# Pion scattering in the isospin I=2 channel from elongated lattices

## TL;DR

This study uses lattice QCD to analyze pion-pion scattering in the I=2 channel, extracting phase shifts and scattering lengths that agree with experimental data, across different lattice configurations and quark masses.

## Contribution

First lattice QCD calculation of I=2 pion scattering using elongated lattices with a combined analysis at multiple quark masses.

## Key findings

- Finite-volume spectra match experimental phase shifts.
- Scattering lengths agree with chiral perturbation theory.
- Results are consistent across different lattice geometries.

## Abstract

Pion-pion elastic scattering in the isospin I=2 channel is investigated in two-flavor dynamical lattice QCD. Six ensembles are used with lattices elongated in one of the spatial dimensions at two quark masses corresponding to a pion mass of 315 MeV and 226 MeV. The energy of the low-lying states below the inelastic threshold are extracted in each case using the standard variational method.The extracted finite-volume spectrum is fitted by the inverse amplitude method simultaneously for both quark masses and extrapolated thereafter to the physical point. The resulting phase-shifts and scattering length are compared with those from experiment, leading-order chiral perturbation theory and other lattice studies. Our calculations match the experimental results.