B0−B0mixing in quenched lattice QCD

We present our results of lattice calculations of B parameters, which parametrize $\Delta B=2\mathrm{}$ transition amplitudes together with the leptonic decay constant. Calculations are made in the quenched approximation at $\beta =5.7,$ 5.9, 6.0 and 6.1, using NRQCD action for heavy quarks and the $O\left(a\right)\mathrm{}$-improved Wilson action for light quarks. The operators are perturbatively renormalized including the correction of $O\left({\alpha }_s{/\left(\mathrm{aM}\right)\mathrm{}}^m\right)(m>~0).$ 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 ${\alpha }_s$ expansions. We find $B_{B_d}{(m}_b)=0.84\mathrm{}(3\left)\mathrm{}\right(5),$ $B_{B_s}{/B}_{B_d}{=1.020\mathrm{}\left(21\right)(}_{-16}^{+15\mathrm{}}{\left)\right(}_{-0}^{+5\mathrm{}})$ and $B_{S_s}{(m}_b{)=0.85\mathrm{}(1\left)\mathrm{}\right(5\left)\right(}_{-0}^{+1\mathrm{}})$ in the quenched approximation. The errors represent statistical and systematic errors as well as the uncertainty in the determination of strange quark mass.