especially the so-called soft pion theorem, and its link with the Axial-Vector Ward-Takahashi identity. The limitation of the impulse approximation are also explained. Beyond impulse approximation computations are reviewed in the forward case. Finally, we stress the advantages of the overlap of lightcone wave functions, and possible ways to construct covariant GPD models within this framework, in a two-body approximation.
Schwinger-Dyson equations and the quark-antiquark static potential
Bicudo, P; Cardoso, M; Cardoso, N; Oliveira, O
2009-01-01
In lattice QCD, a confining potential for a static quark-antiquark pair can be computed with the Wilson loop technique. This potential, dominated by a linear potential at moderate distances, is consistent with the confinement with a flux tube, an extended and scalar system also directly observable in lattice QCD. Quantized flux tubes have also been observed in another class of confinement, the magnetic confinement in type II superconductors. On the other hand the solution of Schwinger Dyson Equations, say with the Landau gauge fixing and the truncation of the series of Feynman diagrams, already at the rainbow level for the self energy and at the ladder level for the Bethe Salpeter equation, provides a signal of a possible inverse quartic potential in momentum space derived from one gluon and one ghost exchange, consistent with confinement. Here we address the successes, difficulties and open problems of the matching of these two different perspectives of confinement, the Schwinger-Dyson perspective versus the...
A detailed study of nonperturbative solutions of two-body Dirac equations
Crater, H.W.; Becker, R.L.; Wong, C.Y.; Van Alstine, P.
1992-12-01
In quark model calculations of the meson spectrums fully covariant two-body Dirac equations dictated by Dirac's relativistic constraint mechanics gave a good fit to the entire meson mass spectrum for light quark mesons as well as heavy quark mesons with constituent world scalar and vector potentials depending on just one or two parameters. In this paper, we investigate the properties of these equations that made them work so well by solving them numerically for quantum electrodynamics (QED) and related field theories. The constraint formalism generates a relativistic quantum mechanics defined by two coupled Dirac equations on a sixteen component wave function which contain Lorentz covariant constituent potentials that are initially undetermined. An exact Pauli reduction leads to a second order relativistic Schroedinger-like equation for a reduced eight component wave function determined by an effective interaction -- the quasipotential. We first determine perturbatively to lowest order the relativistic quasipotential for the Schroedinger-like equation by comparing that form with one derived from the Bethe-Salpeter equation. Insertion of this perturbative information into the minimal interaction structures of the two-body Dirac equations then completely determines their interaction structures. Then we give a procedure for constructing the full sixteen component solution to our coupled first-order Dirac equations from a solution of the second order equation for the reduced wave function. Next, we show that a perturbative treatment of these equations yields the standard spectral results for QED and related interactions.
A detailed study of nonperturbative solutions of two-body Dirac equations
Crater, H.W.; Becker, R.L.; Wong, C.Y.; Van Alstine, P.
1992-12-01
In quark model calculations of the meson spectrums fully covariant two-body Dirac equations dictated by Dirac`s relativistic constraint mechanics gave a good fit to the entire meson mass spectrum for light quark mesons as well as heavy quark mesons with constituent world scalar and vector potentials depending on just one or two parameters. In this paper, we investigate the properties of these equations that made them work so well by solving them numerically for quantum electrodynamics (QED) and related field theories. The constraint formalism generates a relativistic quantum mechanics defined by two coupled Dirac equations on a sixteen component wave function which contain Lorentz covariant constituent potentials that are initially undetermined. An exact Pauli reduction leads to a second order relativistic Schroedinger-like equation for a reduced eight component wave function determined by an effective interaction -- the quasipotential. We first determine perturbatively to lowest order the relativistic quasipotential for the Schroedinger-like equation by comparing that form with one derived from the Bethe-Salpeter equation. Insertion of this perturbative information into the minimal interaction structures of the two-body Dirac equations then completely determines their interaction structures. Then we give a procedure for constructing the full sixteen component solution to our coupled first-order Dirac equations from a solution of the second order equation for the reduced wave function. Next, we show that a perturbative treatment of these equations yields the standard spectral results for QED and related interactions.
A detailed study of nonperturbative solutions of two-body Dirac equations
In quark model calculations of the meson spectrums fully covariant two-body Dirac equations dictated by Dirac's relativistic constraint mechanics gave a good fit to the entire meson mass spectrum for light quark mesons as well as heavy quark mesons with constituent world scalar and vector potentials depending on just one or two parameters. In this paper, we investigate the properties of these equations that made them work so well by solving them numerically for quantum electrodynamics (QED) and related field theories. The constraint formalism generates a relativistic quantum mechanics defined by two coupled Dirac equations on a sixteen component wave function which contain Lorentz covariant constituent potentials that are initially undetermined. An exact Pauli reduction leads to a second order relativistic Schroedinger-like equation for a reduced eight component wave function determined by an effective interaction -- the quasipotential. We first determine perturbatively to lowest order the relativistic quasipotential for the Schroedinger-like equation by comparing that form with one derived from the Bethe-Salpeter equation. Insertion of this perturbative information into the minimal interaction structures of the two-body Dirac equations then completely determines their interaction structures. Then we give a procedure for constructing the full sixteen component solution to our coupled first-order Dirac equations from a solution of the second order equation for the reduced wave function. Next, we show that a perturbative treatment of these equations yields the standard spectral results for QED and related interactions
Meson spectra from two-body dirac equations with minimal interactions
Many authors have used two-body relativistic wave equations with spin in nonperturbative numerical quark model calculations of the meson spectrum. Usually, they adopt a truncation of the Bethe-Salpeter equation of QED and/or scalar. QED and replace the static Coulomb interactions of those field theories with a semiphenomenological Q bar Q potential whose insertion in the Breit terms give the corresponding spin corrections. However, the successes of these wave equations in QED have invariably depended on perturbative treatment of the terms in each beyond the Coulomb terms. There have been no successful nonperturbative numerical test of two-body quantum wave equations in QED, because in most equations the effective potentials beyond the Coulomb are singular and can only be treated perturbatively. This is a glaring omission that we rectify here for the case of the two-body Dirac equations of constraint dynamics. We show in this paper that a nonperturbative numerical treatment of these equations for QED yields the same spectral results as a perturbative treatment of them which in turn agrees with the standard spectral results for positronium and muonium. This establishes that the vector and scalar interaction structures of our equations accurately incorporate field theoretic interactions in a bone fide relativistic wave equation. The last portion of this work will report recent quark model calculations using these equations with the Adler-Piran static Q bar Q potential
Relativistic two-and three-particle scattering equations using instant and light-front dynamics
Starting from the Bethe-Salpeter equation for two particles in the ladder approximation and integrating over the time component of momentum we derive three dimensional scattering integral equations satisfying constraints of unitarity and relativity, both employing the light-front and instant-form variables. The equations we arrive at are those first derived by Weinberg and by Blankenbecler and Sugar, and are shown to be related by a transformation of variables. Hence we show how to perform and relate identical dynamical calculation using these two equations. We extends this procedure to the case of three particles interacting via two-particle separable potentials. Using light-front and instant form variables we suggest a couple of three dimensional three-particle scattering equations satisfying constraints of two and three-particle unitarity and relativity. The three-particle light-front equation is shown to be approximately related by a transformation of variables to one of the instant-form three-particle equations. (author)
The neutron structure function F2n(x) is evaluated within the kinematic range 10-32D(x) and several assumptions on the high-x asymptotics of F2n(x)/F2p(x). It is shown that new measurements of F2D(x) in the range 0.6< x≤0.8 would substantially improve understanding of the relation between d and u valence quarks in the limit x→1
Markov-Yukawa transversality principle and 3D-4D interlinkage of Bethe-Salpeter amplitudes
This article is designed to focus attention on the Markov-Yukawa Transversality Principle (MYTP) as a novel paradigm for an exact 3D-4D interlinkage between the corresponding BSE amplitudes. This unique feature of MYTP owes its origin to a Lorentz- covariant 3D support to the BSE kernel. Two specific types of MYTP, which provide 3D support to the BSE kernel, are considered. Both lead to formally identical 3D BSE reductions but produces sharply different 4D structures. This is illustrated by the pion form factor. The reconstruction of the 4D qqq wave function is achieved by Green's function techniques
Accounting for the analytical properties of the quark propagator from Dyson-Schwinger equation
Dorkin, S M; Kampfer, B
2014-01-01
An approach based on combined solutions of the Bethe-Salpeter (BS) and Dyson-Schwinger (DS) equations within the ladder-rainbow approximation in the presence of singularities is proposed to describe the meson spectrum as quark antiquark bound states. We consistently implement into the BS equation the quark propagator functions from the DS equation, with and without pole-like singularities, and show that, by knowing the precise positions of the poles and their residues, one is able to develop reliable methods of obtaining finite interaction BS kernels and to solve the BS equation numerically. We show that, for bound states with masses $M 1 $ GeV, however, the propagator functions reveal pole-like structures. Consequently, for each type of mesons (unflavored, strange and charmed) we analyze the relevant intervals of $M$ where the pole-like singularities of the corresponding quark propagator influence the solution of the BS equation and develop a framework within which they can be consistently accounted for. The...
Beyond rainbow-ladder in bound state equations
In this work we devise a new method to study quark-anti-quark interactions beyond simple ladder-exchange that yield massless pions in the chiral limit. The method is based on the requirement to have a representation of the quark-gluon vertex that is explicitly given in terms of quark dressings functions. We outline a general procedure to generate the Bethe-Salpeter kernel for a given vertex representation. Our method allows not only the identification of the mesons' masses but also the extraction of their Bethe-Salpeter wave functions exposing their internal structure. We exemplify our method with vertex models that are of phenomenological interest. (orig.)
Wilson loop approach to the qqbar interaction problem
Brambilla, N.; Prosperi, G. M.
1995-01-01
It is shown that the semirelativistic $q \\bar{q}$ potential, the relativistic flux tube model and a confining Bethe--Salpeter equation can be derived from QCD first principles in a unified point of view.
Frederico, T; Pasquini, B; Salme', G
2009-01-01
The generalized parton distributions of the pion are studied within different light-front approaches for the quark-hadron and quark-photon vertices, exploring different kinematical regions in both the valence and non-valence sector. Moments of the generalized parton distributions which enter the definition of generalized form factors are also compared with recent lattice calculations.
Mainland, G.B.
1988-01-01
Zero four-momentum, helicity eigenstates of the Bethe--Salpeter equation are found for a composite system consisting of a charged, spin-0 constituent and a charged, spin- 1/2 constituent bound by minimal electrodynamics. The form of the Bethe--Salpeter equation used to describe the bound state includes the contributions from both single photon exchange (ladder approximation) and the ''seagull'' diagram. Attention is restricted to zero orbital angular momentum states since these appear to be the most interesting physically.
The mathematical statement of boundary problems is formulated for the quark potential QCD model on the basis of Schwinger-Dyson and Bethe-Salpeter equations in the case of the combination of Coulomb and linear potentials. Mathematical statement of problem for renormalization of the Schwinger-Dyson system is considered. Iterative method on the base of continuous analogue of the Newton method is presented for numerical solution of the Bethe-Salpeter equation in the framework of considered approach. Conditions of description of the mass and the leptonic decay constant of pion are discussed. (author). 15 refs., 4 tabs
Covariant meson-baryon scattering with chiral and large Nc constraints
We give a review of recent progress on the application of the relativistic chiral SU(3) Lagrangian to meson-baryon scattering. It is shown that a combined chiral and 1/Nc expansion of the Bethe-Salpeter interaction kernel leads to a good description of the kaon-nucleon, antikaon-nucleon and pion-nucleon scattering data typically up to laboratory momenta of plab ≅ 500 MeV. We solve the covariant coupled channel Bethe-Salpeter equation with the interaction kernel truncated to chiral order Q3 where we include only those terms which are leading in the large Nc limit of QCD. (orig.)
The unified BS wavefunctions of mesons with natural Jsup(PC)
From the Bethe-Salpeter equation with a spin-independent kernel, a unified wavefunction is derived for mesons with natural Jsup(PC). Masses of vector mesons calculated from this wavefunction yield a spectrum which agrees with the observed one. (orig.)
eta, eta-prime --> pi+ pi- l+ l- in a chiral unitary approach
Borasoy, B
2007-01-01
The decays eta, eta-prime --> pi+ pi- l+ l- with l = e, mu are investigated within a chiral unitary approach which combines the chiral effective Lagrangian with a coupled-channels Bethe-Salpeter equation. Predictions for the decay widths and spectra are given.
Effect of negative energy component on baryon spectra
Employing instantaneous Bethe-Salpeter equation and taking into account the confection of negative energy component of Dirac spinor to one-gluon exchange interaction, the calculation of the Δ, N baryon spectra is carried out. We find that the effect changes the potential parameters significantly, but leaves the global structures of spectrum almost untouched. (author)
(Pi+Pi-) Atom in Chiral Perturbation Theory
Ivanov, M. A.; Lyubovitskij, V. E.; Lipartia, E. Z.; Rusetsky, A. G.
