The mass of the scalar boson beyond the large-N_c limit

Abstract

Within the framework of the $1/N_c$ expansion of four-fermion interaction models, we analyse the next to leading $1/N_c$ corrections to the well known large-$N_c$ result $M_S=2M_Q$ where $M_S$ is the mass of the scalar boson and $M_Q$ is the constituent quark mass. The calculation is performed in the Extended Nambu-Jona Lasinio (ENJL) model which is suitable for describing low energy hadron properties. We treat the model as fully non renormalizable and discuss the comparison with approaches based on the equivalence with renormalizable Yukawa type models. We consider both the $G_V=0$ and the $G_V\neq 0$ cases with $n_f=2$ flavours and study the dependence upon the regularization scheme. We find that pure next-to-leading $1/N_c$ corrections are large and negative, while a partially resummed treatment can induce positive and smaller corrections. A triplet-singlet states' splitting is observed.