Convergence of the chiral expansion in two-flavor lattice QCD

TL;DR

This study investigates the convergence of chiral perturbation theory in two-flavor lattice QCD using overlap fermions, showing good agreement at NLO for pions lighter than 450 MeV and improved convergence with a resummed expansion.

Contribution

It demonstrates the convergence properties of chiral expansion in lattice QCD with overlap fermions and provides precise determinations of low energy constants and quark masses.

Findings

Chiral expansion converges well at NLO for pions < 450 MeV.

Resummed expansion parameter $\xi$ improves convergence up to NNLO.

Accurate values for low energy constants and quark masses obtained.

Abstract

We test the convergence property of the chiral perturbation theory (ChPT) using a lattice QCD calculation of pion mass and decay constant with two dynamical quark flavors. The lattice calculation is performed using the overlap fermion formulation, which realizes exact chiral symmetry at finite lattice spacing. By comparing various expansion prescriptions, we find that the chiral expansion is well saturated at the next-to-leading order (NLO) for pions lighter than $\sim$450 MeV. Better convergence behavior is found in particular for a resummed expansion parameter $\xi$, with which the lattice data in the pion mass region 290$\sim$750 MeV can be fitted well with the next-to-next-to-leading order (NNLO) formulae. We obtain the results in two-flavor QCD for the low energy constants $\bar{l}_3$ and $\bar{l}_4$ as well as the pion decay constant, the chiral condensate, and the average up and down quark mass.