# SU(3) Flavor Breaking in Hadronic Matrix Elements for $B - \bar B$ Oscillations

## TL;DR

This paper analyzes SU(3) flavor symmetry breaking effects in hadronic matrix elements relevant for B meson oscillations using lattice QCD, providing preliminary ratios and parameters crucial for CKM matrix element determination.

## Contribution

It offers the first lattice QCD calculation of the SU(3) breaking ratio $ ext{MS}/ ext{MB}$ for B mesons and determines B parameters at a specific scale.

## Key findings

- Preliminary ratio $ ext{MS}/ ext{MB}=1.54(13)(32)$.
- B parameters $B_{bs}(2 ext{GeV})=B_{bd}(2 ext{GeV})=1.02(13)$.
- Results aid in constraining CKM matrix elements.

## Abstract

We present an analysis, using quenched configurations at $6/g^2=$5.7, 5.85, 6.0, and 6.3 of the matrix element $\MP\equiv\langle \bar P_{hl}|\bar h \gamma_\mu (1-\gamma_5)l \bar h \gamma_\mu(1-\gamma_5)l|P_{hl}\rangle$ for heavy-light pseudoscalar mesons. The results are extrapolated to the physical $B$ meson states, $\Bd$ and $\Bs$. We directly compute the ratio $\MS/\MB$, and obtain the preliminary result $\MS/\MB=1.54(13)(32)$. A precise value of this SU(3) breaking ratio is important for determining $V_{td}$ once the mixing parameter $x_s$ for $\Bs-\bar\Bs$ is measured experimentally. We also determine values for the corresponding B parameters, $B_{bs}(2 \rm{GeV})=B_{bd}(2 \rm{GeV})=1.02(13)$, which we cannot distinguish in the present analysis.