$B_K$ in unquenched QCD using improved staggered fermions

TL;DR

This paper reports preliminary lattice QCD calculations of the kaon bag parameter $B_K$ using improved staggered fermions, exploring effects of non-degenerate quark masses and taste-breaking in chiral fits.

Contribution

It introduces a mixed action approach with HYP-smeared valence and AsqTad sea quarks, analyzing non-degenerate quark effects on $B_K$ and fitting to chiral perturbation theory.

Findings

Including non-degenerate quark masses improves fit quality.

Deviations in light quark mass region suggest taste-breaking effects.

Preliminary results indicate potential need for taste-breaking inclusion in models.

Abstract

We present preliminary results for $B_K$ calculated using improved staggered fermions with a mixed action (HYP-smeared staggered valence quarks and AsqTad staggered sea quarks). We investigate the effect of non-degenerate quarks on $B_K$ and attempt to estimate the ${\cal O}(a^2)$ effect due to non-Goldstone pions in loops. We fit the data to continuum partially quenched chiral perturbation theory. We find that the quality of fit for $B_K$ improves if we include non-degenerate quark mass combinations. We also observe, however, that the fitting curve deviates from the data points in the light quark mass region. This may indicate the need to include taste-breaking in pion loops.