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We calculate—for the first time in three-flavor lattice QCD—the hadronic matrix elements of all five local operators that contribute to neutral B0- and Bs-meson mixing in and beyond the Standard Model. We present a complete error budget for each matrix element and also provide the full set of correlations among the matrix elements. We also present the corresponding bag parameters and their correlations, as well as specific combinations of the mixing matrix elements that enter the expression for the neutral B-meson width difference. We obtain the most precise determination to date of the SU(3)-breaking ratio ξ=1.206(18)(6), where the second error stems from the omission of charm-sea quarks, while the first encompasses all other uncertainties. The threefold reduction in total uncertainty, relative to the 2013 Flavor Lattice Averaging Group results, tightens the constraint from B mixing on the Cabibbo-Kobayashi-Maskawa (CKM) unitarity triangle. Our calculation employs gauge-field ensembles generated by the MILC Collaboration with four lattice spacings and pion masses close to the physical value. We use the asqtad-improved staggered action for the light-valence quarks and the Fermilab method for the bottom quark. We use heavy-light meson chiral perturbation theory modified to include lattice-spacing effects to extrapolate the five matrix elements to the physical point. We combine our results with experimental measurements of the neutral B-meson oscillation frequencies to determine the CKM matrix elements |Vtd|=8.00(34)(8)×10−3, |Vts|=39.0(1.2)(0.4)×10−3, and |Vtd/Vts|=0.2052(31)(10), which differ from CKM-unitarity expectations by about 2σ. These results and others from flavor-changing-neutral currents point towards an emerging tension between weak processes that are mediated at the loop and tree levels.

We compute the form factors for the B→Kl+l− semileptonic decay process in lattice QCD using gauge-field ensembles with 2+1 flavors of sea quark, generated by the MILC Collaboration. The ensembles span lattice spacings from 0.12 to 0.045 fm and have multiple sea-quark masses to help control the chiral extrapolation. The asqtad improved staggered action is used for the light valence and sea quarks, and the clover action with the Fermilab interpretation is used for the heavy b quark. We present results for the form factors f+(q2), f0(q2), and fT(q2), where q2 is the momentum transfer, together with a comprehensive examination of systematic errors. Lattice QCD determines the form factors for a limited range of q2, and we use the model-independent z expansion to cover the whole kinematically allowed range. We present our final form-factor results as coefficients of the z expansion and the correlations between them, where the errors on the coefficients include statistical and all systematic uncertainties. We use this complete description of the form factors to test QCD predictions of the form factors at high and low q2.

The rare decay B→πℓ+ℓ− arises from b→d flavor-changing neutral currents and could be sensitive to physics beyond the standard model. Here, we present the first ab initio QCD calculation of the B→π tensor form factor fT. Together with the vector and scalar form factors f+ and f0 from our companion work [J. A. Bailey et al., Phys. Rev. D 92, 014024 (2015)], these parametrize the hadronic contribution to B→π semileptonic decays in any extension of the standard model. We obtain the total branching ratio BR(B+→π+μ+μ−)=20.4(2.1)×10−9 in the standard model, which is the most precise theoretical determination to date, and agrees with the recent measurement from the LHCb experiment [R. Aaij et al., J. High Energy Phys. 12 (2012) 125].

We present the first unquenched lattice-QCD calculation of the hadronic form factors for the exclusive decay B¯→Dℓν¯ at nonzero recoil. We carry out numerical simulations on 14 ensembles of gauge-field configurations generated with 2+1 flavors of asqtad-improved staggered sea quarks. The ensembles encompass a wide range of lattice spacings (approximately 0.045 to 0.12 fm) and ratios of light (up and down) to strange sea-quark masses ranging from 0.05 to 0.4. For the b and c valence quarks we use improved Wilson fermions with the Fermilab interpretation, while for the light valence quarks we use asqtad-improved staggered fermions. We extrapolate our results to the physical point using rooted staggered heavy-light meson chiral perturbation theory. We then parametrize the form factors and extend them to the full kinematic range using model-independent functions based on analyticity and unitarity. We present our final results for f+(q2) and f0(q2), including statistical and systematic errors, as coefficients of a series in the variable z and the covariance matrix between these coefficients. We then fit the lattice form-factor data jointly with the experimentally measured differential decay rate from BABAR to determine the CKM matrix element, |Vcb|=(39.6±1.7QCD+exp±0.2QED)×10−3. As a byproduct of the joint fit we obtain the form factors with improved precision at large recoil. Finally, we use them to update our calculation of the ratio R(D) in the Standard Model, which yields R(D)=0.299(11).

