Convergence issues in ChPT: a lattice perspective

TL;DR

This review examines the convergence of ChPT series in lattice QCD, highlighting recent results in SU(2), slow progress in SU(3), and issues related to lattice artifacts and quark mass ratios.

Contribution

It provides new estimates of low-energy constants in SU(2) ChPT and discusses convergence challenges in extended ChPT frameworks including lattice artifacts.

Findings

Improved estimates of arll_3 and arll_4 in SU(2) ChPT.

Slow progress in refining low-energy constants L_i in SU(3) ChPT.

Quark mass ratios do not require reordering of the chiral series.

Abstract

This review addresses the practical convergence of the ChPT series in the p-regime. In the SU(2) framework there is a number of new results, and improved estimates of \bar\ell_3 and \bar\ell_4 are available. In the SU(3) framework few new lattice computations have appeared and the improvement in the precision of the low-energy constants L_i is comparatively slow. I sketch some of the convergence issues genuine to extensions of ChPT which include additional sources of chiral symmetry breaking (finite lattice spacing) and/or violations of unitarity (different sea and valence quark masses). Finally, it is pointed out that the quark mass ratios m_u/m_d, m_s/m_d happen to be such that no reordering of the chiral series is needed to accommodate the experimental pion and kaon masses.