Non-Goldstone pion masses with NLO in Staggered Chiral Perturbation Theory

TL;DR

This paper calculates non-Goldstone pion and kaon masses up to NLO in SU(3) staggered chiral perturbation theory, providing formulas to analyze taste symmetry breaking effects in lattice QCD data.

Contribution

It derives the NLO expressions for non-Goldstone meson masses in SU(3) SChPT, including 20 unique low energy constants, for various QCD scenarios.

Findings

Derived NLO mass formulas for non-Goldstone pions and kaons.

Provided expressions for full, partially quenched, and quenched QCD cases.

Facilitates quantitative analysis of taste symmetry breaking in lattice simulations.

Abstract

We present results of the masses of taste non-Goldstone $(F \ne \xi_5)$ pions and kaons calculated up to the next-to-leading order in the SU(3) staggered chiral perturbation theory (SChPT). The results can be used to fit data and to understand taste symmetry breaking effect quantitatively. The final expressions for the non-Goldstone masses contain 20 low energy constants unique to the non-Goldstone sector. We have calculated the several cases such as the full QCD, partially quenched QCD, and quenched QCD in the $N_f=1+1+1$ flavor and $N_f=2+1$ flavor cases in the SU(3) and SU(2) SChPT. In this paper, we present only the SU(3) part.