1998-01-01
Hadronic (Pi+Pi-) atom is studied in the relativistic perturbative approach based on the Bethe-Salpeter equation. The general expression for the atom lifetime is derived. Lowest-order corrections to the relativistic Deser-type formula for the atom lifetime are evaluated within the Chiral Perturbation Theory.
Pions and Excited Scalars in Minkowski Space DSBSE Formalism
Šauli, Vladimír
2015-01-01
Roč. 54, č. 11 (2015), s. 4131-4141. ISSN 0020-7748 Institutional support: RVO:61389005 Keywords : non-perturbative QCD * mesons * Bethe-Salpeter equation * confinement Subject RIV: BE - Theoretical Physics Impact factor: 1.184, year: 2014
On the proton exchange contribution to electron-hydrogen atom elastic scattering
It is shown that the exchange contribution to the electron-proton potential Born term in elastic electron-hydrogen atom scattering arises as the non relativistic limit from the exchange of a proton between the two participant electrons - calculated from quantum electrodynamics including properly bound states (as solution of Bethe - Salpeter equation). (Author)
Relativistic Quark Model Calculation of the l1, l2 Coefficients of the Chiral Lagrangian
Llanes-Estrada, Felipe J.; Bicudo, Pedro
2002-01-01
We briefly report on a relativistic quark model scheme to calculate the O(P^4) pion-pion vertex in the planar approximation and in the chiral limit. The calculation is reduced to the solution of simple integral equations (Bethe-Salpeter like) by an effective use of chiral Ward Identities. Specific model computations are provided.
Renormalization of Optical Excitations in Molecules near a Metal Surface
García Lastra, Juan Maria; Thygesen, Kristian Sommer
2011-01-01
The lowest electronic excitations of benzene and a set of donor-acceptor molecular complexes are calculated for the gas phase and on the Al(111) surface using the many-body Bethe-Salpeter equation. The energy of the charge-transfer excitations obtained for the gas phase complexes are found to be...
Model comparison of Delta and Omega masses in a covariant Faddeev approach
Sanchis-Alepuz, Helios; Eichmann, Gernot; Williams, Richard
2011-01-01
We compute the vector-meson, nucleon and delta/omega-baryon masses and their evolution with the current-quark mass using a covariant generalized Bethe-Salpeter equation approach. The interaction kernel is truncated to a dressed gluon exchange. We study the model dependence of our results with the quark-gluon dressing to assess the validity of the truncation.
Scattering amplitudes are studied in scalar field theory. The aim of the work carried out is to obtain valid results for all values of the coupling constant, emphasis being given to high energy behavior. A perturbation approach is first presented, the various integral equations are then written in the framework of the multiperipheral and then Bethe-Salpeter models
The Spectrum of Diquark Composites in Cold Dense QCD
Shovkovy, I. A.
2000-01-01
The Bethe-Salpeter equations for spin zero diquark composites in the color superconducting phase of $N_f=2$ and $N_f=3$ cold dense QCD are studied. The explicit form of the spectrum of the diquarks with the quantum numbers of the (pseudo-) Nambu-Goldstone bosons is derived.
Ghost-gluon and ghost-quark bound states and their role in BRST quartets
Alkofer, Natalia
2011-01-01
A non-perturbative version of the BRST quartet mechanism in infrared Landau gauge QCD is proposed for transverse gluons and quarks. Based on the positivity violation for transverse gluons the content of the respective non-perturbative BRST quartet is derived. To identify the gluon's BRST-daughter and second parent state, a truncated Bethe-Salpeter equation for the gluon-(anti-)ghost bound state is investigated. We comment shortly on several equivalent forms of this equation. Repeating the same construction for quarks leads to a truncated Bethe-Salpeter equation for a fundamentally charged quark-(anti-)ghost bound state. It turns out that a cardinal input to this equation is given by the fully dressed quark-gluon vertex, and that it is indispensable to dress the quark-gluon vertex in this equation in order to obtain a consistent truncation.
Quasi-equilibrium optical nonlinearities in spin-polarized GaAs
Joshua, Arjun; V. Venkataraman
2007-01-01
Semiconductor Bloch equations, which microscopically describe the dynamics of a Coulomb interacting, spin-unpolarized electron-hole plasma, can be solved in two limits: the coherent and the quasi-equilibrium regime. These equations have been recently extended to include the spin degree of freedom, and used to explain spin dynamics in the coherent regime. In the quasi-equilibrium limit, one solves the Bethe-Salpeter equation in a two-band model to describe how optical absorption is affected by...
Calculation of the π Meson Electromagnetic Form Factor
王志刚; 汪克林; 完绍龙
2001-01-01
The modified flat-bottom potential (MFBP) is given by the combination of the flat-bottom potential with considerations for the infrared and ultraviolet asymptotic behaviour of the effective quark-gluon coupling. The πmeson electromagnetic form factor is calculated in the framework of the coupled Schwinger-Dyson equation andthe Bethe-Salpeter equation in the simplified impulse approximation (dressed vertex) with the MFBP. All ournumerical results give a good fit to experimental values.
Modeling the pion Generalized Parton Distribution
Mezrag, C
2015-01-01
We compute the pion Generalized Parton Distribution (GPD) in a valence dressed quarks approach. We model the Mellin moments of the GPD using Ans\\"atze for Green functions inspired by the numerical solutions of the Dyson-Schwinger Equations (DSE) and the Bethe-Salpeter Equation (BSE). Then, the GPD is reconstructed from its Mellin moment using the Double Distribution (DD) formalism. The agreement with available experimental data is very good.
Modeling the Pion Generalized Parton Distribution
Mezrag, C.
2016-02-01
We compute the pion Generalized Parton Distribution (GPD) in a valence dressed quarks approach. We model the Mellin moments of the GPD using Ansätze for Green functions inspired by the numerical solutions of the Dyson-Schwinger Equations (DSE) and the Bethe-Salpeter Equation (BSE). Then, the GPD is reconstructed from its Mellin moment using the Double Distribution (DD) formalism. The agreement with available experimental data is very good.
Normalization of the covariant three-body bound state vertex function
Adam, J; Savkli, C; Van Orden, J W; Gross, Franz; Savkli, Cetin
1997-01-01
The normalization condition for the relativistic three nucleon Bethe-Salpeter and Gross bound state vertex functions is derived, for the first time, directly from the three body wave equations. It is also shown that the relativistic normalization condition for the two body Gross bound state vertex function is identical to the requirement that the bound state charge be conserved, proving that charge is automatically conserved by this equation.
Nonperturbative Aspects of Axial Vector Vertex
ZONG Hong-Shi; CHEN Xiang-Song; WANG Fan; CHANG Chao-Hsi; ZHAO En-Guang
2002-01-01
It is shown how the axial vector current of current quarks is related to that of constituent quarks within the framework of the global color symmetry model.Gluon dressing of the axial vector vertex and the quark self-energy functions are described by the inhomogeneous Bethe-Salpeter equation in the ladder approximation and the Schwinger Dyson equation in the rainbow approximation,respectively.
Particle-vibration coupling within covariant density functional theory
Litvinova, E.; Ring, P.; Tselyaev, V.
2007-01-01
Covariant density functional theory, which has so far been applied only within the framework of static and time dependent mean field theory is extended to include Particle-Vibration Coupling (PVC) in a consistent way. Starting from a conventional energy functional we calculate the low-lying collective vibrations in Relativistic Random Phase Approximation (RRPA) and construct an energy dependent self-energy for the Dyson equation. The resulting Bethe-Salpeter equation in the particle-hole ($ph...
Decay constants of the pseudoscalar charmonium and bottomonium
In this Letter, we investigate the structures of the pseudoscalar charmonium and bottomonium in the framework of the coupled rainbow Schwinger-Dyson equation and ladder Bethe-Salpeter equation with the confining effective potential (infrared modified flat bottom potential). As the current masses are very large, the dressing or renormalization for the c and b quarks are tender, however, mass poles in the timelike region are absent. The Euclidean time Fourier transformed quark propagator has no mass poles in the timelike region which naturally implements confinement. The Bethe-Salpeter wavefunctions for those mesons have the same type (Gaussian type) momentum dependence and center around zero momentum with spatial extension to about q2=1 GeV2 which happen to be the energy scale for chiral symmetry breaking, the strong interactions in the infrared region result in bound states. The decay constants for those pseudoscalar heavy quarkonia are compatible with the values of experimental extractions and theoretical calculations
Sangalli, Davide; Manzoni, Cristian; Cerullo, Giulio; Marini, Andrea
2016-01-01
The calculation of the equilibrium optical properties of bulk silicon by using the Bethe--Salpeter equation solved in the Kohn--Sham basis represents a cornerstone in the development of an ab--initio approach to the optical and electronic properties of materials. Nevertheless calculations of the {\\em transient} optical spectrum using the same efficient and successful scheme are scarce. We report, here, a joint theoretical and experimental study of the transient reflectivity spectrum of bulk silicon. Femtosecond transient reflectivity is compared to a parameter--free calculation based on the non--equilibrium Bethe--Salpeter equation. By providing an accurate description of the experimental results we disclose the different phenomena that determine the transient optical response of a semiconductor. We give a parameter--free interpretation of concepts like bleaching, photo--induced absorption and stimulated emission, beyond the Fermi golden rule. We also introduce the concept of optical gap renormalization, as a...
Symmetry-preserving contact interaction model for heavy-light mesons
Serna, F E; Krein, G
2016-01-01
We use a symmetry-preserving regularization method of ultraviolet divergences in a vector-vector contact interac- tion model for low-energy QCD. The contact interaction is a representation of nonperturbative kernels used Dyson-Schwinger and Bethe-Salpeter equations. The regularization method is based on a subtraction scheme that avoids standard steps in the evaluation of divergent integrals that invariably lead to symmetry violation. Aiming at the study of heavy-light mesons, we have implemented the method to the pseudoscalar pion and Kaon mesons. We have solved the Dyson-Schwinger equation for the u, d and s quark propagators, and obtained the bound-state Bethe-Salpeter amplitudes in a way that the Ward-Green-Takahashi identities reflecting global symmetries of the model are satisfied for arbitrary routing of the momenta running in loop integrals.
Schleife, A; Bechstedt, F
2012-02-15
Many-body perturbation theory is applied to compute the quasiparticle electronic structures and the optical-absorption spectra (including excitonic effects) for several transparent conducting oxides. We discuss HSE+G{sub 0}W{sub 0} results for band structures, fundamental band gaps, and effective electron masses of MgO, ZnO, CdO, SnO{sub 2}, SnO, In{sub 2}O{sub 3}, and SiO{sub 2}. The Bethe-Salpeter equation is solved to account for excitonic effects in the calculation of the frequency-dependent absorption coefficients. We show that the HSE+G{sub 0}W{sub 0} approach and the solution of the Bethe-Salpeter equation are very well-suited to describe the electronic structure and the optical properties of various transparent conducting oxides in good agreement with experiment.
Some issues linked to the description of systems in strong interaction
In the first part of this work we have dealt with some issues that are relevant in the area of nucleonic resonances within different constituent quark models. In this context we have concentrated on the theoretical description of Pi and Nu decays for N and Delta resonances. The results obtained point to the necessity of a more microscopic description of the dynamics which is at the same time responsible for the binding of quarks inside baryons and the decay of the latter ones. In the second part we have contributed to the study of crossed two-boson exchanges in the Bethe-Salpeter equation as well as to the investigation of different three-dimensional approaches that follow from the Bethe-Salpeter equation in a certain non-relativistic reduction scheme. These one include in particular an equation whose interaction depends on the total energy of the system. It was shown that such an equation is able to account for a certain number of properties of Bethe-Salpeter equation, in particular, that there also arise abnormal solutions in such an approach. (author)
First-Principles Structural and Electronic Characterization of Ordered SiO2 Nanowires
Martínez, José I.; Calle-Vallejo, Federico; Krowne, Clifford M.; Alonso, Julio A.
2012-01-01
Density functional theory and molecular dynamics simulations have been used to optimize the structure of nanowires of SiO2. The starting structures were based on b-cristobalite, orthotridymite, b-tridymite, and rutile crystals. The analysis of the electronic structure has been validated by many-body perturbation calculations using the G0W0 and GW + Bethe-Salpeter equation approximations, in order to account for quasi-particle and excitonic effects. The calculations indicate that many of these...
Communication: Strong excitonic and vibronic effects determine the optical properties of Li₂O₂
García Lastra, Juan Maria; Bass, J. D.; Thygesen, Kristian Sommer
2011-01-01
The band structure and optical absorption spectrum of lithium peroxide (Li2O2) is calculated from first-principles using the G0W0 approximation and the Bethe-Salpeter equation, respectively. A strongly localized (Frenkel type) exciton corresponding to the π*→σ* transition on the O2 −2 peroxide ion...... of the high potential losses and low current densities, which are presently limiting the performance of Li-air batteries....
