Sigma resonance parameters from a $N_f=2$ lattice QCD simulation

TL;DR

This paper analyzes the sigma resonance in pion-pion scattering using a two-flavor lattice QCD simulation, extracting resonance parameters at different pion masses and extrapolating to the physical point.

Contribution

It provides the first lattice QCD determination of the sigma resonance parameters with systematic and stochastic error estimates, including extrapolation to the physical pion mass.

Findings

Sigma mass: 440 MeV at physical point

Sigma width: approximately 480 MeV

Resonance parameters vary with pion mass

Abstract

In this work we present the analysis of the energy spectrum from a recent two-flavor ($N_f=2$) lattice QCD calculation for pion-pion scattering in the scalar, isoscalar channel (the $\sigma$-meson). The lattice simulation was performed for two quark masses corresponding to a pion mass of 315 MeV and 227 MeV. The $\sigma$-meson parameters are extracted using various parametrizations of the scattering amplitude. The results obtained from a chiral unitary parametrization are extrapolated to the physical point and read $M_\sigma =( 440^{+10}_{-16}(50) - i\,240(20)(25))$ MeV, where the uncertainties in the parentheses denote the stochastic and systematic ones. The behavior of the $\sigma$-meson parameters with increasing pion mass is discussed as well.