Flavor Physics and Lattice QCD

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 of 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.Comment: Invited review of lattice QCD in quark and lepton flavor physics. Presentation at the DPF 2013 Meeting of the American Physical Society Division of Particles and Fields, Santa Cruz, California, August 13-17, 201

Testing the Standard Model under the weight of heavy flavors

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.Comment: 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

Bs→KℓνB_s \to K \ell \nu form factors from lattice QCD

We report the first lattice QCD calculation of the form factors for the standard model tree-level decay $B_s\to K \ell\nu$. 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 $B_s\to K\tau\nu$ and $B_s\to K\mu\nu$. We also present standard model predictions for differential decay rate forward-backward asymmetries, polarization fractions, and calculate potentially useful ratios of $B_s\to K$ form factors with those of the fictitious $B_s\to\eta_s$ decay. Our lattice simulations utilize NRQCD $b$ and HISQ light quarks on a subset of the MILC Collaboration's $2+1$ asqtad gauge configurations, including two lattice spacings and a range of light quark masses.Comment: 24 pages, 21 figures; Ver. 2 matches published versio

B and Bs semileptonic decay form factors with NRQCD/HISQ quarks

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.Comment: 7 pages, 5 figures, presented at the 31st International Symposium on Lattice Field Theory (Lattice 2013), 29 July - 3 August 2013, Mainz, German

B-(s)(0)-mixing matrix elements from lattice QCD for the Standard Model

We calculate-for the first time in three-flavor lattice QCD-the hadronic matrix elements of all five local operators that contribute to neutral B-0- and B-s-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 xi = 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 vertical bar V-td vertical bar = 8.00(34)(8) x 10(-3), vertical bar V-ts vertical bar = 39.0(1.2)(0.4) x 10(-3), and vertical bar V-td/V-ts vertical bar = 0.2052(31)(10), which differ from CKM-unitarity expectations by about 2 sigma. 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

B - \u3e Kl(+)l(-) decay form factors from three-flavor lattice QCD

We compute the form factors for the B -- \u3e 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(+)(q(2)), f(0)(q2), and f(T)(q2), where q(2) is the momentum transfer, together with a comprehensive examination of systematic errors. Lattice QCD determines the form factors for a limited range of q(2), 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 q(2)

One-Loop Self Energy and Renormalization of the Speed of Light for some Anisotropic Improved Quark Actions

One-loop corrections to the fermion rest mass M_1, wave function renormalization Z_2 and speed of light renormalization C_0 are presented for lattice actions that combine improved glue with clover or D234 quark actions and keep the temporal and spatial lattice spacings, a_t and a_s, distinct. We explore a range of values for the anisotropy parameter \chi = a_s/a_t and treat both massive and massless fermions.Comment: 45 LaTeX pages with 4 postscript figure

B - \u3e Dl nu form factors at nonzero recoil and vertical bar V-cb vertical bar from 2+1-flavor lattice QCD

We present the first unquenched lattice-QCD calculation of the hadronic form factors for the exclusive decay (B) over bar -\u3e Dl (nu) over bar 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 + (q(2)) and f (0)(q(2)), 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 formfactor data jointly with the experimentally measured differential decay rate from BABAR to determine the CKM matrix element, vertical bar V-cb vertical bar = (39.6 +/- 1.7(QCD+exp) +/- 0.2(QED)) x 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)

vertical bar V-ub vertical bar from B -\u3e pi l nu decays and (2+1)-flavor lattice QCD

We present a lattice-QCD calculation of the B -\u3e pi l nu semileptonic form factors and a new determination of the CKM matrix element vertical bar V-ub vertical bar. 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 vertical bar V-ub vertical bar, we simultaneously fit the experimental data for the B -\u3e pi l nu differential decay rate obtained by the BABAR and Belle collaborations together with our lattice form-factor results. We find vertical bar V-ub vertical bar = (3.72 +/- 0.16) x 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 vertical bar V-ub vertical bar to the same level as the experimental error. We also provide results for the B -\u3e pi l nu 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