Lubatsch, Andreas; Frank, Regine
2012-01-01
We report a quantum field theoretical description of light transport and random lasing. The Bethe-Salpeter equation is solved including maximally crossed diagrams and non-elastic scattering. This is the first theoretical framework that combines so called off-shell scattering and lasing in random media. We present results for the self-consistent scattering mean free path that varies over the width of the sample. Further we discuss the density dependent correlation length of self-consistent tra...
Impact of Weak Localization on Wave Dynamics: Crossover from Quasi-1D to Slab Geometry
Zhang, Z. Q.; Cheung, S. K.; X. D. Zhang; Chabanov, A. A.; Genack, A. Z.
2005-01-01
We study the dynamics of wave propagation in nominally diffusive samples by solving the Bethe-Salpeter equation with recurrent scattering included in a frequency-dependent vertex function, which renormalizes the mean free path of the system. We calculate the renormalized time-dependent diffusion coefficient, $D(t)$, following pulsed excitation of the system. For cylindrical samples with reflecting side walls and open ends, we observe a crossover in dynamics in the transformation from...
Scalar bosons in Minimal and Ultraminimal Technicolor: Masses, trilinear couplings and widths
Doff, A.(Universidade Tecnológica Federal do Paraná – UTFPR – DAFIS, Av. Monteiro Lobato Km 04, 84016-210 Ponta Grossa, PR, Brazil); Natale, A. A.
2009-01-01
We compute masses, trilinear self-couplings and decay widths into weak bosons of the scalar composite bosons in the case of the Minimal and Ultraminimal technicolor models. The masses, computed via the Bethe-Salpeter equation, turn out to be light and the trilinear couplings smaller than the one that would be expected when compared to a fundamental Standard Model scalar boson with the same mass. The decay widths into electroweak bosons of the Ultraminimal model scalars bosons are much smaller...
Mass and width of a composite Higgs boson
Doff, A.(Universidade Tecnológica Federal do Paraná – UTFPR – DAFIS, Av. Monteiro Lobato Km 04, 84016-210 Ponta Grossa, PR, Brazil); Natale, A. A.
2009-01-01
The scalar Higgs boson mass in a Technicolor model was obtained by Elias and Scadron with the analysis of an homogeneous Bethe-Salpeter equation (BSE), however it was performed before the most recent developments of walking gauge theories. It was not observed in their work that dynamically generated technifermion mass may vary according to the theory dynamics that forms the scalar bound state. This will be done in this work and we also call attention that their calculation must change to take...
Theory of Exciton Energy Transfer in Carbon Nanotube Composites
Davoody, A. H.; F Karimi; Arnold, M. S.; Knezevic, I.
2016-01-01
We compute the exciton transfer (ET) rate between semiconducting single-wall carbon nanotubes (SWNTs). We show that the main reasons for the wide range of measured ET rates reported in the literature are 1) exciton confinement in local quantum wells stemming from disorder in the environment and 2) exciton thermalization between dark and bright states due to intratube scattering. The SWNT excitonic states are calculated by solving the Bethe-Salpeter equation using tight-binding basis functions...
On the covariant relativistic separable kernel
Bondarenko, S G; Rogochaya, E P; Yanev, Y
2008-01-01
Two different methods of the covariant relativistic separable kernel construction in the Bethe-Salpeter approach are considered. One of them leads in the center-of-mass system of two particles to the quasipotential equation. The constructed 4-dimensional covariant functions are used to reproduce neutron-proton phase shifts for total angular momenta $J=0,1$. Obtained results are compared with other model calculations.
The Productions of $X(3940)$ and $X(4160)$ in $B_c$ decays
Wang, Zhi-Hui; Wang, Tian-hong; Jiang, Yue; Wang, Guo-Li
2016-01-01
Considering $X(3940)$ and $X(4160)$ as $\\eta_c(3S)$ and $\\eta_c(4S)$, we study the productions of $X(3940)$ and $X(4160)$ in exclusive weak decays of $B_c$ meson by the improved Bethe-Salpeter(B-S) Method. Using the relativistic B-S equation and Mandelstam formalism, we calculate the corresponding decay form factors. The predictions of the corresponding branching ratios are: $Br(B_c^+\\to X(3940)e^+\
We investigate relativistic bound states for a hypothetical light scalar gluino pair (gluinonium), in the framework of the covariant Bethe-Salpeter equation (BSE). In this paper, we derive, from the covariant BSE for a fermion-anti-fermion system, using charge conjugation, the corresponding bound-state equation for a gluino pair and we then formulate, for a static harmonic kernel, the coupled differential equations for the corresponding static Bethe-Salpeter amplitude. The steps of our approach then include a numerical solution of the Bethe-Salpeter amplitude for a two-body interaction consisting of scalar, pseudo-scalar, and four-vector components and the determination of the energy spectrum for the ground and the radially excited states of massive gluinonium. We found the energy spectrum and radial distributions of fundamental and excited states of gluinonium. The comparison of the values obtained in the extreme relativistic case with the corresponding values predicted by a harmonic oscillator potential model shows that there is good agreement between the two formulations. The predictions of the binding energy of glunionium in the non-relativistic model are however systematically higher. (author)
Beyond the Tamm-Dancoff approximation for extended systems using exact diagonalization
Sander, Tobias; Maggio, Emanuele; Kresse, Georg
2015-07-01
Linear optical properties can be accurately calculated using the Bethe-Salpeter equation. After introducing a suitable product basis for the electron-hole pairs, the Bethe-Salpeter equation is usually recast into a complex non-Hermitian eigenvalue problem that is difficult to solve using standard eigenvalue solvers. In solid-state physics, it is therefore common practice to neglect the problematic coupling between the positive- and negative-frequency branches, reducing the problem to a Hermitian eigenvalue problem [Tamm-Dancoff approximation (TDA)]. We use time-inversion symmetry to recast the full problem into a quadratic Hermitian eigenvalue problem, which can be solved routinely using standard eigenvalue solvers even at a finite wave vector q . This allows us to access the importance of the coupling between the positive- and negative-frequency branch for prototypical solids. As a starting point for the Bethe-Salpeter calculations, we use self-consistent Green's-function methods (GW ), making the present scheme entirely ab initio. We calculate the optical spectra of carbon (C), silicon (Si), lithium fluoride (LiF), and the cyclic dimer Li2F2 and discuss why the differences between the TDA and the full solution are tiny. However, at finite momentum transfer q , significant differences between the TDA and our exact treatment are found. The origin of these differences is explained.
Spectroscopy of mesons in the QCD-inspired potential model with harmonic oscillator approximation
The spectrum of pseudoscalar, scalar, vector and axial-vector mesons are investigated in the frame of QCD-inspired potential model with harmonic oscillator approximation. Numerical solutions of the Bethe-Salpeter (BS) equation with the using of continuous analogy of Newton's method (CANM) have been obtained. It was shown that solutions of BS equation in harmonic approximation at quantity level describes observed spectrum of mesons and their radial- and orbital-excited states. The contrary 'progonka' (driving) method for numerical solution of the BS equation was briefly described. (author). 9 refs.; 4 tabs
Scalar tetraquark boundstates in a covariant DSE-BSE approach
The bound state of the scalar tetraquark with quantum numbers 0+ is solved via a Fadeev-like equation. The genuine four-body equation is reduced to an effective two-body problem using a meson-meson/antidiquark-diquark picture. All ingredients of the boundstate equation are calculated in a covariant Dyson-Schwinger/Bethe-Salpeter approach employing a rainbow-ladder truncation together with the Maris-Tandy effective interaction. First results hinting at a bound mass in the 450 MeV region are presented.
A divergence-free method to extract observables from correlation functions
Correlation functions provide information on the properties of mesons in vacuum and of hot nuclear matter. In this work, we present a new method to derive a well-defined spectral representation for correlation functions. Combining this method with the quark gap equation and the inhomogeneous Bethe-Salpeter equation in the rainbow-ladder approximation, we calculate in-vacuum masses of light mesons and the electrical conductivity of the quark-gluon plasma. The analysis can be extended to other observables of strong-interaction systems
A divergence-free method to extract observables from correlation functions
Qin, Si-xue, E-mail: sixueqin@th.physik.uni-frankfurt.de
2015-03-06
Correlation functions provide information on the properties of mesons in vacuum and of hot nuclear matter. In this work, we present a new method to derive a well-defined spectral representation for correlation functions. Combining this method with the quark gap equation and the inhomogeneous Bethe-Salpeter equation in the rainbow-ladder approximation, we calculate in-vacuum masses of light mesons and the electrical conductivity of the quark-gluon plasma. The analysis can be extended to other observables of strong-interaction systems.
Relativistic proton-nucleus scattering and one-boson-exchange models
Relativistic p-40Ca elastic scattering observables are calculated using four sets of relativistic NN amplitudes obtained from different one-boson-exchange (OBE) models. The first two sets are based upon a relativistic equation in which one particle is on mass shell and the other two sets are obtained from a quasipotential reduction of the Bethe-Salpeter equation. Results at 200, 300, and 500 MeV are presented for these amplitudes. Differences between the predictions of these models provide a study of the uncertainty in constructing Dirac optical potentials from OBE-based NN amplitudes
General QED/QCD aspects of simple systems
This paper discusses the following topics: renormalization theory; the Kinoshita-Lee-Nauenberg theorem; the Yennie-Frautschi-Suura relation; scale invariance at large momentum transfer; scaling and scaling violation at large momentum transfers; low-energy theorem in Compton scattering; does the perturbation series in QED converge; renormalization of the weak angle Θw; the Nambu-Bethe-Salpeter (NBS) equation; the decay rate of 3S, positronium; radiative corrections to QCD Born cross section; and progress on the relativistic 2-body equation
Static correlation beyond the random phase approximation
Olsen, Thomas; Thygesen, Kristian Sommer
2014-01-01
derived from Hedin's equations (Random Phase Approximation (RPA), Time-dependent Hartree-Fock (TDHF), Bethe-Salpeter equation (BSE), and Time-Dependent GW) all reproduce the correct dissociation limit. We also show that the BSE improves the correlation energies obtained within RPA and TDHF significantly...... for intermediate binding distances. A Hubbard model for the dimer allows us to obtain exact analytical results for the various approximations, which is readily compared with the exact diagonalization of the model. Moreover, the model is shown to reproduce all the qualitative results from the ab initio...
Excited hadrons and the analytical structure of bound-state interaction kernels
El-Bennich, Bruno; Rojas, Eduardo; Serna, Fernando E
2016-01-01
We highlight Hermiticity issues in bound-state equations whose kernels are subject to a highly asymmetric mass and momentum distribution and whose eigenvalue spectrum becomes complex for radially excited states. We trace back the presence of imaginary components in the eigenvalues and wave functions to truncation artifacts and suggest how they can be eliminated in the case of charmed mesons. The solutions of the gap equation in the complex plane, which play a crucial role in the analytic structure of the Bethe-Salpeter kernel, are discussed for several interaction models and qualitatively and quantitatively compared to analytic continuations by means of complex-conjugate pole models fitted to real solutions.
Hyperon elastic electromagnetic form factors in the space-like momentum region
Sanchis-Alepuz, Helios [Justus-Liebig-Universitaet Giessen, Institut fuer Theoretische Physik, Giessen (Germany); Karl-Franzens-Universitaet Graz, Institut fuer Physik, Graz (Austria); Fischer, Christian S. [Justus-Liebig-Universitaet Giessen, Institut fuer Theoretische Physik, Giessen (Germany)
2016-02-15
We present a calculation of the electric and magnetic form factors of ground-state octet and decuplet baryons including strange quarks. We work with a combination of Dyson-Schwinger equations for the quark propagator and covariant Bethe-Salpeter equations describing baryons as bound states of three (non-perturbative) quarks. Our form factors for the octet baryons are in good agreement with corresponding lattice data at finite Q{sup 2}; deviations in some isospin channels for the magnetic moments can be explained by missing meson cloud effects. At larger Q{sup 2} our quark core calculation has predictive power for both, the octet and decuplet baryons. (orig.)
