Two-Loop Chiral Perturbation Theory and the Pion-Pion Phase Shifts

We want to test the predictive power of Chiral Perturbation Theory (ChPT). In this work, we use the ChPT pion-pion scattering amplitude, including two loop contributions, and we obtain S- and P-wave low-energy phase shifts. We show that, by varying just one free parameter, the resulting S- and P-wave phase shifts are in reasonable agreement with the experimental data.