Regularizing the quark-level $\sigma$ model

Abstract

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

Comments: 9 pages, 2 figures, Latex, to appear in Mod. Phys. Lett. A