Chiral logs with staggered fermions

TL;DR

This paper calculates chiral logarithms for staggered fermions considering taste symmetry breaking, correcting previous errors and enabling better fits to lattice QCD data with additional parameters.

Contribution

It generalizes the Lee-Sharpe Lagrangian to include taste-breaking effects and corrects prior errors, improving the theoretical framework for analyzing staggered fermion simulations.

Findings

Corrected an error in previous chiral log calculations.

Successfully fit MILC lattice data with new formulas.

Identified new parameters needed for precise physical coefficient extraction.

Abstract

We compute chiral logarithms in the presence of "taste" symmetry breaking of staggered fermions. The lagrangian of Lee and Sharpe is generalized and then used to calculate the logs in $\pi$ and $K$ masses. We correct an error in Ref. [1] [C. Bernard, hep-lat/0111051]; the issue turns out to have implications for the comparison with simulations, even at tree level. MILC data with three light dynamical flavors can be well fit by our formulas. However, two new chiral parameters, which describe order $a^2$ hairpin diagrams for taste-nonsinglet mesons, enter in the fits. To obtain precise results for the physical coefficients at order $p^4$, these new parameters will need to be bounded, at least roughly.