Regularizing the quark-level $\sigma$ model

R. Delbourgo, A. A. Rawlinson, M. D. Scadron

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 $…