Chiral extrapolation of the sigma and rho mesons from dispersion relations and Chiral Perturbation Theory

TL;DR

This paper investigates how the masses and couplings of the rho and sigma mesons depend on the pion mass using Chiral Perturbation Theory and dispersion relations, providing insights relevant for lattice QCD studies.

Contribution

It introduces a modified Inverse Amplitude Method that accurately captures pion mass dependence of meson resonances, including the Adler zero region, up to next-to-leading order in ChPT.

Findings

Rho-pi-pi coupling is nearly pion mass independent

Rho mass varies smoothly with pion mass

Sigma mass exhibits strong non-analytic behavior

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). In order to properly account for the Adler zero region, we also review the recently obtained modified version of the IAM; which is based on analyticity, elastic unitarity and ChPT at low energies, thus yielding the correct pion mass dependence of the resonance pole positions up to next-to-leading order in ChPT. As main results we find that the rho-pi-pi coupling constant is almost pion mass independent and that the rho mass shows a smooth pion mass dependence while that of the sigma shows a strong non-analyticity. These findings are important for studies of the meson spectrum on the lattice.