We present a lattice-QCD calculation of the B→πℓν semileptonic form factors and a new determination of the CKM matrix element |Vub|. We use the MILC asqtad (2+1)-flavor lattice configurations at four lattice spacings and light-quark masses down to 1/20 of the physical strange-quark mass. We extrapolate the lattice form factors to the continuum using staggered chiral perturbation theory in the hard-pion and SU(2) limits. We employ a model-independent z parametrization to extrapolate our lattice form factors from large-recoil momentum to the full kinematic range. We introduce a new functional method to propagate information from the chiral-continuum extrapolation to the z expansion. We present our results together with a complete systematic error budget, including a covariance matrix to enable the combination of our form factors with other lattice-QCD and experimental results. To obtain |Vub|, we simultaneously fit the experimental data for the B→πℓν differential decay rate obtained by the BABAR and Belle collaborations together with our lattice form-factor results. We find |Vub|=(3.72±0.16)×10−3, where the error is from the combined fit to lattice plus experiments and includes all sources of uncertainty. Our form-factor results bring the QCD error on |Vub| to the same level as the experimental error. We also provide results for the B→πℓν vector and scalar form factors obtained from the combined lattice and experiment fit, which are more precisely determined than from our lattice-QCD calculation alone. These results can be used in other phenomenological applications and to test other approaches to QCD.

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 precision 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., 18 pages, 9 figures; Review at The 32nd International Symposium on Lattice Field Theory, 23-28 June, 2014, Columbia University New York, NY; PoS(LATTICE2014)002: Ver. 2 fixes several several typos, including labels in Fig. 3 and updates references, including the addition of recent results to Figs. 7 and 8

We report the first lattice QCD calculation of the form factors for the standard model tree-level decay\ud Bs → Klν. In combination with future measurement, this calculation will provide an alternative exclusive\ud semileptonic determination of jVubj. We compare our results with previous model calculations, make\ud predictions for differential decay rates and branching fractions, and predict the ratio of differential\ud branching fractions between Bs → Kτν and Bs → Kμν. We also present standard model predictions for\ud differential decay rate forward-backward asymmetries and polarization fractions and calculate potentially\ud useful ratios of Bs → K form factors with those of the fictitious Bs → ηs decay. Our lattice simulations\ud utilize nonrelativistic QCD b and highly improved staggered light quarks on a subset of the MILC\ud Collaboration 2 þ 1 asqtad gauge configurations, including two lattice spacings and a range of light quark\ud masses.

We compute the zero-recoil form factor for the semileptonic decay B¯0→D*+ℓ−ν¯ (and modes related by isospin and charge conjugation) using lattice QCD with three flavors of sea quarks. We use an improved staggered action for the light valence and sea quarks (the MILC asqtad configurations), and the Fermilab action for the heavy quarks. Our calculations incorporate higher statistics, finer lattice spacings, and lighter quark masses than our 2008 work. As a byproduct of tuning the new data set, we obtain the Ds and Bs hyperfine splittings with few-MeV accuracy. For the zero-recoil form factor, we obtain F(1)=0.906(4)(12), where the first error is statistical and the second is the sum in quadrature of all systematic errors. With the latest Heavy Flavor Averaging Group average of experimental results and a cautious treatment of QED effects, we find |Vcb|=(39.04±0.49expt±0.53QCD±0.19QED)×10−3. The QCD error is now commensurate with the experimental error.