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

TL;DR

This paper investigates how pion-pion scattering phase shifts depend on pion mass using standard and unitarized Chiral Perturbation Theory, providing insights relevant for lattice QCD studies and resonance behavior near thresholds.

Contribution

It offers a detailed analysis of pion-pion phase shifts across a range of pion masses using both standard and unitarized Chiral Perturbation Theory, including uncertainty estimates.

Findings

Phase shifts vary with pion mass, especially near resonances.

Unitarized Chiral Perturbation Theory captures resonance behavior effectively.

Uncertainties are mainly due to O(p^6) chiral parameters.

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.