B_K in Staggered Chiral Perturbation Theory

TL;DR

This paper calculates the kaon B-parameter, B_K, at next-to-leading order in staggered chiral perturbation theory, accounting for taste breaking and matching factor effects across different QCD scenarios.

Contribution

It extends staggered chiral perturbation theory to include perturbative matching effects and taste breaking, providing comprehensive expressions for B_K in various QCD contexts.

Findings

Derived B_K expressions for partially quenched, quenched, and full QCD.

Analyzed taste breaking effects and operator mixing.

Presented continuum chiral perturbation theory results for N_f=3.

Abstract

We calculate the kaon B-parameter, B_K, to next-to-leading order in staggered chiral perturbation theory. We find expressions for partially quenched QCD with three sea quarks, quenched QCD, and full QCD with m_u = m_d but not equal to m_s. We extend the usual power counting to include the effects of using perturbative (rather than non-perturbative) matching factors. Taste breaking enters through the O(a^2) terms in the effective action, through O(a^2) terms from the discretization of operators, and through the truncation of matching factors. These effects cause mixing with several additional operators, complicating the chiral and continuum extrapolations. In addition to the staggered expressions, we present B_K at next-to-leading order in continuum partially quenched chiral perturbation theory for N_f=3 sea quarks with m_u = m_d but not equal to m_s.