The Kaon B-parameter in Mixed Action Chiral Perturbation Theory

TL;DR

This paper calculates the kaon B-parameter in a mixed action chiral perturbation theory framework, showing minimal discretization errors and finite volume effects, with implications for lattice QCD computations.

Contribution

It derives a simplified expression for B_K in mixed action theories with Ginsparg-Wilson and staggered quarks, including one-loop corrections and discretization effects.

Findings

The expression for B_K is similar to the continuum with only two additional parameters.

Taste-symmetry violations contribute to flavor-disconnected diagrams as O(a^2) shifts.

Numerical results show discretization errors and finite volume effects are small on MILC lattices.

Abstract

We calculate the kaon B-parameter, B_K, in chiral perturbation theory for a partially quenched, mixed action theory with Ginsparg-Wilson valence quarks and staggered sea quarks. We find that the resulting expression is similar to that in the continuum, and in fact has only two additional unknown parameters. At one-loop order, taste-symmetry violations in the staggered sea sector only contribute to flavor-disconnected diagrams by generating an O(a^2) shift to the masses of taste-singlet sea-sea mesons. Lattice discretization errors also give rise to an analytic term which shifts the tree-level value of B_K by an amount of O(a^2). This term, however, is not strictly due to taste-breaking, and is therefore also present in the expression for B_K for pure G-W lattice fermions. We also present a numerical study of the mixed B_K expression in order to demonstrate that both discretization errors and finite volume effects are small and under control on the MILC improved staggered lattices.