Nonanalytic Behavior of theΣTerm inπ−NScattering

Abstract

The $\Sigma$ term in the $\pi N$ scattering amplitude is commonly evaluated at squared nucleon momentum transfer $t=2\mathrm{}{\mu }^2$, where $\mu$ is the pion mass. Because of the nonanalytic nature of perturbations about the chiral SU(2) × SU(2) limit, $\Sigma \left(2\mathrm{}{\mu }^2\right)$ differs from $\Sigma \mathrm{}\left(0\right)\mathrm{}$ by a term linear in $\mu$. We calculate the difference term exactly to $O\left(\mu \right)$ and find