SU(3) flavor breaking in hadronic matrix elements for 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 M hl ≡ P hl |hγµ(1 − γ5)lhγµ(1 − γ5)l|P hl for heavy-light pseudoscalar mesons. The results are extrapolated to the physical B meson states, B 0 and B 0 s . We directly compute the ratio M bs /M bd , and obtain the preliminary result M bs /M bd = 1.54(13)(32). A precise value of this SU(3) breaking ratio is important for determining V td once the mixing parameter xs for B 0 s −B 0 s is measured experimentally. We also determine values for the corresponding B parameters, B bs (2GeV) = B bd (2GeV) = 1.02(13), which we cannot distinguish in the present analysis.

Calculation of theBBparameter in the static limit

“…Even though the ratio B Bs /B B is determined quite precisely, it is not resolved whether B Bs is greater than or less than B B since the B B parameter is found to depend weakly on the quark mass. Other groups [21,50,56] have reported similar findings. Most lattice simulations have found that f Bs is between ten and twenty percent larger than f B [10].…”

“…Most lattice simulations have found that f Bs is between ten and twenty percent larger than f B [10]. Bernard et al [56] have extracted the ratio of gives Eq. (A3) with no order-α 2 terms due to coefficient multiplication.…”

Leptonic Decays of Heavy Quarks on the Lattice

“…Attempts in this direction have been reported in the context of the B parameter B K 84,85 . Lattice results for the B parameter B B have been published recently using the static approximation 100,162,163 and also propagating heavy quarks 114,164,165 . Earlier attempts are discussed in refs.…”

“…Clearly, the currently available data for B B do not allow for such an extrapolation as in the case of decay constants discussed in the previous section. However, preliminary results in the continuum limit for B B and some SU(3)-flavour breaking ratios involving the B parameter have been reported 164,165 . Also, by comparing the results from refs.…”

“…It is worth noting that apart from the estimates for ξ 2 sd in the static approximation (ref. 100,162 ), there is also a preliminary result 165 which treats heavy quarks in the conventional approach. Moreover, in that study ξ 2 sd was computed directly from the ratio of operator matrix elements, viz.…”