Validity of ChPT -- is M_\pi=135 MeV small enough ?

TL;DR

This paper evaluates the convergence of SU(2) Chiral Perturbation Theory using lattice QCD data, finding it reliable up to about 350 MeV pion mass but breaking down beyond 500 MeV.

Contribution

It provides a detailed analysis of ChPT convergence with physical and near-physical pion masses using state-of-the-art lattice data, highlighting the limits of the chiral expansion.

Findings

ChPT is reliable up to ~350 MeV pion mass

Breakdown of the chiral series occurs near 400-500 MeV

Controlled determination of low-energy constants is possible with sufficient data

Abstract

I discuss the practical convergence of the SU(2) ChPT series in the meson sector, based on 2+1 flavor lattice data by the Wuppertal-Budapest and Budapest-Marseille-Wuppertal collaborations. These studies employ staggered and clover-improved Wilson fermions, respectively. In both cases large box volumes and several lattice spacings are used, and the pion masses reach down to the physical mass point. We conclude that LO and NLO low-energy constants can be determined with controlled systematics, if there is sufficient data between the physical mass point and about 350 MeV pion mass. Exploratory LO+NLO+NNLO fits with a wider range reveal some distress of the chiral series near M_\pi ~ 400 MeV and suggest a complete breakdown beyond M_\pi ~ 500 MeV.