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 DBχ. 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)