Chiral effective theory with a light scalar and lattice QCD

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.

Comments: Journal version. Added the study of the scalar two-point function and a discussion of the analytical properties of the sigma pole and its dependence on the quark masses. We clarified the relation of $chi$PT${}_S$ with unitarized $chi$PT. Figures 6 and 8 have been improved. 28 pages, 2 tables, 8 figures