Finite Volume Errors in $B_K$

TL;DR

This paper evaluates finite volume errors in lattice QCD calculations of B_K using improved staggered fermions, finding minimal impact on results when including finite volume corrections via chiral perturbation theory.

Contribution

It introduces the use of GPU-accelerated extrapolation with NLO staggered SU(2) chiral perturbation theory to assess finite volume effects in B_K calculations.

Findings

Finite volume effects cause only a 0.5% shift in B_K in the continuum limit.

GPU computations enable more precise finite volume correction extrapolations.

Finite volume corrections are found to be very small in this study.

Abstract

We discuss finite volume errors in our calculations of $B_K$ using improved staggered fermions on the MILC asqtad lattices. Using GPUs, we are now able to extrapolate using next-to-leading order (NLO) staggered SU(2) chiral perturbation theory including the finite volume corrections arising from pion loops. We find that the impact of FV fitting is very small, giving a 0.5% shift in the continuum limit.