Bethe--Salpeter equation in QCD

Abstract

We extend to regular QCD the derivation of a confining $q\bar{q}$ Bethe--Salpeter equation previously given for the simplest model of scalar QCD in which quarks are treated as spinless particles. We start from the same assumptions on the Wilson loop integral already adopted in the derivation of a semirelativistic heavy quark potential. We show that, by standard approximations, an effective meson squared mass operator can be obtained from our BS kernel and that, from this, by $\frac{1}{m^2}$ expansion the corresponding Wilson loop potential can be reobtained, spin--dependent and velocity--dependent terms included. We also show that, on the contrary, neglecting spin--dependent terms, relativistic flux tube model is reproduced.

23 pages, revtex

References in corpus (6)

• A consistent derivation of the quark--antiquark and three quark potentials in a Wilson loop context
• On the instantaneous Bethe-Salpeter equation
• Fermion Confinement by a Relativistic Flux Tube
• On the validity of the reduced Salpeter equation
• Stability Analysis of the Instantaneous Bethe-Salpeter Equation and the Consequences for Meson Spectroscopy
• Confining Bethe--Salpeter equation from scalar QCD

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• B_{c} meson and the light-heavy quarkonium spectrum
• Concavity of the meson Regge trajectories
• Three-body relativistic flux tube model from QCD Wilson-loop approach
• Bound state equation in the Wilson loop approach with minimal surfaces
• Note on universal description of heavy and light mesons
• Variational Minimization on String-rearrangement Surfaces, Illustrated by an Analysis of the Bilinear Interpolation
• Structure of the meson Regge trajectories
• Regge trajectories and quarkonium spectrum from a first principle Salpeter equation
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• From the Feynman-Schwinger representation to the non-perturbative relativistic bound state interaction
• Integral equation for gauge invariant quark two-point Green's function in QCD
• Regge trajectories for the triply heavy triquarks
• Gauge invariant bound state equations for quark-antiquark systems in QCD
• Confining Bethe--Salpeter equation in QCD