Chiral extrapolation of pion-pion scattering phase shifts within standard and unitarized Chiral Perturbation Theory

Abstract

We calculate the pion-pion elastic scattering phase shifts for pion masses from the chiral limit to values of interest for lattice studies. At low energies, we use the standard Chiral Perturbation Theory expressions to one and two loops. In addition, we study the phase shifts' mass dependence in the resonance region by means of dispersion theory in the form of unitarized Chiral Perturbation Theory and the inverse amplitude method. We pay particular attention to the case when resonances are close to threshold, illustrating the different behavior between scalar and vector resonances. We also provide the estimation of uncertainties, which are dominated by those of the $O({p}^{6})$ chiral parameters.