Formulação preditiva do modelo de Nambu-Jona-Lasinio com quebra explícita de simetria de isospin SU(2)

Abstract

A formulation of the Nambu-Jona-Lasinio model which is free from typical ambiguities associated with the perturbative calculations in quantum field theories is presented and its qualitative and phenomenological consequences are investigated. The present work can be considered as an extension of an early work about the same issue for the case of quarks having different masses and with the Lagrangian density generalized through the inclusion of tensor couplings. The fundamental ingredient adopted is given by an alternative strategy used to manipulate and calculate divergent Feynman amplitudes. Within this strategy all the arbitrariness associated with the divergent character of the physical amplitudes are preserved by the final results. The physical content of the amplitudes is isolated in a set of finite integrals which are integrated without restrictions. The purely divergent sector, on the other side, is conveniently organized in a set of basic divergent objects. Through physical consistency constraints imposed over the calculated amplitudes we obtain a set of relations among the divergent objects which are denominated consistency relations. The consistency relations are the necessary conditions in order to eliminate both the arbitrariness associated with the momenta routing of internal lines in the loops as well as the arbitrariness related with a parameter used to isolate the finites parts from the divergent ones, which plays a role of scale. We show that a set of relations among irreducible divergent objects, obtained by the imposition of scale invariance of the physical amplitudes consistently treated, plays a crucial role in order to fix a remaining arbitrariness which one may identify with the freedom which we have in choosing a particular regularization. Detailed analytical and numerical results for the phenomenology of the scalar, pseudoscalar, vector and axial mesons are presented. Quantitatively, special attention is given to the explicitly isospin symmetry breaking contributions for the well known differences between the masses of charged and neutral mesons.