'Relativistic' quark model for mesons with flavour-independent potential
On the base of the Bethe-Salpeter equation in instantaneous approximation a unified model for the mass spectrum of the mesons was designed. The 'relativistic' structure of the Bethe-Salpeter equation allows a natural inclusion of the spin dependences and an extension of the model to small quark masses. The model contains as essential property two potential contributions where one represents the one-gluon exchange while the other represents the confinement potential. The annihilation of qanti q into gluons was not regarded. The spectrum and the amplitudes of the Bethe-Salpeter equation were solved approximatively in numerical way for the lowest states. The free parameters of the model were determined by a fit of the spectrum to a wellknown part of the meson spectrum. The results yield even at small quark masses a quantitatively good picture for all meson families. The result shows that the spectra of the heavy and light mesons can be described by a flavor-independent potential which contains 5 free parameters. Both the internal spin dependent structure and the absolute position of the families can so correctly be described. Especially the position of the D, Ds, and B states and the position of the uanti u, danti d states can be simultaneously described by a constant C in the long-range part of the potential. The constant C is thereby essentially determined by the splitting between the Υ family and the B family repectively Ψ and D family. The 3S1-3D1 respectively the 3P2-3F2 configuration mixing was regarded. The results show that this mixing is negligibly small. (orig./HSI)
Light-front Hamiltonian and path integral formulations of large N scalar QCD2
Recently Grinstein, Jora and Polosa (2009) have studied a model of large N scalar quantum chromodynamics (QCD) in one-space one-time dimensions (cf. G. 't Hooft (1974) ). This theory admits a Bethe-Salpeter equation describing the discrete spectrum of qq¯ bound states. They consider the gauge fields in the adjoint representation of SU(N) and the scalar fields in the fundamental representation. The theory is asymptotically free and linearly confining. In this work, we present the light-front quantization of this theory using the Hamiltonian and path integral formulations under appropriate light-cone gauges.
Light-front Hamiltonian and path integral formulations of large N scalar QCD{sub 2}
Kulshreshtha, Usha, E-mail: ushakulsh@gmail.com [Department of Physics, Kirori Mal College, University of Delhi, Delhi-110007 (India); Kulshreshtha, D.S., E-mail: dskulsh@gmail.com [Department of Physics and Astrophysics, University of Delhi, Delhi-110007 (India); Vary, J.P., E-mail: jvary@iastate.edu [Department of Physics and Astronomy, Iowa State University, Ames, IA 50011 (United States)
2012-02-14
Recently Grinstein, Jora and Polosa (2009) have studied a model of large N scalar quantum chromodynamics (QCD) in one-space one-time dimensions (cf. G. 't Hooft (1974) ). This theory admits a Bethe-Salpeter equation describing the discrete spectrum of qq{sup Macron} bound states. They consider the gauge fields in the adjoint representation of SU(N) and the scalar fields in the fundamental representation. The theory is asymptotically free and linearly confining. In this work, we present the light-front quantization of this theory using the Hamiltonian and path integral formulations under appropriate light-cone gauges.
Light-front Hamiltonian and path integral formulations of large N scalar QCD2
Kulshreshtha, Usha; Kulshreshtha, D. S.; Vary, J. P.
2012-02-01
Recently Grinstein, Jora and Polosa (2009) [5] have studied a model of large N scalar quantum chromodynamics (QCD) in one-space one-time dimensions (cf. G. 't Hooft (1974) [6]). This theory admits a Bethe-Salpeter equation describing the discrete spectrum of qqbar bound states. They consider the gauge fields in the adjoint representation of SU (N) and the scalar fields in the fundamental representation. The theory is asymptotically free and linearly confining. In this work, we present the light-front quantization of this theory using the Hamiltonian and path integral formulations under appropriate light-cone gauges.
Imaging dynamical chiral symmetry breaking: pion wave function on the light front
Chang, Lei; Cobos-Martinez, J J; Roberts, C D; Schmidt, S M; Tandy, P C
2013-01-01
We project onto the light-front the pion's Poincare'-covariant Bethe-Salpeter wave-function, obtained using two different approximations to the kernels of QCD's Dyson-Schwinger equations. At an hadronic scale both computed results are concave and significantly broader than the asymptotic distribution amplitude, \\phi_\\pi^{asy}(x)=6 x(1-x); e.g., the integral of \\phi_\\pi(x)/\\phi_\\pi^{asy}(x) is 1.8 using the simplest kernel and 1.5 with the more sophisticated kernel. Independent of the kernels, the emergent phenomenon of dynamical chiral symmetry breaking is responsible for hardening the amplitude.
Impact of weak localization in the time domain
Cheung, S. K.; Zhang, X.; Zhang, Z. Q.; Chabanov, A. A.; Genack, A. Z.
2003-01-01
We find a renormalized "time-dependent diffusion coefficient", D(t), for pulsed excitation of a nominally diffusive sample by solving the Bethe-Salpeter equation with recurrent scattering. We observe a crossover in dynamics in the transformation from a quasi-1D to a slab geometry implemented by varying the ratio of the radius, R, of the cylindrical sample with reflecting walls and the sample length, L. Immediately after the peak of the transmitted pulse, D(t) falls linearly with a nonuniversa...
Renormalization of Optical Excitations in Molecules near a Metal Surface
García Lastra, Juan Maria; Thygesen, Kristian Sommer
2011-01-01
consequence we find that close to the metal surface the optical gap of benzene can exceed its quasiparticle gap. A classical image charge model for the screened Coulomb interaction can account for all these effects which, on the other hand, are completely missed by standard time-dependent density functional......The lowest electronic excitations of benzene and a set of donor-acceptor molecular complexes are calculated for the gas phase and on the Al(111) surface using the many-body Bethe-Salpeter equation. The energy of the charge-transfer excitations obtained for the gas phase complexes are found to be...
Three-particle correlation from a Many-Body Perspective: Trions in a Carbon Nanotube
Deilmann, Thorsten; Drüppel, Matthias; Rohlfing, Michael
2016-01-01
Trion states of three correlated particles (e.g., two electrons and one hole) are essential to understand the optical spectra of doped or gated nanostructures, like carbon nanotubes or transition-metal dichalcogenides. We develop a theoretical many-body description for such correlated states using an ab-initio approach. It can be regarded as an extension of the widely used $GW$ method and Bethe-Salpeter equation, thus allowing for a direct comparison with excitons. We apply this method to a s...
Relativistic description of quark-antiquark bound states. Spin-independent treatment
We present the results of a detailed study of light- and heavy-quark--antiquark bound states in the context of the reduced Bethe-Salpeter equation with static vector and scalar interactions. In the present paper, we consider the spin-averaged spectra. Spin effects are considered in a separate paper. We find that this approach, although apparently successful for the heavy-quark b bar b and c bar c states, fails for the s bar s, l bar l, and light-heavy states. The reasons for the failure are intrinsic to the method, as we discuss. Difficulties are already evident for the c bar c states
Research in theoretical nuclear physics. Progress report
In the past eight months of the present three year contract there have been three major achievements which have set the stage for realistic calculations of hadron-hadron interactions in nuclei and hypernuclei. These achievements are : (a) a solution of the instantaneous Bethe-Salpeter two particle equation has been obtained for the first time; (b) elimination of Van der Waal-like interactions in calculations of hadron-hadron interactions; and (c) the ability to make full use of the CSPI/MAP-6400 array processor capabilities has been demonstrated. The significance of each of these achievements are outlined
NJL model approach to diquarks and baryons in quark matter
Blaschke, D.; Dubinin, A.; Zablocki, D.
2015-01-01
We describe baryons as quark-diquark bound states at finite temperature and density within the NJL model for chiral symmetry breaking and restoration in quark matter. Based on a generalized Beth-Uhlenbeck approach to mesons and diquarks we present in a first step the thermodynamics of quark-diquark matter which includes the Mott dissociation of diquarks at finite temperature. In a second step we solve the Bethe-Salpeter equation for the baryon as a quark-diquark bound state in quark-diquark m...
Introduction to recoil effects in bound state problems
A description is given of some of the considerations which are necessary to treat two-body hydrogen-like systems when the electron's relativistic properties must be taken into account. Most modern approaches to the two-body problem are based on the physics of the Bethe-Salpeter approach, although the methodology is different. One uses some three-dimensional reference equation which incorporates as much physics as possible and the corrections appears as four-dimensinal kernels which are treated by a procedure resembling usual perturbuation theory. An example is given where both reduced mass effects and relativistic effects are treated in a unified approach
Analysis of πN → 2πN reactions within the Giessen coupled-channel model
Shklyar, Vitaly; Lenske, Horst; Mosel, Ulrich [Institut fuer Theoretische Physik, Justus-Liebig-Universitaet Giessen (Germany)
2014-07-01
An unitary coupled-channel Lagrangian model is developed for simultaneous analysis of pion- and photon-induced reactions in the resonance energy region. The πN, ρN, πΔ, σN, ηN, ωN, KΛ, KΣ final states are treated on the same basis. The three-body unitarity is approximately maintained up to interference between different isobar channels in Bethe-Salpeter equation. Results of the analysis of the π{sup -}p → π{sup 0}π{sup 0} n reaction in the first resonance energy region are presented and discussed.
The nucleon-nucleon scattering and Δ degrees of freedom
The authors report the results of a study of the NN-scattering below Esub(lab)=350 MeV, with and without Δ degrees of freedom. At these energies the Δ can be treated as elementary. The study is based on the numerical calculation of the relativistic T-matrix in the full momentum-spin space, instead of a generally used partial wave expansion. The relativistic T-matrix can be found by solving the Bethe-Salpeter equation. The authors have chosen the stationary approach which for the case of a T-matrix without Δ degrees of freedom corresponds with the Blankenbecler-Sugar approximation. (Auth.)
Gordon decompositions for γ-type matrices and some of their applications
Some decomposotion formulas of γ-type matrices are derived based on Gordon identities. As and illustration of the application of these formulas, the one gluon exchange potential between quark and antiquark is rederived, which appears to be different from that obtained by Faessler, et al. As another illustration, the correct reduction of the γ-matrices appearing in the kernel function of Bethe-Salpeter equation for quark-antiquark system is achieved and yields an expression different from that derived by Mitre whose calculation was grounded on a wrong decomposition formula for one γ-type matrix
无
2004-01-01
At the beginning of 16th century, mathematicians found it easy to solve equations of the first degree(linear equations, involving x) and of the second degree(quadratic equatiorts, involving x2). Equations of the third degree(cubic equations, involving x3)defeated them.
Exploring dynamical gluon mass generation in three dimensions
Cornwall, John M
2015-01-01
In the d=3 gluon mass problem in pure-glue non-Abelian $SU(N)$ gauge theory we pay particular attention to the observed (in Landau gauge) violation of positivity for the spectral function of the gluon propagator. This causes a large bulge in the propagator at small momentum. Mass is defined through $m^{-2}=\\Delta (p=0)$, where $\\Delta(p)$ is the scalar function for the gluon propagator in some chosen gauge, it is not a pole mass and is generally gauge-dependent, except in the gauge-invariant Pinch Technique (PT). We truncate the PT equations with a new method called the vertex paradigm that automatically satisfies the QED-like Ward identity relating the 3-gluon PT vertex function with the PT propagator. The mass is determined by a homogeneous Bethe-Salpeter equation involving this vertex and propagator. This gap equation also encapsulates the Bethe-Salpeter equation for the massless scalar excitations, essentially Nambu-Goldstone fields, that necessarily accompany gauge-invariant gluon mass. The problem is to...
Quasiequilibrium optical nonlinearities from spin-polarized carriers in GaAs
Joshua, Arjun; Venkataraman, V.
2008-02-01
Semiconductor Bloch equations, which microscopically describe the dynamics of a Coulomb interacting, spin-unpolarized electron-hole plasma, can be solved in two limits: the coherent and the quasiequilibrium regimes. These equations have been recently extended to include the spin degree of freedom and used to explain spin dynamics in the coherent regime. In the quasiequilibrium limit, one solves the Bethe-Salpeter equation in a two-band model to describe how optical absorption is affected by Coulomb interactions within a spin unpolarized plasma of arbitrary density. In this work, we modified the solution of the Bethe-Salpeter equation to include spin polarization and light holes in a three-band model, which allowed us to account for spin-polarized versions of many-body effects in absorption. The calculated absorption reproduced the spin-dependent, density-dependent, and spectral trends observed in bulk GaAs at room temperature, in a recent pump-probe experiment with circularly polarized light. Hence, our results may be useful in the microscopic modeling of density-dependent optical nonlinearities due to spin-polarized carriers in semiconductors.
The relativistic and nonrelativistic quark-antiquark bound state problem in a Wilson loop context
Brambilla, Nora
1996-01-01
Taking advantage of a semirelativistic and a full relativistic representation of the quark propagator in an external field we present an unified derivation of the semirelativistic potential and of a Bethe-Salpeter like equation for the quark-antiquark system. We consider three different models for the evaluation of the Wilson loop: the Modified Area Law model (MAL), the Stochastic Vacuum Model (SVM) and the Dual QCD (DQCD). We compare the corresponding potentials and show that they all agree at the short and the long distances. In the case of the Bethe-Salpeter equation we treat explicitly only the MAL model and give an expression for the kernel. Then we show that an effective mass operator can be obtained which agrees with the MAL potential in the semirelativistic limit. In the light quark mass limit this mass operator produces straight Regge trajectories with Nambu-Goto slope in agreement with the data. Finally we briefly discuss the mass independence of the hyperfine splitting in the heavy-light case.
String equation from field equation
Gurovich, V T
1996-01-01
It is shown that the string equation can be obtain from field equations. Such work is performed to scalar field. The equation obtained in nonrelativistic limit describes the nonlinear string. Such string has the effective elasticity connencted with the local string curvature. Some examples of the movement such nonlinear elastic string are considered.
