$B^0-{\bar{B}}^0$ mixing in quenched lattice QCD

Abstract

We present our results of lattice calculations of $B$ parameters, which parameterize $\hat{I}”B$=2 transition amplitudes together with the leptonic decay constant. Calculations are made in the quenched approximation at ${\hat{I}}^2$=5.7, 5.9, 6.0 and 6.1, using NRQCD action for heavy quark and the $O(a)$-improved Wilson action for light quark. The operators are perturbatively renormalized including the correction of $O(\hat{I}{\pm }_s/(aM{)}^m)$ ($m\ge$0). We examine the scaling behavior of $B$ parameters, and discuss the systematic uncertainties based on the results with several different truncations of higher order terms in 1/M and $\hat{I}{\pm }_s$ expansions. We find $B_{B_d}(m_b)=0.84(3)(5)$, $B_{B_s}/B_{B_d}=1.020(21){(}_{-16}^{+15}){(}_{-0}^{+5})$ and $B_{S_s}(m_b)=0.85(1)(5){(}_{-0}^{+1})$ in the quenched approximation. The errors represent statistical and systematic as well as the uncertainty in the determination of strange quark mass.

56 pages, 15 figures, LaTeX2e with RevTeX4. Systematic error from excited states and reference added, typo corrected. Appearing in PRD