We present a lattice QCD determination of the Bs → Ds ν scalar and vector form factors over the full physical range of momentum transfer. The result is derived from correlation functions computed using the Highly Improved Staggered Quark (HISQ) formalism, on the second generation MILC gluon ensembles accounting for up, down, strange and charm contributions from the sea. We calculate correlation functions for three lattice spacing values and an array of unphysically light b-quark masses, and extrapolate to the physical value. Using the HISQ formalism for all quarks means that the lattice current coupling to the W can be renormalized non-perturbatively, giving a result free from perturbative matching errors for the first time. Our results are in agreement with, and more accurate than, previous determinations of these form factors. From the form factors we also determine the ratio of branching fractions that is sensitive to violation of lepton universality: R(Ds) = B(Bs → Dsτ ντ )/B(Bs → Ds ν l ), where is an electron or a muon. We find R(Ds) = 0.2987(46), which is also more accurate than previous lattice QCD results. Combined with a future measurement of R(Ds), this could supply a new test of the Standard Model. We also compare the dependence on heavy quark mass of our form factors to expectations from Heavy Quark Effective Theory.

We present details of a lattice QCD calculation of the B s → D Ã s axial form factor at zero recoil using the highly improved staggered quark (HISQ) formalism on the second-generation MILC gluon ensembles that include up, down, strange and charm quarks in the sea. Using the HISQ action for all valence quarks means that the lattice axial vector current that couples to the W can be renormalized fully nonperturbatively, giving a result free of the perturbative matching errors that previous lattice QCD calculations have had. We calculate correlation functions at three values of the lattice spacing, and multiple b-quark masses, for physical c and s. The functional dependence on the b-quark mass can be determined and compared to heavy quark effective theory expectations, and a result for the form factor obtained at the physical value of the b-quark mass. We find F B s →D Ã s ð1Þ ¼ h s A 1 ð1Þ ¼ 0.9020ð96Þ stat ð90Þ sys. This is in agreement with earlier lattice QCD results, which use NRQCD b quarks, with a total uncertainty reduced by more than a factor of 2. We discuss implications of this result for the B → D Ã axial form factor at zero recoil and for determinations of V cb .

We present progress on an ongoing calculation of the B s → D ( * ) s lν form factors calculated on the n f = 2 + 1 + 1 MILC ensembles and using the Highly Improved Staggered Quark action for all valence quarks. We perform the calculation at a range of b quark masses (and lattice spacings) so that we can extrapolate to the physical b-quark mass.

We report on progress of a lattice QCD calculation of the B → Dlν and B s → D s lν semileptonic form factors. We use a relativistic staggered action (HISQ) for light and charm quarks, and an improved non-relativistic (NRQCD) action for bottom, on the second generation MILC ensembles.

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