Moiseiwitsch, B L
2005-01-01
Two distinct but related approaches hold the solutions to many mathematical problems--the forms of expression known as differential and integral equations. The method employed by the integral equation approach specifically includes the boundary conditions, which confers a valuable advantage. In addition, the integral equation approach leads naturally to the solution of the problem--under suitable conditions--in the form of an infinite series.Geared toward upper-level undergraduate students, this text focuses chiefly upon linear integral equations. It begins with a straightforward account, acco
NJL model approach to diquarks and baryons in quark matter
Blaschke, D; Zablocki, D
2015-01-01
We describe baryons as quark-diquark bound states at finite temperature and density within the NJL model for chiral symmetry breaking and restoration in quark matter. Based on a generalized Beth-Uhlenbeck approach to mesons and diquarks we present in a first step the thermodynamics of quark-diquark matter which includes the Mott dissociation of diquarks at finite temperature. In a second step we solve the Bethe-Salpeter equation for the baryon as a quark-diquark bound state in quark-diquark matter. We obtain a stable, bound baryon even beyond the Mott temperature for diquark dissociation since the phase space occupation effect (Pauli blocking for quarks and Bose enhancement for diquarks) in the Bethe-Salpeter kernel for the nucleon approximately cancel so that the nucleon mass follows the in-medium behaviour of the quark and diquark masses towards chiral restoration. In this situation the baryon is obtained as a "borromean" three-quark state in medium because the two-particle state (diquark) is unbound while ...
Benner, Peter; Khoromskaia, Venera; Khoromskij, Boris N.
2016-04-01
The Bethe-Salpeter equation (BSE) is a reliable model for estimating the absorption spectra in molecules and solids on the basis of accurate calculation of the excited states from first principles. This challenging task includes calculation of the BSE operator in terms of two-electron integrals tensor represented in molecular orbital basis, and introduces a complicated algebraic task of solving the arising large matrix eigenvalue problem. The direct diagonalization of the BSE matrix is practically intractable due to $O(N^6)$ complexity scaling in the size of the atomic orbitals basis set, $N$. In this paper, we present a new approach to the computation of Bethe-Salpeter excitation energies which can lead to relaxation of the numerical costs up to $O(N^3)$. The idea is twofold: first, the diagonal plus low-rank tensor approximations to the fully populated blocks in the BSE matrix is constructed, enabling easier partial eigenvalue solver for a large auxiliary system relying only on matrix-vector multiplications with rank-structured matrices. And second, a small subset of eigenfunctions from the auxiliary eigenvalue problem is selected to build the Galerkin projection of the exact BSE system onto the reduced basis set. We present numerical tests on BSE calculations for a number of molecules confirming the $\\varepsilon$-rank bounds for the blocks of BSE matrix. The numerics indicates that the reduced BSE eigenvalue problem with small matrices enables calculation of the lowest part of the excitation spectrum with sufficient accuracy.
Tricomi, FG
2012-01-01
Based on his extensive experience as an educator, F. G. Tricomi wrote this practical and concise teaching text to offer a clear idea of the problems and methods of the theory of differential equations. The treatment is geared toward advanced undergraduates and graduate students and addresses only questions that can be resolved with rigor and simplicity.Starting with a consideration of the existence and uniqueness theorem, the text advances to the behavior of the characteristics of a first-order equation, boundary problems for second-order linear equations, asymptotic methods, and differential
Hochstadt, Harry
2012-01-01
Modern approach to differential equations presents subject in terms of ideas and concepts rather than special cases and tricks which traditional courses emphasized. No prerequisites needed other than a good calculus course. Certain concepts from linear algebra used throughout. Problem section at end of each chapter.
Viljamaa, Panu; Jacobs, J. Richard; Chris; JamesHyman; Halma, Matthew; EricNolan; Coxon, Paul
2014-07-01
In reply to a Physics World infographic (part of which is given above) about a study showing that Euler's equation was deemed most beautiful by a group of mathematicians who had been hooked up to a functional magnetic-resonance image (fMRI) machine while viewing mathematical expressions (14 May, http://ow.ly/xHUFi).
Derivation of a Closed Expression of the B-S Interaction Kernel for Quark-Antiquark Bound States
SU Jun-Chen
2002-01-01
The interaction kernel in the Bethe-Salpeter (B-S) equation for quark-antiquark bound states is derivedfrom B-S equations satisfied by the quark-antiquark four-point Green's function. The latter equations are establishedbased on the equations of motion obeyed by the quark and antiquark propagators, the four-point Green's function andsome other kinds of Green's functions, which follow directly from the QCD generating functional. The derived B-Skernel is given by a closed and explicit expression which contains only a few types of Green's functions. This expressionis not only convenient for perturbative calculations, but also applicable for nonperturbative investigations. Since thekernel contains all the interactions taking place in the quark-antiquark bound states, it actually appears to be the mostsuitable starting point of studying the QCD nonperturbative effect and quark confinement.
1998-09-21
In the late 1950s to early 1960s Rudolph A. Marcus developed a theory for treating the rates of outer-sphere electron-transfer reactions. Outer-sphere reactions are reactions in which an electron is transferred from a donor to an acceptor without any chemical bonds being made or broken. (Electron-transfer reactions in which bonds are made or broken are referred to as inner-sphere reactions.) Marcus derived several very useful expressions, one of which has come to be known as the Marcus cross-relation or, more simply, as the Marcus equation. It is widely used for correlating and predicting electron-transfer rates. For his contributions to the understanding of electron-transfer reactions, Marcus received the 1992 Nobel Prize in Chemistry. This paper discusses the development and use of the Marcus equation. Topics include self-exchange reactions; net electron-transfer reactions; Marcus cross-relation; and proton, hydride, atom and group transfers.
Tricomi, Francesco Giacomo
1957-01-01
This classic text on integral equations by the late Professor F. G. Tricomi, of the Mathematics Faculty of the University of Turin, Italy, presents an authoritative, well-written treatment of the subject at the graduate or advanced undergraduate level. To render the book accessible to as wide an audience as possible, the author has kept the mathematical knowledge required on the part of the reader to a minimum; a solid foundation in differential and integral calculus, together with some knowledge of the theory of functions is sufficient. The book is divided into four chapters, with two useful
Papavassiliou, Joannis
2011-01-01
The generation of a momentum-dependent gluon mass proceeds through a sophisticated implementation, at the level of the Schwinger-Dyson equation for the gluon propagator, of the Schwinger mechanism, whose central dynamical ingredient is the nonperturbative formation of longitudinally coupled massless bound-state excitations. In addition to triggering the aforementioned mechanism, these excitations introduce poles in the various off-shell Green's functions of the theory, in such a way as to maintain the Slavnov-Taylor identities intact in the presence of massive gluon propagators, acting effectively as composite Nambu-Goldstone bosons. In this work we focus on the dynamics leading to the actual formation of such bound states. Specifically, we derive and solve numerically an approximate version of the homogeneous Bethe-Salpeter equation governing the wave function of this special bound state. It is found that this integral equation admits physically meaningful non-trivial solutions, indicating that the QCD dynam...
Hadron Phenomenology from First-Principle QCD Studies
Papavassiliou, Joannis
2016-03-01
The form of the kernel that controls the dynamics of the Bethe-Salpeter equations is essential for obtaining quantitatively accurate predictions for the observable properties of hadrons. In the present work we briefly review the basic physical concepts and field-theoretic techniques employed in a first-principle derivation of a universal (process-independent) component of this kernel. This "top-down" approach combines nonperturbative ingredients obtained from lattice simulations and Dyson-Schwinger equations, and furnishes a renormalization-group invariant quark-gluon interaction strength, which is in excellent agreement with the corresponding quantity obtained from a systematic "bottom-up" treatment, where bound-state data are fitted within a well-defined truncation scheme.
$B^+\\to K^-\\pi^+\\pi^+$: three-body final state interactions and $K\\pi$ isospin states
Nogueira, J H Alvarenga; Lourenço, O
2016-01-01
Final state interactions are considered to formulate the $B$ meson decay amplitude for the $K\\pi\\pi$ channel. The Faddeev decomposition of the Bethe-Salpeter equation is used in order to build a relativistic three-body model within the light-front framework. The S-wave scattering amplitude for the $K\\pi$ system is considered in the $1/2$ and $3/2$ isospin channels with the set of inhomogeneous integral equations solved perturbatively. In comparison with previous results for the $D$ meson decay in the same channel, one has to consider the different partonic processes, which build the source amplitudes, and the larger absorption to other decay channels appears, that are important features to be addressed. As in the $D$ decay case, the convergence of the rescattering perturbative series is also achieved with two-loop contributions.
Aspects of the confinement mechanism in Coulomb-gauge QCD
Full text: Phenomenological consequences of the infrared singular, instantaneous part of the gluon propagator in Coulomb gauge are investigated. The corresponding quark Dyson-Schwinger equation is solved, neglecting retardation and transverse gluons and regulating the resulting infrared singularities. While the quark propagator vanishes as the infrared regulator goes to zero, the frequency integral over the quark propagator, and thus the quark condensate, stays finite and well-defined. Solutions of the homogeneous Bethe-Salpeter equation for the pseudoscalar and vector mesons as well as for scalar and axial-vector diquarks are obtained. In the limit of a vanishing infrared regulator the diquark masses diverge, while meson properties and diquark radii remain finite and well-defined. These features are interpreted with respect to the resulting aspects of confinement for colored quark-quark correlations. The qualitative features are stable when including transverse gluons. Corresponding preliminary results are presented. (author)
Hadron phenomenology from first-principle QCD studies
Papavassiliou, J
2016-01-01
The form of the kernel that controls the dynamics of the Bethe-Salpeter equations is essential for obtaining quantitatively accurate predictions for the observable properties of hadrons. In the present work we briefly review the basic physical concepts and field-theoretic techniques employed in a first-principle derivation of a universal (process-independent) component of this kernel. This "top-down" approach combines nonperturbative ingredients obtained from lattice simulations and Dyson-Schwinger equations, and furnishes a renormalization-group invariant quark-gluon interaction strength, which is in excellent agreement with the corresponding quantity obtained from a systematic "bottom-up" treatment, where bound-state data are fitted within a well-defined truncation scheme.
Looking for bound states and resonances in the $\\eta^\\prime K\\bar K$ system
Torres, A Martínez
2016-01-01
Motivated by the continuous experimental investigations of $X(1835)$ in three-body decay channels like $\\eta^\\prime \\pi^+ \\pi^-$, we investigate the $\\eta^\\prime K \\bar K$ system with the aim of searching for bound states and/or resonances when the dynamics involved in the $K\\bar K$ subsystem can form the resonances: $f_0(980)$ in isospin 0 or $a_0(980)$ in isospin 1. For this, we solve the Faddeev equations for the three-body system. The input two-body $t$-matrices are obtained by solving Bethe-Salpeter equations in a coupled channel formalism. As a result, no signal of a three-body bound state or resonance is found.
Exotic states in the S=1 N-pi-K system and low-lying 1/2+ S=-1 resonances
Oset E.
2010-04-01
Full Text Available In this manuscript we discuss about our study of the $N pi ar{K}$ and the NπK systems made by solving the Faddeev equations with the two-body t-matrices obtained by solving the Bethe-Salpeter equations with the potentials obtained from chiral dynamics. In the strangeness = -1 case, we found that all the Λ and Σ resonances listed by the particle data group, with spin-parity 1/2+ , in the 1550-1800 MeV region get generated due to the involved three-body dynamics. This motivated us to study the strangeness =1 three-body system, i.e., NπK , where we did not ﬁnd any evidence for the Θ+ (1542 but found a broad bump around 1700 MeV which has a κ(800N structure.
Quarkonia and heavy-light mesons in a covariant quark model
Leitão Sofia
2016-01-01
Full Text Available Preliminary calculations using the Covariant Spectator Theory (CST employed a scalar linear confining interaction and an additional constant vector potential to compute the mesonic mass spectra. In this work we generalize the confining interaction to include more general structures, in particular a vector and also a pseudoscalar part, as suggested by a recent study [1]. A one-gluon-exchange kernel is also implemented to describe the short-range part of the interaction. We solve the simplest CST approximation to the complete Bethe-Salpeter equation, the one-channel spectator equation, using a numerical technique that eliminates all singularities from the kernel. The parameters of the model are determined through a fit to the experimental pseudoscalar meson spectra, with a good agreement for both quarkonia and heavy-light states.
