2002/12/18 by Mandar S. Bhagwat, M. Bhagwat, M. A. Pichowsky +1 · 8 citations
Physics and Astronomy · #Analytic continuation #Bethe–Salpeter equation #Feynman diagram #High-Energy Particle Collisions Research #Mathematical analysis #Mathematical physics #Meson #Particle physics #Particle physics theoretical and experimental studies #Physics #Pion #Propagator #Quantum Chromodynamics and Particle Interactions #Quantum chromodynamics #Quantum electrodynamics #Quark #Vector meson #hep-ph #nucl-th
paper · pdf · doi:10.1103/physrevd.67.054019
published as Phys.Rev. D67 (2003) 054019 · Submitted for publication; 10.5x2-column pages, REVTEX 4, 3 postscript files making 3 figs
arxiv created 2002/12/18 · openalex publication_date 2003/03/28 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We consider the solution of the Bethe-Salpeter equation in the Euclidean metric for a qq vector meson in the circumstance where the dressed quark propagators have timelike 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 qq width to the meson generated from one quark pole is exactly canceled by the effect of the conjugate partner pole; the meson mass remains real and there is no spurious qq 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.