Hadron-Hadron Interactions from $N_f=2+1+1$ Lattice QCD: isospin-2 $\pi\pi$ scattering length

TL;DR

This study computes the isospin-2 pion-pion scattering length using advanced lattice QCD techniques, reducing errors and systematically analyzing effects to provide a precise physical value.

Contribution

It introduces improved lattice QCD calculations with reduced statistical errors and comprehensive systematic analysis for the $I=2$ $$ scattering length.

Findings

Precise value of $M_ a_0$ with quantified uncertainties.

Reduced statistical errors through Laplacian Heaviside smearing.

Systematic effects thoroughly investigated and accounted for.

Abstract

We present results for the $I=2$ $\pi\pi$ scattering length using $N_f=2+1+1$ twisted mass lattice QCD for three values of the lattice spacing and a range of pion mass values. Due to the use of Laplacian Heaviside smearing our statistical errors are reduced compared to previous lattice studies. A detailed investigation of systematic effects such as discretisation effects, volume effects, and pollution of excited and thermal states is performed. After extrapolation to the physical point using chiral perturbation theory at NLO we obtain $M_\pi a_0=-0.0442(2)_\mathrm{stat}(^{+4}_{-0})_\mathrm{sys}$.