Sharma, Anju ; Mitra, A. N. (1997) ThreeQuark BetheSalpeter vertex function under pairwise gluonexchangelike interaction: application to np mass difference Arxiveprints . pp. 123.

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Official URL: http://arxiv.org/abs/hepph/9707503
Abstract
A qqq BSE formalism based on an input 4fermion Lagrangian of 'current' u, d quarks interacting pairwise via a gluonexchangelike propagator in its nonperturbative regime, is employed for the construction of a relativistic qqqwave function under the Covariant Instantaneity Ansatz (CIA). The chiral invariance of the input Lagrangian is automatically ensured by the vector character of the gluonic propagator, while the 'constituent' masses are the low momentum limits of the dynamical mass function m(p) generated by the standard mechanism of DB_{χ}S in the solution of the Schwinger Dyson Equation (SDE). The CIA gives an exact reduction of the BSE to a 3D form which is appropriate for baryon spectroscopy, while the reconstructed 4D form identifies the hadron quark vertex function as the key ingredient for evaluating transition amplitudes via quarkloop integrals. In this paper the second stage of this 'twotier' BSE formalism is extended from the 4D qq̅meson to the 4D qqqbaryon vertex reconstruction through a reversal of steps offered by the CIA structure. As a first application of this 4D qqq wave function, we evaluate the quark loop integrals for the neutron (n)  proton (p) mass difference which receives contributions from two sources : i) the strong SU(2) effect arising from the ud mass difference (4 MeV); ii) the e.m. effect of the respective quark charges. The resultant np difference works out at 1.28 MeV (vs. 1.29 expt), with two free parameters C_{0}, ω_{0} characterizing the infrared structure of the gluonic, which have been precalibrated from a common fit to qq̅ and qqq spectra as well as several other observable quark loop integrals. A formal derivation, based on Green's function techniques for 3 spinless quarks, of the CIA structure of the 4D qqqbaryon vertex function as employed in the text, is given for completeness in Appendix B.
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Deposited On:  07 May 2012 13:13 
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