Kaon B parameter from quenched domain-wall QCD

TL;DR

This paper calculates the kaon B parameter ($B_K$) using quenched domain-wall fermions in lattice QCD, examining systematic effects and providing a continuum estimate consistent with previous results.

Contribution

First calculation of $B_K$ with quenched domain-wall fermions including systematic effect analysis and continuum extrapolation.

Findings

$B_K(2 GeV)=0.5746(61)(191)$ in the $ar{MS}$ scheme

Systematic effects due to finite lattice sizes are analyzed

Results are consistent with previous Kogut-Susskind quark action calculations

Abstract

We report on a calculation of $B_K$ with domain wall fermion action in quenched QCD. Simulations are made with a renormalization group improved gauge action at $\beta=2.6$ and 2.9 corresponding to $a^{-1}\approx 2$GeV and 3GeV. Effects due to finite fifth dimensional size $N_5$ and finite spatial size $N_\sigma$ are examined in detail. Matching to the continuum operator is made perturbatively at one loop order. We obtain $B_K(\mu = 2 GeV)= 0.5746(61)(191)$, where the first error is statistical and the second error represents an estimate of scaling violation and ${\cal O}(\alpha^2)$ errors in the renormalization factor added in quadrature, as an estimate of the continuum value in the $\msbar$ scheme with naive dimensional regularization. This value is consistent, albeit somewhat small, with $B_K(\mu = 2 {GeV})= 0.628(42)$ obtained by the JLQCD Collaboration using the Kogut-Susskind quark action. Results for light quark masses are also reported.