Relativistic analysis of the constituent quark model for mesons

Abstract

Extensions of the constituent quark potential model for mesons are formulated and analyzed which include relativistic dynamics and the full Dirac structure of both positive and negative energy states. The meson wave equations are transformed to configuration space where they can easily be solved numerically. Thus we present the first systematic description of the mass spectra of light, mixed and heavy mesons which takes into account the full Dirac structure without approximations. The pion form factor and radiative, leptonic and electroweak meson decay are studied.We find that the projection on the full Dirac structure of the confining potential and of the meson decay vertices gives unexpected large modifications to the nonrelativistic mass spectra and decay vertices.