Unquenched determination of the kaon parameterBKfrom improved staggered fermions

Abstract

The use of improved staggered actions (HYP, Asqtad) has been proved to reduce the scaling corrections that affected previous calculations of ${B}_{K}$ with unimproved (standard) staggered fermions in the quenched approximation. This improved behavior allows us to perform a reliable calculation of ${B}_{K}$ including quark vacuum polarization effects, using the MILC configurations with ${n}_{f}=2+1$ flavors of sea fermions. We perform such a calculation for a single lattice spacing, $a=0.125\text{ }\text{ }\mathrm{fm}$, and with kaons made up of degenerate quarks with ${m}_{s}/2$. The valence strange quark mass ${m}_{s}$ is fixed to its physical value and we use two different values of the light sea quark masses. After a chiral extrapolation of the results to the physical value of the sea quark masses, we find ${\stackrel{^}{B}}_{K}=0.83\ifmmode\pm\else\textpm\fi{}0.18$, where the error is dominated by the uncertainty in the lattice to continuum matching at $\mathcal{O}({\ensuremath{\alpha}}_{s}^{2})$. The matching will need to be improved to get the precision needed to make full use of the experimental data on ${\ensuremath{\epsilon}}_{K}$ to constrain the unitarity triangle.