# A cross-channel study of pion scattering from lattice QCD

## TL;DR

This study performs a comprehensive analysis of pion-pion scattering using lattice QCD data across multiple isospin channels, employing a chiral model to improve parameter determination and physical extrapolation.

## Contribution

It introduces a simultaneous multi-channel analysis of lattice QCD pion scattering data with a chiral model, enhancing parameter accuracy and physical extrapolation over single-channel methods.

## Key findings

- Precise determination of scattering lengths: $m_ a_0^{I=0}=0.2132(9)$ and $m_ a_0^{I=2}=0.0433(2)$.
- Extraction of resonance parameters: $m_ \sigma=443(3)-i221(6)$ MeV, $m_
ho=724(4)-i67(1)$ MeV.
- Improved parameter constraints through cross-channel fitting.

## Abstract

We use a chiral model for pion interactions, in the inverse amplitude formalism, to perform a simultaneous analysis of lattice QCD results for pion-pion scattering in all three isospin channels. The input is the finite-volume two-pion spectrum computed using lattice QCD from six ensembles on lattices elongated in one of the spatial dimensions. A two-flavor dynamical lattice QCD action is used with two quark masses corresponding to a pion mass of 315 MeV and 224 MeV. The spectrum in the elastic region is subjected to a global fit which takes into account full correlations across isospin, pion mass and decay constant. The parameters from the fit are used to perform a chiral extrapolation to the physical point. The cross-channel fit results in a more precise determination of the parameters of the model when compared with single channel fits. We obtain $m_\pi a_0^{I=0}=0.2132(9)$, and $m_\pi a_0^{I=2}=0.0433(2)$ as well as $m_\sigma=443(3)-i221(6)$ MeV and $m_\rho=724(4)-i67(1)$ MeV. Several aspects of scale setting and consistency with previous analyses of lattice QCD results are discussed as well.