Null-plane dynamics for few-quark systems

Abstract

A Lorentz-invariant formulation of the 3-dimensional harmonic oscillator is proposed for serving as the confining part of the kernel of a Bethe-Salpeter equation for a qq̅ system, and likewise for a qqq system. Such a kernel is amenable to an effective 3-dimensional reduction in the null-plane approximation (NPA), so as to maintain explicit NPA-covariance for the (reduced) BS equations as well as the corresponding wave functions. This rectifies the mathematical limitation of an earlier BS formulation (by Mitra and coworkers) for qq̅ and qqq systems with non-covariant h. o. kernels which was restricted to the instantaneous approximation and was therefore valid only for slowly moving hadrons. The present (covariant) formulation agrees exactly with the earlier (non-covariant) treatment for hadrons at rest, thus preserving all the physical results on mass spectra, etc., obtained with the latter, but is now formally applicable to processes involving hadrons in motion.