Within a model calculation the influence of the Pauli exclusion principle on the electrical conductivity of a fully ionized and degenerate hydrogen plasma is investigated. Basing on a quantum kinetic equation solved with the relaxation time ansatz, the electron-ion contribution to the resistivity is calculated. The thermodynamical T-matrix for electron-ion scattering processes is evaluated under special account for the Pauli blocking of the intermediate scattering states. The corresponding Bethe-Salpeter equation is solved analytically using a separable approximation of the statically screened potential. The Pauli exclusion principle has been found to give rise for a considerable enhancement of the transport cross section near the Fermi energy. Thus, degeneracy effects tend to diminish the electrical conductivity in the density-temperature region considered here. (author)
Quasiequilibrium nonlinearities in Faraday and Kerr rotation from spin-polarized carriers in GaAs
Joshua, Arjun; Venkataraman, V.
2010-01-01
Semiconductor Bloch equations (SBEs), which microscopically describe optical properties in terms of the dynamics of a Coulomb interacting, spin-unpolarized electron-hole plasma, can be solved in two limits: the coherent and the quasiequilibrium regimes. Recently, Nemec et al. [1] reported circularly polarized pump-probe absorption spectra in the quasiequilibrium regime for carrier spin-polarized bulk GaAs at room temperature, which lacked a suitable microscopic theoretical understanding. We have very recently explained their results by solving the spin-SBEs in the quasiequilibrium regime (spin-Bethe-Salpeter equation), and accounted for spin-dependent mechanisms of optical nonlinearity [2]. Here, we extend our theory to the microscopic calculation of Kerr and Faraday rotation in the quasiequilibrium regime, for which there are no experimental or theoretical results available.
Relativistic meson-exchange NN-interaction and nuclear matter in the Dirac-Brueckner approach
Starting from the full Bonn meson-exchange model for the NN-interaction an OBEP is constructed in the framework of the Thompson version of the Blankenbecler-Sugar reduction of the Bethe-Salpeter equation. The pseudo-vector coupling of the pion to the nucleon is assumed. An excellent quantitative description of the deuteron and the latest phase-shift analyses of NN-scattering is achieved. This potential is applied to the system of infinite nuclear matter in the relativistic Dirac-Brueckner approach. Due to additional strongly density dependent relativistic saturation effects, which do not occur in conventional Brueckner theory, the empirical saturation energy and density of nuclear matter are reproduced. This potential may serve as a good starting point for the evaluation of the optical potential to be applied in nucleon-nucleus scattering
Getting excited: Challenges in quantum-classical studies of excitons in polymeric systems
Bagheri, Behnaz; Karttunen, Mikko
2016-01-01
A combination of classical molecular dynamics (MM/MD) and quantum chemical calculations based on the density functional theory (DFT) was performed to describe conformational properties of diphenylethyne (DPE), methylated-DPE and poly para phenylene ethynylene (PPE). DFT calculations were employed to improve and develop force field parameters for MM/MD simulations. Many-body Green's functions theory within the GW approximation and the Bethe-Salpeter equation were utilized to describe excited states of the systems. Reliability of the excitation energies based on the MM/MD conformations was examined and compared to the excitation energies from DFT conformations. The results show an overall agreement between the optical excitations based on MM/MD conformations and DFT conformations. This allows for calculation of excitation energies based on MM/MD conformations.
Ab-initio calculation of excitons in conventional and anorganic semiconductors
Ambrosch-Draxl, Claudia; Laskowsky, Robert
2005-03-01
The excitonic effects on the optical absorption properties of organic as well as inorganic semiconductors are studied from first-principles. The Coulomb interaction between the electron and the hole is accounted for by solving the two-particle Bethe-Salpeter equation. In the organic semiconductors the exciton binding energies strongly depend on the molecular size, the crystalline packing, as well as the polarization direction of the incoming light. We show that the electron-hole interaction can lead to strongly bound excitons with binding energies of the order of 1eV or to a mere redistribution of oscillator strength. In several cases, the screening is efficient enough such that free charge carriers govern the optical absorption process. In the inorganic counterparts the sensitivity of the exciton binding energy is tested against the structural parameters and the screening of the electron-hole Coulomb interaction.
The excited states of small-diameter diamond nanoparticles in the gas phase are studied using the GW method and Bethe-Salpeter equation (BSE) within the ab initio many-body perturbation theory. The calculated ionization potentials and optical gaps are in agreement with experimental results, with the average error about 0.2 eV. The electron affinity is negative and the lowest unoccupied molecular orbital is rather delocalized. Precise determination of the electron affinity requires one to take the off-diagonal matrix elements of the self-energy operator into account in the GW calculation. BSE calculations predict a large exciton binding energy which is an order of magnitude larger than that in the bulk diamond
Surprises from the resummation of ladders in the ABJ(M) cusp anomalous dimension
Bonini, Marisa; Griguolo, Luca; Preti, Michelangelo; Seminara, Domenico
2016-05-01
We study the cusp anomalous dimension in mathcal{N} = 6 ABJ(M) theory, identifying a scaling limit in which the ladder diagrams dominate. The resummation is encoded into a Bethe-Salpeter equation that is mapped to a Schroedinger problem, exactly solvable due to the surprising supersymmetry of the effective Hamiltonian. In the ABJ case the solution implies the diagonalization of the U( N ) and U( M ) building blocks, suggesting the existence of two independent cusp anomalous dimensions and an unexpected exponentiation structure for the related Wilson loops. While consistent with previous perturbative analysis, the strong coupling limit of our result does not agree with the string theory computation, emphasizing a difference with the analogous resummation in the mathcal{N} = 4 case.
Leptonic decays of D-wave vector quarkonia
Krassnigg, A; Hilger, T
2016-01-01
We give a short and basic introduction to our covariant Dyson-Schwinger-Bethe-Salpeter-equation approach using a rainbow-ladder truncated model of QCD, in which we investigate the leptonic decay properties of heavy quarkonium states in the pseudoscalar and vector channels. Comparing the magnitudes of decay constants, we identify radial 1-- excitations in our calculation with experimental excitations of J/\\Psi and \\Upsilon. Particular attention is paid to those states regarded as D-wave states in the quark model. We predict e+e- decay width of the \\Upsilon(1^3D_1) and \\Upsilon(2^3D_1) states of the order of ca. 15 eV or more. We also provide a set of predictions for decay constants of pseudoscalar radial excitations in heavy quarkonia.
We have given several pieces of evidence that perturbation theory manages to reproduce various salient features of the conjectured exact S-matrices of ATFT. At present, we do not see how to use perturbation theory to provide an efficient description of the quantum field theory; an alternative formulation may well be required in order to find a proper understanding of the conjectured S-matrices and other features such as the mass-renormalization and the Clebsch-Gordan property. Certainly, the knowledge from other approaches, for example, the Quantum Group approach to imaginary coupling ATFT, investigations of the Bethe-Salpeter equations for the bound states in ATFT and the algebraic Bethe ansatz method advocated for many years by Faddeev and others would be helpful in the search for such a re-formulation. (J.P.N.)
Gauge invariance and Compton scattering from relativistic composite systems
Using the Ward-Takahashi (W-T) identity and the Bethe-Salpeter (B-S) wave equation, we investigate the dynamical requirements imposed by electromagnetic gauge invariance on Compton scattering from relativistic composite system. The importance of off-shell rescattering in intermediate states, which is equivalent to final state interactions in inclusive processes, is clarified in the context of current conservation. It is shown that, if the nuclear force is nonlocal, there will be both two-photon interaction currents and rescattering contributions to terms involving one-photon interaction currents. We derive the two-body W-T identity for the two-photon interaction currents, and obtain explicit forms for the interaction current operators for three illustrative models of nuclear forces: (a) two-pion exchange forces with baryon resonances, (b) covariant separable forces, and (c) charged one-pion exchange
Mass and width of a composite Higgs boson
The scalar Higgs boson mass in a Technicolor model was obtained by Elias and Scadron with the analysis of an homogeneous Bethe-Salpeter equation (BSE), however it was performed before the most recent developments of walking gauge theories. It was not observed in their work that dynamically generated technifermion mass may vary according to the theory dynamics that forms the scalar bound state. This will be done in this work and we also call attention that their calculation must change to take into account the normalization condition of the BSE. We compute the width of the composite boson and show how the gauge group and fermion content of a technicolor theory can be inferred from the measurement of the mass and width of the scalar boson.
Pion dissociation and Levinson's theorem in hot PNJL quark matter
Pion dissociation by the Mott effect in quark plasma is described within the generalized Beth-Uhlenbeck approach on the basis of the PNJL model, which allows for a unified description of bound, resonant and scattering states. As a first approximation, we utilize the Breit-Wigner ansatz for the spectral function and clarify its relation to the complex mass pole solution of the pion Bethe-Salpeter equation. Application of the Levinson theorem proves that describing the pion Mott dissociation solely by means of spectral broadening of the pion bound state beyond TMott leaves out a significant aspect. Thus, we acknowledge the importance of the continuum of scattering states and show its role for the thermodynamics of pion dissociation
Tuning Many-Body Interactions in Graphene: The Effects of Doping on Excitons and Carrier Lifetimes
Mak, Kin Fai; da Jornada, Felipe H.; He, Keliang; Deslippe, Jack; Petrone, Nicholas; Hone, James; Shan, Jie; Louie, Steven G.; Heinz, Tony F.
2014-05-01
The optical properties of graphene are strongly affected by electron-electron (e-e) and electron-hole (e-h) interactions. Here we tune these many-body interactions through varying the density of free charge carriers. Measurements from the infrared to the ultraviolet reveal significant changes in the optical conductivity of graphene for both electron and hole doping. The shift, broadening, and modification in shape of the saddle-point exciton resonance reflect strong screening of the many-body interactions by the carriers, as well as changes in quasiparticle lifetimes. Ab initio calculations by the GW Bethe-Salpeter equation method, which take into account the modification of both the repulsive e-e and the attractive e-h interactions, provide excellent agreement with experiment. Understanding the optical properties and high-energy carrier dynamics of graphene over a wide range of doping is crucial for both fundamental graphene physics and for emerging applications of graphene in photonics.
Fields, particles and analyticity: recent results or 30 goldberg (ER) variations on B.A.C.H
As it is known, Axiomatic Field Theory (A) implies double analyticity of the η-point functions in space-time and energy-momentum Complex Variables (C), with various interconnections by Fourier-Laplace analysis. When the latter is replaced by. Harmonic Analysis (H) on spheres and hyperboloids, a new kind of double analyticity results from (A) (i.e. from locality, spectral condition, temperateness and invariance): complex angular momentum is thereby introduced (a missing chapter in (A)). Exploitation of Asymptotic Completeness via Bethe-Salpeter-type equations (B) leads to new developments of the previous theme on (A, C, H) (complex angular momentum) and of other themes on (A,C) (crossing, Haag-Swieca property etc...). Various aspects of (A) + (B) have been implemented in Constructive Field Theory (composite spectrum, asymptotic properties etc...) by a combination of specific techniques and of model-independent methods
Baryons as relativistic three-quark bound states
Eichmann, Gernot; Williams, Richard; Alkofer, Reinhard; Fischer, Christian S
2016-01-01
We review the spectrum and electromagnetic properties of baryons described as relativistic three-quark bound states within QCD. The composite nature of baryons results in a rich excitation spectrum, whilst leading to highly non-trivial structural properties explored by the coupling to external (electromagnetic and other) currents. Both present many unsolved problems despite decades of experimental and theoretical research. We discuss the progress in these fields from a theoretical perspective, focusing on nonperturbative QCD as encoded in the functional approach via Dyson-Schwinger and Bethe-Salpeter equations. We give a systematic overview as to how results are obtained in this framework and explain technical connections to lattice QCD. We also discuss the mutual relations to the quark model, which still serves as a reference to distinguish 'expected' from 'unexpected' physics. We confront recent results on the spectrum of non-strange and strange baryons, their form factors and the issues of two-photon proce...
Palummo, Maurizia; Hogan, Conor; Sottile, Francesco; Bagalá, Paolo; Rubio, Angel
2009-08-28
We present a theoretical investigation of electronic and optical properties of free-base porphyrins based on density functional theory and many-body perturbation theory. The electronic levels of free-base porphine (H(2)P) and its phenyl derivative, free-base tetraphenylporphyrin (H(2)TPP) are calculated using the ab initio GW approximation for the self-energy. The approach is found to yield results that compare favorably with the available photoemission spectra. The excitonic nature of the optical peaks is revealed by solving the Bethe-Salpeter equation, which provides an accurate description of the experimental absorption spectra. The lowest triplet transition energies are in good agreement with the measured values. PMID:19725603
We have employed the framework of Bethe-Salpeter equation under Covariant Instantaneous Ansatz to calculate the leptonic decay constants of unequal mass pseudoscalar mesons. In the Dirac structure of BS wave function, the covariants are incorporated from their complete set in accordance with a recently proposed power counting rule, order-by-order in powers of inverse of meson mass. The decay constants are calculated incorporating both Leading Order (LO) as well as Next-to-leading Order (NLO) Dirac covariants. The contribution of both LO as well as NLO covariants to decay constants are studied in detail in this paper. The results are found to improve dramatically, and hence validating the power counting rule which also provides a practical means of incorporating Dirac covariants in the BS wave function of a hadron. (author)
Many-body effects and excitonic features in 2D biphenylene carbon.
