SU(2) chiral perturbation theory low-energy constants from 2+1 flavor staggered lattice simulations

TL;DR

This paper determines the low-energy constants _3 and _4 of SU(2) chiral perturbation theory using precise lattice QCD data for pion properties, analyzing the mass range needed for reliable extrapolation.

Contribution

It provides a novel extraction of _3 and _4 from 2+1 flavor staggered lattice simulations, exploring mass ranges for chiral extrapolation.

Findings

Determined _3 and _4 constants with lattice data.

Identified pion mass range for reliable chiral extrapolation.

Validated continuum chiral perturbation theory formulas for staggered fermions.

Abstract

We extract the next-to-leading-order low-energy constants \bar\ell_3 and \bar\ell_4 of SU(2) chiral perturbation theory, based on precise lattice data for the pion mass and decay constant on ensembles generated by the Wuppertal-Budapest Collaboration for QCD thermodynamics. These ensembles feature 2+1 flavors of two-fold stout-smeared dynamical staggered fermions combined with Symanzik glue, with pion masses varying from 135 to 435 MeV, lattice scales between 0.7 and 2.0 GeV, while m_s is kept fixed at its physical value. Moderate taste splittings and the scale being set through the pion decay constant allow us to restrict ourselves to the taste pseudoscalar state and to use formulas from continuum chiral perturbation theory. Finally, by dropping the data points near 135 MeV from the fits, we can explore the range of pion masses that is needed in SU(2) chiral perturbation theory to reliably extrapolate to the physical point.