Three-Quark Bethe-Salpeter Vertex Function Under Pairwise Gluon-Exchange-Like Interaction : Application to n-p Mass Difference

Abstract

A qqq BSE formalism based on an input 4-fermion Lagrangian of `current' u,d quarks, is employed for the construction of a relativistic qqq-wave function) via the BSE. Chiral invariance is ensured by the vector character of the gluonic propagator in the infrared regime, while the `constituent' masses are the low momentum limits of the dynamicalmass function generated by standard DB{\chi}. The Covariant Instantaneity Ansatz (CIA) gives an exact 3D reduction of the BSE for baryon spectroscopy, while the reconstructed 4D form identifies the baryon quark vertex function reconstructed through a reversal of steps offered by the CIA structure. It is employed for the quark loop integrals for the neutron - proton mass difference which receives contributions from two sources : i) the strong SU(2) effect arising from the $u-d$ mass difference (4 MeV); ii) the e.m. effect of the respective quark charges. The resultant n-p difference works out at 1.28 MeV (vs. 1.29 expt), with only two free parameters characterizing the infrared structure of the gluonic propagator, precalibrated via a common fit to meson and baryonspectra plus several other observable amplitudes. (PACS : 11.10 st ; 12.35 Ht ; 12.70 + q)