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We report the first lattice QCD calculation of the form factors for the standard model treelevel decay Bs → K ν. In combination with future measurement, this calculation will provide an alternative exclusive semileptonic determination of |V ub |. We compare our results with previous model calculations, make predictions for differential decay rates and branching fractions, and predict the ratio of differential branching fractions between Bs → Kτ ν and Bs → Kµν. We also present standard model predictions for differential decay rate forward-backward asymmetries, polarization fractions, and calculate potentially useful ratios of Bs → K form factors with those of the fictitious Bs → ηs decay. Our lattice simulations utilize NRQCD b and HISQ light quarks on a subset of the MILC 2 + 1 asqtad gauge configurations, including two lattice spacings and a range of light quark masses.

We present a lattice QCD calculation of the B → Dlν semileptonic decay form factors f+(q 2 ) and f0(q 2 ) for the entire physical q 2 range. Non-relativistic QCD (NRQCD) bottom quarks and Highly Improved Staggered Quark (HISQ) charm and light quarks are employed together with N f = 2 + 1 MILC gauge configurations. A joint fit to our lattice and BaBar experimental data allows an extraction of the CKM matrix element |V cb |. We also determine the phenomenologically interesting ratio R(D) = B(B → Dτ ντ )/B(B → Dlν l ) (l = e, µ). We find |V cb | B→D excl. = 0.0402 (17)(13), where the first error consists of the lattice simulation errors and the experimental statistical error and the second error is the experimental systematic error. For the branching fraction ratio we find R(D) = 0.300(8).

We present a new study of D semileptonic decays on the lattice which employs the highly improved staggered quark action for both the charm and the light valence quarks. We work with MILC unquenched N f ¼ 2 þ 1 lattices and determine the scalar form factor f 0 ðq 2 Þ for D ! K, l semileptonic decays. The form factor is obtained from a scalar current matrix element that does not require any operator matching. We develop a new approach to carrying out chiral/continuum extrapolations of f 0 ðq 2 Þ. The method uses the kinematic ''z''variable instead of q 2 or the kaon energy E K and is applicable over the entire physical q 2 range. We find f D!K 0 ð0Þ f D!K þ ð0Þ ¼ 0:747ð19Þ in the chiral plus continuum limit and hereby improve the theory error on this quantity by a factor of $4 compared to previous lattice determinations. Combining the new theory result with recent experimental measurements of the product f D!K þ ð0Þ Ã jV cs j from BABAR and CLEO-c leads to a very precise direct determination of the CKM matrix element jV cs j, jV cs j ¼ 0:961ð11Þð24Þ, where the first error comes from experiment and the second is the lattice QCD theory error. We calculate the ratio f D!K þ ð0Þ=f D s and find 2:986 AE 0:087 GeV À1 and show that this agrees with experiment.

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