Isospin-0 $\pi\pi$ s-wave scattering length from twisted mass lattice QCD

TL;DR

This study calculates the isospin-0 $$ scattering length using twisted mass lattice QCD, achieving results consistent with experiments, but with some systematic uncertainties due to single lattice spacing.

Contribution

First lattice QCD calculation of the isospin-0 $$ scattering length using twisted mass fermions at physical pion mass.

Findings

Result $M_ a_0^{I=0} = 0.198(9)(6)$ agrees with experimental data.

Used stochastic Laplacian Heaviside smearing for precise correlation functions.

Performed chiral extrapolation to physical pion mass.

Abstract

We present results for the isospin-0 $\pi\pi$ s-wave scattering length calculated with Osterwalder-Seiler valence quarks on Wilson twisted mass gauge configurations. We use three $N_f = 2$ ensembles with unitary (valence) pion mass at its physical value (250$\sim$MeV), at 240$\sim$MeV (320$\sim$MeV) and at 330$\sim$MeV (400$\sim$MeV), respectively. By using the stochastic Laplacian Heaviside quark smearing method, all quark propagation diagrams contributing to the isospin-0 $\pi\pi$ correlation function are computed with sufficient precision. The chiral extrapolation is performed to obtain the scattering length at the physical pion mass. Our result $M_\pi a^\mathrm{I=0}_0 = 0.198(9)(6)$ agrees reasonably well with various experimental measurements and theoretical predictions. Since we only use one lattice spacing, certain systematics uncertainties, especially those arising from unitary breaking, are not controlled in our result.