Regularizing the quark-level $σ$ model

Abstract

We show that the finite difference, $-iπ^2 m^2$, between quadratic and logarithmic divergent integrals $\int d^4p[m^2(p^2-m^2)^{-2}-(p^2-m^2)^{-1}]$, as encountered in the linear $σ$ model, is in fact regularization independent.