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

Understand

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.