# Miscellanies of $ K^0 - \bar{K}^0 $ mixing and $ B_K $

## TL;DR

This paper calculates the parameter $ B_K $ related to neutral kaon mixing using lattice QCD with staggered fermions, comparing two methods and analyzing effects of non-degenerate quark pairs.

## Contribution

It introduces two different computational methods for $ B_K $ on a lattice and examines the impact of non-degenerate quark pairs on the calculation.

## Key findings

- No effect of non-degenerate quark pairs on $ B_K $
- Effects observed on individual terms making up $ B_K $
- Results consistent across methods

## Abstract

We have computed $ B_K $, using two different methods with staggered fermions on a $ 16^3 \times 40 $ lattice at $ \beta = 5.7 $ with two dynamical flavors of a mass 0.01. % Using an improved wall source method, we have studied a series of non-degenerate quark antiquark pairs and observed no effect on $ B_K $, although effects were seen on the individual terms making up $ B_K $.