# Scattering from finite size methods in lattice QCD

## TL;DR

This paper uses lattice QCD with twisted mass fermions to compute pion-pion scattering parameters, extrapolating to physical pion mass and analyzing resonance properties through finite size methods.

## Contribution

It introduces lattice calculations of pion-pion scattering lengths and phase shifts using finite size techniques, providing new insights into resonance parameters.

## Key findings

- Scattering length for I=2 channel at physical pion mass: -0.04385(28)(38)
- Resonance mass and decay width of rho meson estimated from phase shifts
- Finite size methods effectively extract scattering phases in lattice QCD

## Abstract

Using two flavors of maximally twisted mass fermions, we calculate the S-wave pion-pion scattering length in the isospin I=2 channel and the P-wave pion-pion scattering phase in the isospin I=1 channel. In the former channel, the lattice calculations are performed at pion masses ranging from 270 MeV to 485 MeV. We use chiral perturbation theory at next-to-leading order to extrapolate our results. At the physical pion mass, we find m_pi a_pipi(I=2)=-0.04385(28)(38) for the scattering length. In the latter channel, the calculation is currently performed at a single pion mass of 391 MeV. Making use of finite size methods, we evaluate the scattering phase in both the center of mass frame and the moving frame. The effective range formula is employed to fit our results, from which the rho resonance mass and decay width are evaluated.