# A Study of the Static-Light $B_B$ Parameter

## TL;DR

This paper presents a lattice gauge theory calculation of the $B_B$ parameter, crucial for understanding B-meson mixing, employing improved techniques to reduce errors and uncertainties in the simulation.

## Contribution

It introduces an optimized variational method for better signal extraction and linearizes renormalization to minimize higher-order uncertainties.

## Key findings

- Reduced statistical errors with improved sources
- Minimized excited-state contamination
- Estimated renormalization with lower order uncertainties

## Abstract

We calculate the $B_B$ parameter, relevant for $\overline{B}^0$--$B^0$ mixing, from a lattice gauge theory simulation using the static approximation for the heavy quark and the Wilson action for the light quark and gauge fields. Improved sources, produced by an optimized variational technique, {\sc most}, reduce statistical errors and minimize excited-state contamination of the ground-state signal. Renormalization of four-fermion operator coefficients, using the Lepage-Mackenzie procedure for estimating typical momentum scales, is linearized to reduce order $\alpha_s^2$ uncertainties.