Extraction of isoscalar $\pi\pi$ phase-shifts from lattice QCD

TL;DR

This study uses lattice QCD to calculate pion-pion scattering phase-shifts in the scalar isoscalar channel, extracting the properties of the sigma meson at different pion masses and extrapolating to physical conditions.

Contribution

First lattice QCD calculation of isoscalar pion-pion phase-shifts with detailed sigma meson parameter extraction and pion mass dependence analysis.

Findings

Sigma meson mass: approximately 440 MeV at physical point.

Sigma meson width: approximately 240 MeV.

Phase-shifts consistent with experimental data at physical pion mass.

Abstract

We conduct a two-flavor ($N_f=2$) lattice QCD calculation of the elastic phase-shifts for pion-pion scattering in the scalar, isoscalar channel (the $\sigma$-meson). The calculation is performed for two quark masses corresponding to a pion mass of $315\text{ MeV}$ and $227\text{ MeV}$. 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 $M_\sigma = (440^{+10}_{-16}(50) - i\,240(20)(25))\text{ MeV}$, 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.