From scale properties of physical amplitudes to a predictive formulation of the Nambu-Jona-Lasinio model

Abstract: The predictive power of the NJL model is considered in the light of a novel strategy to handle the divergences typical of perturbative calculations. The referred calculational strategy eliminates unphysical dependencies on the arbitrary choices for the routing of internal momenta and symmetry violating terms. In the present work we extend a previous one on the same issue by including vector interactions and performing the discussion in a more general context: it is considered the role of scale arbitrariness for the consistency of the calculations. We show that the imposition of arbitrary scale independence for the consistent regularized amplitudes lead to additional properties for the irreducible divergent objects. These properties allow us to parametrize the remaining freedom in terms of a unique constant where resides all the arbitrariness involved. By searching for the best value for the arbitrary parameter we find a critical condition for the existence of an acceptable physical value for the dynamically generated quark mass. Such critical condition fixes the remaining arbitrariness turning the NJL into a predictive model in the sense that its phenomenological consequences do not depend on possible choices made in intermediary steps. Numerical results are obtained for physical quantities like the vector and axial-vector masses and their coupling constants as genuine predictions.