Solving Bethe-Salpeter scattering state equation in Minkowski space

Carbonell, J.; Karmanov, V. A.

doi:10.1103/physrevd.90.056002

Cited by 33 publications

(41 citation statements)

References 45 publications

(115 reference statements)

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“…Before applying these relations to QCD, let us take a step back and illustrate the basic solution techniques for Euclidean Bethe-Salpeter equations, since this may be helpful for the non-expert reader and the standard methods are quite different from analogous treatments in Minkowski space [291][292][293]. We consider a simple toy model: a scalar bound state (mass M ) of two scalar constituents (with equal masses m for simplicity), which are bound by a scalar exchange particle (mass µ); all propagators are at tree level.…”

Section: Bound-state Equationsmentioning

confidence: 99%

Baryons as relativistic three-quark bound states

Eichmann

Sanchis-Alepuz

Williams

et al. 2016

Progress in Particle and Nuclear Physics

416

530

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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 processes and Compton scattering determined in the DysonSchwinger framework with those of lattice QCD and the available experimental data. The general aim is to identify the underlying physical mechanisms behind the plethora of observable phenomena in terms of the underlying quark and gluon degrees of freedom.

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Section: Bound-state Equationsmentioning

confidence: 99%

Baryons as relativistic three-quark bound states

Eichmann

Sanchis-Alepuz

Williams

et al. 2016

Progress in Particle and Nuclear Physics

416

530

View full text Add to dashboard Cite

show abstract

“…Equation (14) is a N × N system of linear equations of the type B = A C with the inhomogeneous term given by the Euclidean BS amplitude B ≡ i j and as unknowns the array C ≡ c i j of coefficients of the expansion (12). The solution of this system C = A −1 B, will provide the coefficients c i j and by this the Nakanishi weight function g(x, z) at any point.…”

Section: Solving Eqs (8) and (10)mentioning

confidence: 99%

“…To avoid instability, one can, of course, keep N small enough. However, for small N the expansions (12) and (16) give a very crude reproduction of the unknown g. Therefore, to find a solution, we will use a special mathematical method -the Tikhonov regularization method (TRM) [25].…”

Section: Solving Eqs (8) and (10)mentioning

confidence: 99%

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Euclidean to Minkowski Bethe–Salpeter amplitude and observables

2017

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We propose a method to reconstruct the BetheSalpeter amplitude in Minkowski space given the Euclidean Bethe-Salpeter amplitude -or alternatively the light-front wave function -as input. The method is based on the numerical inversion of the Nakanishi integral representation and computing the corresponding weight function. This inversion procedure is, in general, rather unstable, and we propose several ways to considerably reduce the instabilities. In terms of the Nakanishi weight function, one can easily compute the BS amplitude, the LF wave function and the electromagnetic form factor. The latter ones are very stable in spite of residual instabilities in the weight function. This procedure allows both, to continue the Euclidean BS solution in the Minkowski space and to obtain a BS amplitude from a LF wave function.

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“…For the interested reader we refer to analogous calculations in Coulomb-gauge QCD [107][108][109][110] or Minkowski space [111][112][113][114][115][116][117][118][119].…”

Section: Introductionmentioning

confidence: 99%

Light-quarkonium spectra and orbital-angular-momentum decomposition in a Bethe–Salpeter-equation approach

2017

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We investigate the light-quarkonium spectrum using a covariant Dyson-Schwinger-Bethe-Salpeter-equation approach to QCD. We discuss splittings among as well as orbital angular momentum properties of various states in detail and analyze common features of mass splittings with regard to properties of the effective interaction. In particular, we predict the mass ofss exotic 1 −+ states, and identify orbital angular momentum content in the excitations of the ρ meson. Comparing our covariant model results, the ρ and its second excitation being predominantly S-wave, the first excitation being predominantly D-wave, to corresponding conflicting lattice-QCD studies, we investigate the pion-mass dependence of the orbital-angular-momentum assignment and find a crossing at a scale of m π ∼ 1.4 GeV. If this crossing turns out to be a feature of the spectrum generated by lattice-QCD studies as well, it may reconcile the different results, since they have been obtained at different values of m π .

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Solving Bethe-Salpeter scattering state equation in Minkowski space

Cited by 33 publications

References 45 publications

Baryons as relativistic three-quark bound states

Baryons as relativistic three-quark bound states

Euclidean to Minkowski Bethe–Salpeter amplitude and observables

Light-quarkonium spectra and orbital-angular-momentum decomposition in a Bethe–Salpeter-equation approach

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