# Toward the Continuum Limit of $B_K$ with the Quenched Kogut-Susskind Quark Action

## TL;DR

This paper reports on precise lattice QCD calculations of the kaon B parameter using quenched Kogut-Susskind quarks, revealing the lattice spacing dependence and providing a continuum limit estimate.

## Contribution

It presents new results at different lattice spacings, analyzes the curvature change in B_K dependence, and refines the continuum limit estimate with an $O(a^2)$ fit.

## Key findings

- B_K in the continuum limit is 0.587(7)(17).
- The lattice spacing dependence of B_K changes curvature at finer lattices.
- Finite-size effects and theoretical behavior of $O(a^2)$ are analyzed.

## Abstract

We present new results of our ongoing project toward a precision determination of the kaon $B$ parameter with the Kogut-Susskind quark action in quenched QCD. New results taken at $\beta$=6.4 and $\beta=5.7$ suggest that an apparently linear $a$ dependence of $B_K$ previously observed for $\beta=5.85-6.2$ arises from a change of curvature from convex to concave as the lattice spacing is reduced. Fitting data for $\beta\geq 5.93$ with an $O(a^2)$ form yields $B_K$(NDR,2 GeV)=0.587(7)(17) in the continuum limit. We also describe a finite-size study of $B_K$ at $\beta=$ 6.0 and 6.4, and a reanalysis of the theoretical argument for $O(a^2)$ behavior.