Pion scattering in Wilson ChPT

Abstract

We compute the scattering amplitude for pion scattering in Wilson chiral perturbation theory for two degenerate quark flavors. We consider two different regimes where the quark mass m is of order (i) a\Lambda_QCD^2 and (ii) a^2\Lambda_QCD^3. Analytic expressions for the scattering lengths in all three isospin channels are given. As a result of the O(a^2) terms the I=0 and I=2 scattering lengths do not vanish in the chiral limit. Moreover, additional chiral logarithms proportional to a^2\ln M_{\pi}^2 are present in the one-loop results for regime (ii). These contributions significantly modify the familiar results from continuum chiral perturbation theory.Comment: 20 pages, 4 figures. V3: Comments on finite size effects and the axial vector current added, one more reference. To be published in PR