QCD-motivated BSE-SDE framework for quark-dynamics under Markov-Yukawa transversality: a unified view of Q Q̅ and QQQ systems

Abstract

This article aims at an integrated formulation of BSE's for 2- and 3-quark hadrons under the Markov-Yukawa Transversality Principle (MYTP) which provides a deep interconnection between the 3D and 4D BSE forms, and hence offers a unified treatment of 3D spectroscopy with 4D quark-loop integrals for hadronic transitions. For the actual dynamics, an NJL-type realization of DBχS is achieved via the interplay of Bethe-Salpeter (BSE) and Schwinger-Dyson (SDE) equations, which are simultaneously derivable from a chiral Lagrangian with a gluonic (Vector-exchange) 4-fermion interaction of 'current' uds quarks, specifically addressing the non-perturbative regime. A prior critique of the literature on various aspects of the non-perturbative QCD problem, on the basis of some standard criteria, helps converge on a BSE-SDE framework with a 3D-4D interconnection based on MYTP. This framework is then employed for a systematic self-contained presentation of 2- and 3-quark dynamics on the lines of MYTP-governed DBχS, with enough calculational details illustrating the techniques involved. Specific topics include: 3D-4D interconnection of q q̅ and qqq wave functions by Green's Function methods; pion form factor; 3-hadron form factors with unequal mass loops; SU(2) mass splittings; Vacuum condensates (direct and induced); Complex H.O. techniques and SO(2,1).