Pion and Kaon masses in Staggered Chiral Perturbation Theory

TL;DR

This paper develops a method to compute chiral logarithms for pion and kaon masses in staggered chiral perturbation theory, accounting for taste-symmetry breaking and the fourth-root trick, with corrections to previous work.

Contribution

It introduces a generalized approach to calculate chiral logarithms in staggered fermion frameworks, correcting prior errors and applying to various quenching scenarios.

Findings

Computed one-loop chiral logarithm corrections for pion and kaon masses.

Accounted for taste-symmetry breaking and the fourth-root trick in calculations.

Provided corrected and generalized formulas for unquenched, partially quenched, and quenched cases.

Abstract

We show how to compute chiral logarithms that take into account both the $\cO(a^2)$ taste-symmetry breaking of staggered fermions and the fourth-root trick that produces one taste per flavor. The calculation starts from the Lee-Sharpe Lagrangian generalized to multiple flavors. An error in a previous treatment by one of us is explained and corrected. The one loop chiral logarithm corrections to the pion and kaon masses in the full (unquenched), partially quenched, and quenched cases are computed as examples.