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

TL;DR

This study calculates the isospin-0 $cc$ s-wave scattering length using twisted mass lattice QCD across multiple ensembles, providing results that align well with experimental and theoretical values at the physical pion mass.

Contribution

It presents the first lattice QCD calculation of the isospin-0 $cc$ scattering length using twisted mass fermions at physical pion mass, including a chiral extrapolation.

Findings

The scattering length at physical pion mass is $0.198(9)(6)$.

Results agree with experimental measurements and theoretical predictions.

Qualitative pion mass dependence discussed from $N_f=2+1+1$ ensembles.

Abstract

We present results for the isospin-0 $\pi\pi$ s-wave scattering length calculated in twisted mass lattice QCD. We use three $N_f = 2$ ensembles with unitary pion mass at its physical value, 240~MeV and 330~MeV respectively. We also use a large set of $N_f = 2 + 1 +1$ ensembles with unitary pion masses varying in the range of 230~MeV - 510~MeV at three different values of the lattice spacing. A mixed action approach with the Osterwalder-Seiler action in the valence sector is adopted to circumvent the complications arising from isospin symmetry breaking of the twisted mass quark action. Due to the relatively large lattice artefacts in the $N_f = 2 + 1 +1$ ensembles, we do not present the scattering lengths for these ensembles. Instead, taking the advantage of the many different pion masses of these ensembles, we qualitatively discuss the pion mass dependence of the scattering properties of this channel based on the results from the $N_f = 2 + 1 +1$ ensembles. The scattering length is computed for the $N_f = 2$ ensembles and the chiral extrapolation is performed. 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.