Confinement Phenomenology in the Bethe-Salpeter Equation

Abstract

We consider the solution of the Bethe-Salpeter equation in Euclidean metric for a qbar-q vector meson in the circumstance where the dressed quark propagators have time-like complex conjugate mass poles. This approximates features encountered in recent QCD modeling via the Dyson-Schwinger equations; the absence of real mass poles simulates quark confinement. The analytic continuation in the total momentum necessary to reach the mass shell for a meson sufficiently heavier than 1 GeV leads to the quark poles being within the integration domain for two variables in the standard approach. Through Feynman integral techniques, we show how the analytic continuation can be implemented in a way suitable for a practical numerical solution. We show that the would-be qbar-q width to the meson generated from one quark pole is exactly cancelled by the effect of the conjugate partner pole; the meson mass remains real and there is no spurious qbar-q production threshold. The ladder kernel we employ is consistent with one-loop perturbative QCD and has a two-parameter infrared structure found to be successful in recent studies of the light SU(3) meson sector.

arXiv commentSubmitted for publication; 10.5x2-column pages, REVTEX 4, 3 postscript files making 3 figs

References in corpus (23)

• Dyson-Schwinger Equations: Density, Temperature and Continuum Strong QCD
• pi- and K-meson Bethe-Salpeter Amplitudes
• Bethe-Salpeter Study of Vector Meson Masses and Decay Constants
• Pion mass and decay constant
• Goldstone Theorem and Diquark Confinement Beyond Rainbow-Ladder Approximation
• Measurement of the Charged Pion Electromagnetic Form Factor
• The $\pi$, $K^{+}$, and $K^0$ electromagnetic form factors
• Confinement and complex singularities in QED3
• q\bar q$ bound states in the Bethe-Salpeter formalism
• Electromagnetic Pion Form Factor and Neutral Pion Decay Width
• Bethe-Salpeter equation and a nonperturbative quark-gluon vertex
• Pseudovector components of the pion, pi^0 -> gamma gamma, and F_pi(q^2)
• Electromagnetic Transition Form Factors of Light Mesons
• The theory of quark confinement
• Lattice quark propagator with staggered quarks in Landau and Laplacian gauges
• Model gluon propagator and pion and rho-meson observables
• A Systematic Extended Iterative Solution for QCD
• Strong Decays of Light Vector Mesons
• Infrared Behaviour of Propagators and Vertices
• K_{l3} transition form factors
• Production Processes as a Tool to Study Parameterizations of Quark Confinement
• Dyson-Schwinger calculations of meson form factors
• Mesons as Bound States of Confined Quarks: Zero and Finite Temperature

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