Lüder, Johann; Puglia, Carla; Ottosson, Henrik; Eriksson, Olle; Sanyal, Biplab; Brena, Barbara
2016-01-14
The remarkable excitonic effects in low dimensional materials in connection to large binding energies of excitons are of great importance for research and technological applications such as in solar energy and quantum information processing as well as for fundamental investigations. In this study, the unique electronic and excitonic properties of the two dimensional carbon network biphenylene carbon were investigated with GW approach and the Bethe-Salpeter equation accounting for electron correlation effects and electron-hole interactions, respectively. Biphenylene carbon exhibits characteristic features including bright and dark excitons populating the optical gap of 0.52 eV and exciton binding energies of 530 meV as well as a technologically relevant intrinsic band gap of 1.05 eV. Biphenylene carbon's excitonic features, possibly tuned, suggest possible applications in the field of solar energy and quantum information technology in the future. PMID:26772582
Soft and Hard scale QCD Dynamics in Mesons
Nguyen, Trang; Tandy, Peter C
2010-01-01
Using a ladder-rainbow kernel previously established for the soft scale of light quark hadrons, we explore the extension to masses and electroweak decay constants of ground state pseudoscalar and vector quarkonia and heavy-light mesons in the c- and b-quark regions. We make a systematic study of the effectiveness of a constituent mass concept as a replacement for a heavy quark dressed propagator. The difference between vector and axial vector current correlators is examined to estimate the four quark chiral condensate. The valence quark distributions, in the pion and kaon, defined in deep inelastic scattering, and measured in the Drell Yan process, are investigated with the same ladder-rainbow truncation of the Dyson-Schwinger and Bethe-Salpeter equations.
Three-particle correlation from a Many-Body Perspective: Trions in a Carbon Nanotube
Deilmann, Thorsten; Drüppel, Matthias; Rohlfing, Michael
2016-05-01
Trion states of three correlated particles (e.g., two electrons and one hole) are essential to understand the optical spectra of doped or gated nanostructures, like carbon nanotubes or transition-metal dichalcogenides. We develop a theoretical many-body description for such correlated states using an ab initio approach. It can be regarded as an extension of the widely used G W method and Bethe-Salpeter equation, thus allowing for a direct comparison with excitons. We apply this method to a semiconducting (8,0) carbon nanotube, and find that the lowest optically active trions are redshifted by ˜130 meV compared to the excitons, confirming experimental findings for similar tubes. Moreover, our method provides detailed insights in the physical nature of trion states. In the prototypical carbon nanotube we find a variety of different excitations, discuss the spectra, energy compositions, and correlated wave functions.
Electronic excitations in solution-processed oligothiophene small-molecules for organic solar cells.
Gala, F; Mattiello, L; Brunetti, F; Zollo, G
2016-02-28
First principles calculations based on density functional theory and many body perturbation theory have been employed to study the optical absorption properties of a newly synthesized oligo-thiophene molecule, with a quaterthiophene central unit, that has been designed for solution-processed bulk-heterojunction solar cells. To this aim we have employed the GW approach to obtain quasiparticle energies as a pre-requisite to solve the Bethe-Salpeter equation for the excitonic Hamiltonian. We show that the experimental absorption spectrum can be explained only by taking into account the inter-molecular transitions among the π-stacked poly-conjugated molecules that are typically obtained in solid-state organic samples. PMID:26931705
Recent developments in the ABINIT software package
Gonze, X.; Jollet, F.; Abreu Araujo, F.; Adams, D.; Amadon, B.; Applencourt, T.; Audouze, C.; Beuken, J.-M.; Bieder, J.; Bokhanchuk, A.; Bousquet, E.; Bruneval, F.; Caliste, D.; Côté, M.; Dahm, F.; Da Pieve, F.; Delaveau, M.; Di Gennaro, M.; Dorado, B.; Espejo, C.; Geneste, G.; Genovese, L.; Gerossier, A.; Giantomassi, M.; Gillet, Y.; Hamann, D. R.; He, L.; Jomard, G.; Laflamme Janssen, J.; Le Roux, S.; Levitt, A.; Lherbier, A.; Liu, F.; Lukačević, I.; Martin, A.; Martins, C.; Oliveira, M. J. T.; Poncé, S.; Pouillon, Y.; Rangel, T.; Rignanese, G.-M.; Romero, A. H.; Rousseau, B.; Rubel, O.; Shukri, A. A.; Stankovski, M.; Torrent, M.; Van Setten, M. J.; Van Troeye, B.; Verstraete, M. J.; Waroquiers, D.; Wiktor, J.; Xu, B.; Zhou, A.; Zwanziger, J. W.
2016-08-01
ABINIT is a package whose main program allows one to find the total energy, charge density, electronic structure and many other properties of systems made of electrons and nuclei, (molecules and periodic solids) within Density Functional Theory (DFT), Many-Body Perturbation Theory (GW approximation and Bethe-Salpeter equation) and Dynamical Mean Field Theory (DMFT). ABINIT also allows to optimize the geometry according to the DFT forces and stresses, to perform molecular dynamics simulations using these forces, and to generate dynamical matrices, Born effective charges and dielectric tensors. The present paper aims to describe the new capabilities of ABINIT that have been developed since 2009. It covers both physical and technical developments inside the ABINIT code, as well as developments provided within the ABINIT package. The developments are described with relevant references, input variables, tests and tutorials.
Bagheri, Behnaz; Baumeier, Björn
2016-01-01
Electronic excitations in dilute solutions of poly para phenylene ethynylene (poly-PPE) are studied using a QM/MM approach combining many-body Green's functions theory within the $GW$ approximation and the Bethe-Salpeter equation with polarizable force field models. Oligomers up to a length of 7.5\\,nm (10 repeat units) functionalized with nonyl side chains are solvated in toluene and water, respectively. After equilibration using atomistic molecular dynamics (MD), the system is partitioned into a quantum region (backbone) embedded into a classical (side chains and solvent) environment. Optical absorption properties are calculated solving the coupled QM/MM system self-consistently and special attention is paid to the effects of solvents. The model allows to differentiate the influence of oligomer conformation induced by the solvation from electronic effects related to local electric fields and polarization. It is found that the electronic environment contributions are negligible compared to the conformational ...
Optical spectra and band structure of anatase and rutile TiO{sub 2}
Greuling, Andreas; Rohlfing, Michael [Universitaet Osnabrueck, Barbarastr.7, D-49069 Osnabrueck (Germany); Rinke, Patrick [University of California, Santa Barbara (United States)
2009-07-01
TiO{sub 2} is a semiconductor which is used in many applications (e.g. in biotechnology, cosmetic industry, paint industry, in catalysis or photocatalysis). Therefore, the (optical) properties of TiO{sub 2} are of great interest. As these are still not fully understood in theory we address its excited electronic states and optical spectra with ab initio methods beyond DFT. We present results of first principles calculations for anatase und rutile TiO{sub 2}. Starting from the electronic ground state, which is calculated within DFT(LDA), we describe the single particle excitations with an GWA approach. We use Gaussian basis-sets because this results in reasonable computational cost. Then we calculate the electron-hole interaction and solve the Bethe-Salpeter Equation (BSE) in order to obtain coupled electron-hole excitations. Based on the resulting data we evaluate the optical spectra and compare them with experimental data.
Many-body effects and excitonic features in 2D biphenylene carbon
The remarkable excitonic effects in low dimensional materials in connection to large binding energies of excitons are of great importance for research and technological applications such as in solar energy and quantum information processing as well as for fundamental investigations. In this study, the unique electronic and excitonic properties of the two dimensional carbon network biphenylene carbon were investigated with GW approach and the Bethe-Salpeter equation accounting for electron correlation effects and electron-hole interactions, respectively. Biphenylene carbon exhibits characteristic features including bright and dark excitons populating the optical gap of 0.52 eV and exciton binding energies of 530 meV as well as a technologically relevant intrinsic band gap of 1.05 eV. Biphenylene carbon’s excitonic features, possibly tuned, suggest possible applications in the field of solar energy and quantum information technology in the future
Surprises from the resummation of ladders in the ABJ(M) cusp anomalous dimension
Bonini, Marisa; Preti, Michelangelo; Seminara, Domenico
2016-01-01
We study the cusp anomalous dimension in N=6 ABJ(M) theory, identifying a scaling limit in which the ladder diagrams dominate. The resummation is encoded into a Bethe-Salpeter equation that is mapped to a Schroedinger problem, exactly solvable due to the surprising supersymmetry of the effective Hamiltonian. In the ABJ case the solution implies the diagonalization of the U(N) and U(M) building blocks, suggesting the existence of two independent cusp anomalous dimensions and an unexpected exponentiation structure for the related Wilson loops. While consistent with previous perturbative analysis, the strong coupling limit of our result does not agree with the string theory computation, emphasizing a difference with the analogous resummation in the N=4 case.
Advances in Materials Research for Displays from Serendipity to Materials by Design
H.Tolner; Y.Tu; Q.Li; Q.F.Li; L.L.Yang; W.J.Kuang; P.P.Zhang; B.P.Wang
2012-01-01
New materials have been developed for PDP for fast addressing and power reduction.They show the transition in R&D from materials invented accidentally to materials-by-design.Cathode-luminescence on MgO crystals is used to compare thermally assisted recombination and tunneling.Bethe Salpeter equations (BSE) are used to predict the exciton properties of mixed oxides like MgCaO.Using new materials an ultra-thin (300μm) and flexible Shadow-Mask PDP has been realized.The same device is also operated in a reverse mode,where high energy radiation is imaged,using the Gaseous Electron Multiplier (GEM) effect in the Townsend mode
Asymptotic completeness and multiparticle structure in field theories
Previous proofs of asymptotic completeness and related results on scattering in field theories are restricted to P(φ)2 models in the 2- and 3-particle regions. In this paper, new cluster expansions that are well adapted to more direct proofs and generalizations of these results are presented. In contrast to previous ones, they are designed to provide direct graphical definitions of general irreducible kernels satisfying structure equations recently proposed and shown to be closely linked with asymptotic completeness and with the multiparticle structure of Green functions and collision amplitudes in general energy regions. The method can be applied as previously to P(φ)2 and can also be extended to theories involving renormalization which are controlled by phase-space analysis. It is here illustrated in detail for the Bethe-Salpeter kernel in φ24, in which case a new proof of its 4-particle decay (which yields asymptotic completeness in the 2-particle region) is given. (orig.)
Electronic and optical properties of InN nanowires from first principles
Bayerl, Dylan; Kioupakis, Emmanouil
2013-03-01
Group-III-nitride nanowires are promising materials for photovoltaic and solid-state-lighting applications. We use first-principles calculations to investigate the electronic and optical properties of InN nanowires. Density functional theory provides the ground-state properties to which we subsequently apply quasiparticle corrections with the GW method. We thereby accurately predict the electronic band gaps, effective masses, and band dispersions of these nanostructured materials. We further solve the Bethe-Salpeter equation to predict the optical absorption spectra of InN nanowires as a function of cross-sectional dimension and geometry. We demonstrate that quantum confinement can increase the fundamental gap in InN nanowires as high as near-ultraviolet energies. This research was supported as part of CSTEC, an Energy Frontier Research Center funded by the U.S. Department of Energy, Office of Science. Computational resources were provided by the DOE NERSC facility.
Schwinger-Dyson approach and its application to generate a light composite scalar
Doff, A
2016-01-01
We discuss the possibility of generating a light composite scalar boson, in a scenario that we may generically call Technicolor, or in any variation of a strongly interacting theory, where by light we mean a scalar composite mass about one order of magnitude below the characteristic scale of the strong theory. Instead of most of the studies about a composite Higgs boson, which are based on effective Lagrangians, we consider this problem in the framework of non-perturbative solutions of the fermionic Schwinger-Dyson and Bethe-Salpeter equations. We study a range of mechanisms proposed during the recent years to form such light composite boson, and verify that such possibility seems to be necessarily associated to a fermionic self-energy that decreases slowly with the momentum.
Relativistic few quark dynamics for hadrons
A microscopic confinement approach is presented to a few quarks systems through an effective (harmonic) kernel inserted at the level of q-q-bar and q-q pairs, using the vehicle of the Bethe-Salpeter equation for each such system. The formalism, which is realistic for light quark systems (which require an intrinsically relativistic treatment), has been developed in a simple enough form so as to be applicable in practice to a large class of phenomena amenable to experimental test. The comparison over a wide range of hadronic properties (from mass spectra to current matrix elements), all within a single integrated framework, would seem to strongly support the ansatz of universality of the reduced spring constant (ω-tilde) which plays a role analogous to the bag radius, but at a far more microscopic level
Nuclear forces in the parity odd sector and the LS forces
Murano, Keiko
2011-01-01
In this paper, we report our first attempt at determining NN potentials in the parity odd sector including the spin-orbit force in lattice QCD, employing the method to extract successfully parity even NN potentials from Nambu-Bethe-Salpeter (NBS) wave functions through the Schr\\"odinger equation. Using Nf = 2 CP-PACS gauge configurations on a 16^3 x 32 lattice at a = 0.16 fm and m_\\pi \\cong 1.1 GeV, we calculate central, tensor and spin-orbit potentials in the parity odd sector. Although statistical errors are still large, we observe that the qualitative features of these potentials roughly agree with those of phenomenological potentials.
