Lattice determination of the QCD low-energy constant $\ell_{\scriptscriptstyle{7}}$

TL;DR

This paper non-perturbatively determines the QCD low-energy constant rom lattice QCD simulations with 2+1 flavors, achieving controlled extrapolations and improving previous estimates.

Contribution

It introduces a lattice QCD method using staggered fermions to accurately compute rom pion mass splitting, with controlled continuum and chiral limits.

Findings

Final ound to be 2.79(61) imes 10^{-3}

Results agree with and improve upon previous determinations

Controlled extrapolations achieved with multiple ensembles

Abstract

We provide a non-perturbative determination of the scheme- and scale-independent low-energy constant $\ell_{\scriptscriptstyle{7}}$, appearing in the QCD effective chiral Lagrangian at next-to-leading order, by means of lattice QCD simulations with $N_{\scriptscriptstyle{\rm f}}=2+1$ quark flavors. We adopt staggered fermions and extract $\ell_{\scriptscriptstyle{7}}$ from the pion mass splitting by suitably generalizing the method introduced in [Phys. Rev. D 104 (2021) 074513] for the Wilson discretization. Adopting 12 gauge ensembles with 3 different values of the pion mass, and 4 different values of the lattice spacing, we are able to achieve controlled extrapolations towards the continuum, infinite volume, and chiral limits. Our final result $\ell_{\scriptscriptstyle{7}} \,\times \, 10^3 = 2.79(58)_{\scriptscriptstyle{\rm stat}}(19)_{\scriptscriptstyle{\rm syst}} = 2.79(61)_{\scriptscriptstyle{\rm tot}}$ agrees with and substantially improves on previous determinations.