Beta function in the non-Abelian Nambu-Jona-Lasinio model in four dimensions

Abstract

In this paper we present the structure of the renormalization group in non-Abelian Nambu-Jona-Lasinio model up to 1-loop order. The model is not perturbatively renormalizable in the usual power counting sense, but it is treated as an effective theory, valid in a scale of energy in which $p\ensuremath{\ll}\ensuremath{\Lambda}$, where $p$ is the external momenta of the loop and $\ensuremath{\Lambda}$ is a massive parameter that characterizes the couplings of the nonrenormalizable vertex. We clarify the tensorial structure of the interaction vertices and calculate the functions of the renormalization group. The analysis of the fixed points of the theory is also presented using Zimmermann's procedure for reducing the coupling constants. We find that the origin is an infrared-stable fixed point at low energies and also there is a nontrivial ultraviolet stable fixed point, indicating that the theory could be perturbatively investigated in the low momentum regime.