One-loop diagrams in nucleon-nucleon scattering
Within the framework of the Blankenbeckler-Sugar equations the effects of one-loop corrections to the driving force are studied in the two-nucleon system. In particular, contributions from the direct and crossed box two-pion exchange diagrams are calculated. An analysis is made at the one-loop level for both pseudoscalar and pseudovector pion-nucleon coupling using geometric unitarization. In a model with one boson exchanges it is shown that the agreement between the Bethe-Salpeter and the quasipotential results does not improve in all partial waves when the one-loop contributions are included. Various qualitative fits to the experimental data are presented for such a model
Electron-hole excitations and optical spectra of bulk SrO from many-body perturbation theory
This paper reports the quasiparticle band structure and the optical absorption spectrum of SrO, using many-body perturbation theory. The quasiparticle band structure is calculated within the GW approximation. Taking the electron-hole interaction into consideration, electron-hole pair states and optical excitations are obtained by solving the Bethe-Salpeter equation for the electron-hole two-particle Green function. The calculated band gap for SrO is 6.0 eV, which is in good agreement with the corresponding experimental results. The theoretical result of optical absorption spectrum for SrO is also in close agreement with the experimental data. In particular, the calculated excitation energy for the lowest exciton peak in the optical absorption spectra of SrO reproduces very well the corresponding experimental result. (orig.)
Electronic structures and optical spectra of BaO from first principles
We present the results of first-principles study for the electronic structure and optical absorption spectrum of the alkaline-earth metal oxide BaO. The quasiparticle band structure is evaluated within the Hedin's GW approximation [Phys. Rev. 139, A796 (1965)]. Thereafter, the electron-hole interaction is taken into consideration and the Bethe-Salpeter equation for the electron-hole two-particle Green function is solved. The calculated quasiparticle band gap of BaO is 4.1 eV, which is in good agreement with the experimental result. The calculated optical absorption spectrum of BaO is also in agreement with the experimental data. In particular, the calculated excitation energy for the lowest exciton peak in the optical absorption spectrum of BaO reproduces very well the corresponding experimental result
Electronic structures and optical spectra of BaO from first principles
Wu, Chang-Wei; Pan, Bo; Wang, Neng-Ping
2015-08-01
We present the results of first-principles study for the electronic structure and optical absorption spectrum of the alkaline-earth metal oxide BaO. The quasiparticle band structure is evaluated within the Hedin's GW approximation [Phys. Rev. 139, A796 (1965)]. Thereafter, the electron-hole interaction is taken into consideration and the Bethe-Salpeter equation for the electron-hole two-particle Green function is solved. The calculated quasiparticle band gap of BaO is 4.1 eV, which is in good agreement with the experimental result. The calculated optical absorption spectrum of BaO is also in agreement with the experimental data. In particular, the calculated excitation energy for the lowest exciton peak in the optical absorption spectrum of BaO reproduces very well the corresponding experimental result.
Stacking dependent electronic structures of transition metal dichalcogenides heterobilayer
Lee, Yea-Lee; Park, Cheol-Hwan; Ihm, Jisoon
The systematic study of the electronic structures and optical properties of the transition metal dichalcogenides (TMD) heterobilayers can significantly improve the designing of new electronic and optoelectronic devices. Here, we theoretically study the electronic structures and optical properties of TMD heterobilayers using the first-principles methods. The band structures of TMD heterobilayer are shown to be determined by the band alignments of the each layer, the weak interlayer interactions, and angle dependent stacking patterns. The photoluminescence spectra are investigated using the calculated band structures, and the optical absorption spectra are examined by the GW approximations including the electron-hole interaction through the solution of the Bethe-Salpeter equation. It is expected that the weak interlayer interaction gives rise to the substantial interlayer optical transition which will be corresponding to the interlayer exciton.
Hadron-quark vertex function. Interconnection between 3D and 4D wave function
Interconnection between 3D and 4D forms of Bethe-Salpeter equation (EBS) with a kernel depending on relative momenta is used to derive hadron-quark vertex function in Lorentz invariance form. The vertex function which is directly related to a 4D wave function satisfying a corresponding EBS determines the natural continuation outside mass surface for the entire momentum space and serves the basis for computing amplitudes of transitions through appropriate loop quark diagrams. Two applications (fp values for P→ll-bar and Fπ for n0+yy) are discussed briefly to illustrate this formalism. An attention is paid to the problem of complex amplitudes for quark loops with a larger number of external hadrons.A possible solution of the problem is proposed. 29 refs
QCD Effective Coupling in the Infrared Region
Ganbold, Gurjav
2010-01-01
We estimate the QCD effective charge $\\alpha_s$ in the low-energy region by exploiting the conventional meson spectrum within a relativistic quantum-field model based on analytic confinement. The ladder Bethe-Salpeter equation is solved for the masses of two-quark bound states. We found a new, independent and specific infrared-finite behavior of QCD coupling below energy scale 1 GeV. Particularly, an infrared-fixed point is extracted at $\\alpha_s(0)\\simeq 0.757$ for confinement scale $\\Lambda=345$ MeV. As an application, we estimate masses of some intermediate and heavy mesons and obtain results in reasonable agreement with recent experimental data.
Many-body effects and excitonic features in 2D biphenylene carbon
Lüder, Johann, E-mail: johann.luder@physics.uu.se; Puglia, Carla; Eriksson, Olle; Sanyal, Biplab; Brena, Barbara [Department of Physics and Astronomy, Uppsala University, P.O. Box 516, 751 20 Uppsala (Sweden); Ottosson, Henrik [Department of Chemistry–BMC, Uppsala University, P.O. Box 576, 751 23 Uppsala (Sweden)
2016-01-14
The remarkable excitonic effects in low dimensional materials in connection to large binding energies of excitons are of great importance for research and technological applications such as in solar energy and quantum information processing as well as for fundamental investigations. In this study, the unique electronic and excitonic properties of the two dimensional carbon network biphenylene carbon were investigated with GW approach and the Bethe-Salpeter equation accounting for electron correlation effects and electron-hole interactions, respectively. Biphenylene carbon exhibits characteristic features including bright and dark excitons populating the optical gap of 0.52 eV and exciton binding energies of 530 meV as well as a technologically relevant intrinsic band gap of 1.05 eV. Biphenylene carbon’s excitonic features, possibly tuned, suggest possible applications in the field of solar energy and quantum information technology in the future.
Splitting between bright and dark excitons in transition metal dichalcogenide monolayers
Echeverry, J. P.; Urbaszek, B.; Amand, T.; Marie, X.; Gerber, I. C.
2016-03-01
The optical properties of transition metal dichalcogenide monolayers such as the two-dimensional semiconductors MoS2 and WSe2 are dominated by excitons, Coulomb bound electron-hole pairs. The light emission yield depends on whether the electron-hole transitions are optically allowed (bright) or forbidden (dark). By solving the Bethe-Salpeter equation on top of G W wave functions in density functional theory calculations, we determine the sign and amplitude of the splitting between bright and dark exciton states. We evaluate the influence of the spin-orbit coupling on the optical spectra and clearly demonstrate the strong impact of the intra-valley Coulomb exchange term on the dark-bright exciton fine structure splitting.
The dynamical gluon mass in the massless bound-state formalism
Ibanez, David
2014-01-01
We describe the phenomenon of dynamical gluon mass generation within the massless bound-state formalism, which constitutes the general framework for the systematic implementation of the Schwinger mechanism in non-Abelian gauge theories. The main ingredient of this formalism is the dynamical formation of bound states with vanishing mass, which gives rise to effective vertices containing massless poles; these vertices, in turn, trigger the Schwinger mechanism, and allow for the gauge-invariant generation of an effective gluon mass. In this particular approach, the gluon mass is directly related to quantities that are intrinsic to the bound-state formation itself, such as the "transition amplitude" and the corresponding "bound-state wave-function". Specifically, a set of powerful relations discussed in the text, allows one to determine the dynamical evolution of the gluon mass through a Bethe-Salpeter equation, which controls the dynamics of the relevant wave-function. In addition, it is possible to demonstrate ...
Linear response of homogeneous nuclear matter with energy density functionals
Pastore, A; Navarro, J
2014-01-01
Response functions of infinite nuclear matter with arbitrary isospin asymmetry are studied in the framework of the random phase approximation. The residual interaction is derived from a general nuclear Skyrme energy density functional. Besides the usual central, spin-orbit and tensor terms it could also include other components as new density-dependent terms or three-body terms. Algebraic expressions for the response functions are obtained from the Bethe-Salpeter equation for the particle-hole propagator. Applications to symmetric nuclear matter, pure neutron matter and asymmetric nuclear matter are presented and discussed. Spin-isospin strength functions are analyzed for varying conditions of density, momentum transfer, isospin asymmetry, and temperature for some representative Skyrme functionals. Particular attention is paid to the discussion of instabilities, either real or unphysical, which could manifest in finite nuclei.
Theory of two-atom coherence in gases. II. Continuous-wave spectra
Ben-Reuven, Abraham
1980-12-01
General expressions are derived for the spectral line shapes of resonance absorption and scattering of coherent radiation in collision-broadened gases, taking into account effects of coherent excitation of two or more atoms (or molecules), as steady-state solutions of a hierarchy of master equations described in a previous publication (paper I). Coupling between the coherent motions of the atoms, provided by a Bethe-Salpeter-type effective interaction, in the binary-collision approximation, forms the essential mechanism for introducing cooperative coherent effects into the steady-state spectra. Explicit expressions are given for the effects of two-atom coherence in the binary-collision approximation, in which the Bloch-type dressed-atom self-energy superoperator is modified by the presence of collisions in which both atoms retain memory of their coherent propagation before the collision. The self-energies include the effects of resonance exchange symmetrization in self-broadening, and are renormalized by the coincidence of radiative transitions during the collisions. The impact (near-resonance) and the quasistatic (line-wing) limits of the applied-frequency detunings are discussed. In the quasistatic limit, coherent many-atom excitations become irrelevant; however, interactions of both collision partners with the radiation during the collision accounts for such phenomena as collision-induced absorption or radiative collisions. In the impact limit, the inclusion of the Bethe-Salpeter interactions allows for the appearance of two-atom resonances. Magnitude estimates of these effects are discussed. Effects of higher-rank (many-body) coherences are formally discussed with the help of a diagrammatic method, leading into implicit bootstrap equations that can be solved by iterative or other procedures.
Partial Differential Equations
1988-01-01
The volume contains a selection of papers presented at the 7th Symposium on differential geometry and differential equations (DD7) held at the Nankai Institute of Mathematics, Tianjin, China, in 1986. Most of the contributions are original research papers on topics including elliptic equations, hyperbolic equations, evolution equations, non-linear equations from differential geometry and mechanics, micro-local analysis.
Difference equations by differential equation methods
Hydon, Peter E
2014-01-01
Most well-known solution techniques for differential equations exploit symmetry in some form. Systematic methods have been developed for finding and using symmetries, first integrals and conservation laws of a given differential equation. Here the author explains how to extend these powerful methods to difference equations, greatly increasing the range of solvable problems. Beginning with an introduction to elementary solution methods, the book gives readers a clear explanation of exact techniques for ordinary and partial difference equations. The informal presentation is suitable for anyone who is familiar with standard differential equation methods. No prior knowledge of difference equations or symmetry is assumed. The author uses worked examples to help readers grasp new concepts easily. There are 120 exercises of varying difficulty and suggestions for further reading. The book goes to the cutting edge of research; its many new ideas and methods make it a valuable reference for researchers in the field.
Random diophantine equations, I
Brüdern, Jörg; Dietmann, Rainer
2012-01-01
We consider additive diophantine equations of degree $k$ in $s$ variables and establish that whenever $s\\ge 3k+2$ then almost all such equations satisfy the Hasse principle. The equations that are soluble form a set of positive density, and among the soluble ones almost all equations admit a small solution. Our bound for the smallest solution is nearly best possible.
The Generalized Jacobi Equation
Chicone, C.; Mashhoon, B.
2002-01-01
The Jacobi equation in pseudo-Riemannian geometry determines the linearized geodesic flow. The linearization ignores the relative velocity of the geodesics. The generalized Jacobi equation takes the relative velocity into account; that is, when the geodesics are neighboring but their relative velocity is arbitrary the corresponding geodesic deviation equation is the generalized Jacobi equation. The Hamiltonian structure of this nonlinear equation is analyzed in this paper. The tidal accelerat...