SU(3) flavor breaking in hadronic matrix elements forB−B¯oscillations

Abstract

Results in the quenched approximation for SU(3) breaking ratios of the heavy-light decay constants and the $\ensuremath{\Delta}F=2$ mixing matrix elements are reported. Using lattice simulations at ${6/g}^{2}=5.7$, 5.85, 6.0, and 6.3, we directly compute the mixing matrix element ${M}_{\mathrm{hl}}=〈{P}_{\mathrm{hl}}|\overline{h}{\ensuremath{\gamma}}_{\ensuremath{\mu}}(1\ensuremath{-}{\ensuremath{\gamma}}_{5})l\overline{h}{\ensuremath{\gamma}}_{\ensuremath{\mu}}(1\ensuremath{-}{\ensuremath{\gamma}}_{5})l|{P}_{\mathrm{hl}}〉.$ Extrapolating to the physical $B$ meson states, ${B}^{0}$ and ${B}_{s}^{0},$ we obtain ${M}_{\mathrm{bs}}{/M}_{\mathrm{bd}}{=1.76(10)}_{\ensuremath{-}42}^{+57}$ in the continuum limit. The systematic error includes the errors within the quenched approximation but not the errors of quenching. We also obtain the ratio of decay constants, ${f}_{\mathrm{bs}}{/f}_{\mathrm{bd}}{=1.17(2)}_{\ensuremath{-}6}^{+12}.$ For the $B$ parameters we find ${B}_{\mathrm{bs}}(2\phantom{\rule{0ex}{0ex}}\mathrm{GeV}{)=B}_{\mathrm{bd}}(2\phantom{\rule{0ex}{0ex}}\mathrm{GeV})=1.02(13);$ we cannot resolve the SU(3) breaking effects in this case.