Chiral Extrapolations of light resonances from dispersion relations and Chiral Perturbation Theory

TL;DR

This paper investigates how the masses and properties of rho and sigma resonances depend on the pion mass using a modified Chiral Perturbation Theory approach, providing insights relevant for lattice QCD studies.

Contribution

It introduces a modified Inverse Amplitude Method that accurately accounts for the Adler zero in ChPT, improving predictions of resonance behavior with changing pion mass.

Findings

Rho-pi-pi coupling is nearly independent of pion mass.

Predicted rho mass aligns well with recent lattice results.

Method effectively relates low-energy ChPT to resonance properties.

Abstract

We review our recent study of the pion mass dependence of the rho and sigma resonances generated from one-loop SU(2) Chiral Perturbation Theory (ChPT) with the Inverse Amplitude Method (IAM) which was modified to properly account for the Adler zero. The method is based on analyticity, elastic unitarity and ChPT at low energies, thus yielding the pion mass dependence of the resonance pole positions from the ChPT series up to a given order. We find that the rho-pi-pi coupling constant is almost m_pi independent and that our prediction compare well with some recent lattice results for the rho mass. These findings may be relevant for studies of the meson spectrum and form factors on the lattice.