3D-4D Interlinkage Of B-S Amplitudes : Unified View Of QQbar And QQQ Dynamics

TL;DR

This paper explores a unified 3D-4D framework for Bethe-Salpeter amplitudes in strong interaction dynamics, emphasizing the Markov-Yukawa Transversality Principle and comparing covariant instantaneity and light-front approaches.

Contribution

It introduces a novel 3D-4D interlinkage via MYTP, providing a consistent framework for qqbar and qqq BSEs with distinct 4D implementations.

Findings

MYTP offers a two-way 3D-4D connection for BSE amplitudes.

Covariant LF approach avoids Lorentz mismatch issues.

Both approaches yield identical spectral predictions.

Abstract

This article has a 3-fold objective: i) to provide a panoramic view of several types of 3D vs 4D approaches in Field Theory (Tamm-Dancoff, Bethe Salpeter Equation (BSE), Quasi-potentials, Light-Front Dynamics, etc) for strong interaction dunamics; ii) to focus on the role of the Markov-Yukawa Transversality Principle (MYTP) as a novel paradigm for an exact 3D-4D interlinkage between the corresponding BSE amplitudes; iii) Stress on a closely parallel treatment of $q{\bar q}$ and qqq BSE's stemming from a common 4-fermion Lagrangian mediated by gluon (vector)-like exchange. The two-way interlinkage offered by MYTP between the 3D and 4D BSE forms via a Lorentz-covariant 3D support to the BS kernel, gives it a unique status which distinguishes it from most other 3D approaches to strong interaction dynamics, which give at most a one-way connection. Two specific types of MYTP which provide 3D support to the BSE kernel, are considered: a) Covariant Instantaneity Ansatz (CIA); b) Covariant LF/NP ansatz (Cov.LF). Both lead to formaly identical 3D BSE reductions (thus ensuring common spectral predictions), but their 4D manifestations differ sharply: Under CIA, the 4D loop integrals suffer from Lorentz mismatch of the vertex functions, leading to ill-defined time-like momentum integrals, but Cov LF is free from this disease. Some practical uses of MYTP as a basis for evaluating various types of 4D loop integrals are outlined. PACS: 11.10 st ; 12.38 Lg ; 13.40.Fn Keywords: Tamm-Dancoff, Bethe-Salpeter, Quasi-potentials, Light-front (LF), Markov-Yukawa, 3D-4D Interlinkage, CIA, Cov-LF, Spectroscopy.