The Low Energy Constants of $SU(2)$ Partially Quenched Chiral Perturbation Theory from $N_{f}=2+1$ Domain Wall QCD

TL;DR

This paper determines low energy constants of $SU(2)$ partially quenched chiral perturbation theory using lattice QCD data, providing precise fits and predictions for isospin breaking and scattering lengths within a specific pseudoscalar mass range.

Contribution

It presents the first comprehensive extraction of low energy constants at NNLO from $N_f=2+1$ domain wall QCD data, demonstrating the robustness of the chiral expansion.

Findings

NNLO chiral expansion fits lattice data with percent accuracy

Values for 9 NLO and 8 NNLO low energy constants are reported

Predictions for QCD isospin breaking effects and $ ext{S-wave}\pi ext{-} ext{pi}$ scattering lengths are made.

Abstract

We have performed fits of the pseudoscalar masses and decay constants, from a variety of RBC-UKQCD domain wall fermion ensembles, to $SU(2)$ partially quenched chiral perturbation theory at next-to leading order (NLO) and next-to-next-to leading order (NNLO). We report values for 9 NLO and 8 linearly independent combinations of NNLO partially quenched low energy constants, which we compare to other lattice and phenomenological determinations. We discuss the size of successive terms in the chiral expansion and use our large set of low energy constants to make predictions for mass splittings due to QCD isospin breaking effects and the S-wave $\pi \pi$ scattering lengths. We conclude that, for the range of pseudoscalar masses explored in this work, $115~\mathrm{MeV} \lesssim m_{\rm PS} \lesssim 430~\mathrm{MeV}$, the NNLO $SU(2)$ expansion is quite robust and can fit lattice data with percent-scale accuracy.