Baryon Self-Energy With QQQ Bethe-Salpeter Dynamics In The Non-Perturbative QCD Regime: n-p Mass Difference

TL;DR

This paper develops a non-perturbative QCD framework using Bethe-Salpeter equations to calculate baryon self-energy and the neutron-proton mass difference, incorporating quark mass differences and electromagnetic effects.

Contribution

It introduces a 3-body Bethe-Salpeter formalism for baryons based on Dyson-Schwinger equations, extending previous 2-body results to accurately compute mass differences.

Findings

Neutron-proton mass difference calculated as just above 1 MeV.

Dominant contribution from d-u quark mass difference (+1.71 MeV).

Electromagnetic effects offset the strong contribution by -0.44 MeV.

Abstract

A qqq BSE formalism based on DB{\chi}S of an input 4-fermion Lagrangian of `current' u,d quarks interacting pairwise via gluon-exchange-propagator in its {\it non-perturbative} regime, is employed for the calculation of baryon self-energy via quark-loop integrals. To that end the baryon-qqq vertex function is derived under Covariant Instantaneity Ansatz (CIA), using Green's function techniques. This is a 3-body extension of an earlier q{\bar q} (2-body) result on the exact 3D-4D interconnection for the respective BS wave functions under 3D kernel support, precalibrated to both q{\bar q} and qqq spectra plus other observables. The quark loop integrals for the neutron (n) - proton (p) mass difference receive contributions from : i) the strong SU(2) effect arising from the d-u mass difference (4 MeV); ii) the e.m. effect of the respective quark charges. The resultant n-p difference comes dominantly from d-u effect (+1.71 Mev), which is mildly offset by e.m.effect (-0.44), subject to gauge corrections. To that end, a general method for QED gauge corrections to an arbitrary momentum dependent vertex function is outlined, and on on a proportionate basis from the (two-body) kaon case, the net n-p difference works out at just above 1 MeV. A critical comparison is given with QCD sum rules results.