Chiral effective theory with a light scalar and lattice QCD

TL;DR

This paper extends chiral perturbation theory to include a light scalar, using lattice QCD data to analyze pion interactions, quark masses, and the sigma resonance, providing new insights into low-energy QCD phenomena.

Contribution

It introduces a modified chiral effective theory with a light scalar and demonstrates its application to lattice QCD data analysis.

Findings

Determined the impact of the light scalar on low-energy constants.

Extracted the average light quark masses from lattice data.

Estimated the mass and width of the sigma resonance.

Abstract

We extend the usual chiral perturbation theory framework ($\chi$PT) to allow the inclusion of a light dynamical isosinglet scalar. Using lattice QCD results, and a few phenomenological inputs, we explore the parameter space of the effective theory. We discuss the S-wave pion-pion scattering lengths, extract the average value of the two light quark masses and evaluate the impact of the dynamical singlet field in the low--energy constants $\bar{l}_1$, $\bar{l}_3$ and $\bar{l}_4$ of $\chi$PT. We also show how to extract the mass and width of the sigma resonance from chiral extrapolations of lattice QCD data.