I review recently completed (since Lattice 2013) and ongoing lattice calculations in charm and bottom flavor physics. A comparison of the precision of lattice and experiment is made using both current experimental results and projected experimental p
recision in 2020. The combination of experiment and theory reveals several tensions between nature and the Standard Model. These tensions are reviewed in light of recent lattice results.
We report the first lattice QCD calculation of the form factors for the standard model tree-level decay $B_sto K ell u$. 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 $B_sto Ktau u$ and $B_sto Kmu u$. We also present standard model predictions for differential decay rate forward-backward asymmetries, polarization fractions, and calculate potentially useful ratios of $B_sto K$ form factors with those of the fictitious $B_stoeta_s$ decay. Our lattice simulations utilize NRQCD $b$ and HISQ light quarks on a subset of the MILC Collaborations $2+1$ asqtad gauge configurations, including two lattice spacings and a range of light quark masses.
We discuss our ongoing effort to calculate form factors for several B and Bs semileptonic decays. We have recently completed the first unquenched calculation of the form factors for the rare decay B -> K ll. Extrapolated over the full kinematic range
of q^2 via model-independent z expansion, these form factor results allow us to calculate several Standard Model observables. We compare with experiment (Belle, BABAR, CDF, and LHCb) where possible and make predictions elsewhere. We discuss preliminary results for Bs -> K l nu which, when combined with anticipated experimental results, will provide an alternative exclusive determination of |Vub|. We are exploring the possibility of using ratios of form factors for this decay with those for the unphysical decay Bs -> eta_s as a means of significantly reducing form factor errors. We are also studying B -> pi l nu, form factors for which are combined with experiment in the standard exclusive determination of |Vub|. Our simulations use NRQCD heavy and HISQ light valence quarks on the MILC 2+1 dynamical asqtad configurations.
Our ability to resolve new physics effects is, largely, limited by the precision with which we calculate. The calculation of observables in the Standard (or a new physics) Model requires knowledge of associated hadronic contributions. The precision o
f such calculations, and therefore our ability to leverage experiment, is typically limited by hadronic uncertainties. The only first-principles method for calculating the nonperturbative, hadronic contributions is lattice QCD. Modern lattice calculations have controlled errors, are systematically improvable, and in some cases, are pushing the sub-percent level of precision. I outline the role played by, highlight state of the art efforts in, and discuss possible future directions of lattice calculations in flavor physics.
We calculate, for the first time using unquenched lattice QCD, form factors for the rare decay B -> Kll in and beyond the Standard Model. Our lattice QCD calculation utilizes a nonrelativistic QCD formulation for the b valence quarks, the highly impr
oved staggered quark formulation for the light valence quarks, and employs the MILC 2+1 asqtad ensembles. The form factor results, based on the z expansion, are valid over the full kinematic range of q^2. We construct the ratios f0/f+ and fT/f+, which are useful in constraining new physics and verifying effective theory form factor symmetry relations. We also discuss the calculation of Standard Model observables.
We calculate, for the first time using unquenched lattice QCD form factors, the Standard Model differential branching fractions $dB/dq^2(B to Kll)$ for $l=e, mu, tau$ and compare with experimental measurements by Belle, BABAR, CDF, and LHCb. We repor
t on $mathcal{B}(B to Kll)$ in $q^2$ bins used by experiment and predict $mathcal{B}(B to K tau tau) = (1.44 pm 0.15) 10^{-7}$. We also calculate the ratio of branching fractions $R^mu_e = 1.00023(63)$ and predict $R^tau_l = 1.159(40)$, for $l=e, mu$. Finally, we calculate the flat term in the angular distribution of the differential decay rate $F_H^{e, mu, tau}$ in experimentally motivated $q^2$ bins.
We discuss preliminaries of a calculation of the form factors for the semileptonic decays B -> pi lv, B_s -> K lv, and B -> K ll. We simulate with NRQCD heavy and HISQ light valence quarks on the MILC 2+1 dynamical asqtad configurations. The form fac
tors are calculated over a range of momentum transfer to allow determination of their shape and the extraction of |V_ub|. Additionally, we are calculating ratios of these form factors to those for the unphysical decay B_s -> eta_s. We are studying the possibility of combining these precisely determined ratios with future calculations of B_s ->eta_s using HISQ b-quarks to generate form factors with significantly reduced errors.
We use lattice QCD to calculate the B-mixing hadronic matrix elements for a basis of effective four-quark operators that spans the space of all possible contributions in, and beyond, the Standard Model. We present results for the SU(3)-breaking ratio
and discuss our ongoing calculation of the mixing matrix elements, including the first calculation of the beyond the Standard Model matrix elements from unquenched lattice QCD.
