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

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 $\text{MP}\equiv ⟨{\bar{P}}_{hl}|\bar{h}{\gamma }_{\mu }(1-{\gamma }_5)l\bar{h}{\gamma }_{\mu }(1-{\gamma }_5)l|P_{hl}⟩$ for heavy-light pseudoscalar mesons. The results are extrapolated to the physical $B$ meson states, $\text{Bd}$ and $\text{Bs}$. We directly compute the ratio $\text{MS}/\text{MB}$, and obtain the preliminary result $\text{MS}/\text{MB}=1.54(13)(32)$. A precise value of this SU(3) breaking ratio is important for determining $V_{td}$ once the mixing parameter $x_s$ for $\text{Bs}-\overline{\text{Bs}}$ is measured experimentally. We also determine values for the corresponding B parameters, $B_{bs}(2\mathrm{GeV})={\mathrm{B}}_{\mathrm{bd}}(2\mathrm{GeV})=1.02(13)$, which we cannot distinguish in the present analysis.

Comments: Poster presented at LATTICE96(heavy quarks). LaTeX, uses espcrc2.sty and epsf, 4 pages, 4 postscript figures included