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We calculate the form factors for B→πℓν and Bs→Kℓν decay in dynamical lattice quantum chromodynamics (QCD) using domain-wall light quarks and relativistic b-quarks. We use the (2+1)-flavor gauge-field ensembles generated by the RBC and UKQCD collaborations with the domain-wall fermion action and Iwasaki gauge action. For the b-quarks we use the anisotropic clover action with a relativistic heavy-quark interpretation. We analyze data at two lattice spacings of a≈0.11, 0.086 fm with unitary pion masses as light as Mπ≈290  MeV. We simultaneously extrapolate our numerical results to the physical light-quark masses and to the continuum and interpolate in the pion/kaon energy using SU(2) “hard-pion” chiral perturbation theory for heavy-light meson form factors. We provide complete systematic error budgets for the vector and scalar form factors f+(q²) and f0(q²) for both B→πℓν and Bs→Kℓν at three momenta that span the q² range accessible in our numerical simulations. Next we extrapolate these results to q²=0 using a model-independent z-parametrization based on analyticity and unitarity. We present our final results for f+(q²) and f0(q²) as the coefficients of the series in z and the matrix of correlations between them; this provides a parametrization of the form factors valid over the entire allowed kinematic range. Our results agree with other three-flavor lattice-QCD determinations using staggered light quarks, and have comparable precision, thereby providing important independent cross-checks. Both B→πℓν and Bs→Kℓν decays enable determinations of the Cabibbo-Kobayashi-Maskawa matrix element |Vub|. To illustrate this, we perform a combined z-fit of our numerical B→πℓν form-factor data with the experimental measurements of the branching fraction from BABAR and Belle leaving the relative normalization as a free parameter; we obtain |Vub|=3.61(32)×10−3, where the error includes statistical and all systematic uncertainties. The same approach can be applied to the decay Bs→Kℓν to provide an alternative determination of |Vub| once the process has been measured experimentally. Finally, in anticipation of future experimental measurements, we make predictions for B→πℓν and Bs→Kℓν differential branching fractions and forward-backward asymmetries in the Standard Model. [ABSTRACT FROM AUTHOR]

We compute the leptonic decay constants fD+, fDs, and fK+ and the quark-mass ratios mc/ms and ms/ml in unquenched lattice QCD using the experimentally determined value of fπ+ for normalization. We use the MILC highly improved staggered quark ensembles with four dynamical quark flavors--up, down, strange, and charm--and with both physical and unphysical values of the light sea-quark masses. The use of physical pions removes the need for a chiral extrapolation, thereby eliminating a significant source of uncertainty in previous calculations. Four different lattice spacings ranging from a ≈ 0.06 to 0.15 fm are included in the analysis to control the extrapolation to the continuum limit. Our primary results are fD+ = 212.6(0.4)(+1.0-1.2) MeV, fDs = 249.0(0.3)(+1.1-1.5) MeV, and fDs/fD+ = 1.1712(10)(+29-32), where the errors are statistical and total systematic, respectively. The errors on our results for the charm decay constants and their ratio are approximately 2-4 times smaller than those of the most precise previous lattice calculations. We also obtain fK+/fπ+ = 1.1956(10)(+26-18), updating our previous result, and determine the quark-mass ratios ms/ml = 27.35(5)(+10-7) and mc/ms = 11.747(19)(+59-43). When combined with experimental measurements of the decay rates, our results lead to precise determinations of the Cabibbo-Kobayashi-Maskawa matrix elements |Vus| = 0.22487(51)(29)(20)(5), |Vcd| = 0.217(1)(5)(1) and |Vcs| = 1.010(5)(18)(6), where the errors are from this calculation of the decay constants, the uncertainty in the experimental decay rates, structure-dependent electromagnetic corrections, and, in the case of |Vus|, the uncertainty in |Vud|, respectively. [ABSTRACT FROM AUTHOR]

We present results from our simulations of quantum chromodynamics with four flavors of quarks: u, d, s, and c. These simulations are performed with a one-loop Symanzik improved gauge action and the highly improved staggered quark action. We are generating gauge configurations with four values of the lattice spacing ranging from 0.06 to 0.15 fm, and three values of the light quark mass, including the value for which the Goldstone pion mass is equal to the physical pion mass. We discuss simulation algorithms, scale setting, taste symmetry breaking, and the autocorrelations of various quantities. We also present results for the topological susceptibility that demonstrate the improvement of the highly improved staggered quark configurations relative to those generated earlier with the asqtad improved staggered action. [ABSTRACT FROM AUTHOR]

We calculate the masses of bottom mesons using an improved relativistic action for the b-quarks and the RBC/UKQCD Iwasaki gauge configurations with 2+1 flavors of dynamical domain-wall light quarks. We analyze configurations with two lattice spacings: a-1=1.729 GeV (a≈ 0.11 fm) and a-1 = 2.281 GeV (a≈0.086fm). We use an anisotropic, clover-improved Wilson action for the b-quark, and tune the three parameters of the action nonperturbatively such that they reproduce the experimental values of the Bs and Bs* heavy-light meson states. The masses and mass splittings of the low-lying bottomonium states (such as the ηb and ϒ) can then be computed with no additional inputs, and comparison between these predictions and experiment provides a test of the validity of our method. We obtain bottomonium masses with total uncertainties of ~0.5-0.6% and fine-structure splittings with uncertainties of ~45-55%: for all cases we find good agreement with experiment. The parameters of the relativistic heavy-quark action tuned for b-quarks presented in this work can be used for precise calculations of weak matrix elements such as B-meson decay constants and mixing parameters with lattice discretization errors that are of the same size as in light pseudoscalar meson quantities. This general method can also be used for charmed meson masses and matrix elements if the parameters of the heavy-quark action are appropriately tuned. [ABSTRACT FROM AUTHOR]

We calculate the contribution to the muon anomalous magnetic moment hadronic vacuum polarization from the connected diagrams of up and down quarks, omitting electromagnetism. We employ QCD gauge-field configurations with dynamical u, d, s, and c quarks and the physical pion mass, and analyze five ensembles with lattice spacings ranging from a≈0.06 to 0.15 fm. The up- and down-quark masses in our simulations have equal masses ml. We obtain, in this world where all pions have the mass of the π0, 1010allμ(conn.)=637.8(8.8), in agreement with independent lattice-QCD calculations. We then combine this value with published lattice-QCD results for the connected contributions from strange, charm, and bottom quarks, and an estimate of the uncertainty due to the fact that our calculation does not include strong-isospin breaking, electromagnetism, or contributions from quark-disconnected diagrams. Our final result for the total O(α²) hadronic-vacuum polarization to the muon's anomalous magnetic moment is 1010aHVP,LOμ=699(15)u,d(1)s,c,b, where the errors are from the light-quark and heavy-quark contributions, respectively. Our result agrees with both ab-initio lattice-QCD calculations and phenomenological determinations from experimental e+e--scattering data. It is 1.3σ below the "no new physics" value of the hadronic-vacuum-polarization contribution inferred from combining the BNL E821 measurement of aμ with theoretical calculations of the other contributions. [ABSTRACT FROM AUTHOR]

We use lattice QCD to calculate the form factors f+ (q²) and f0 (q²) for the semileptonic decay Bs → Kℓν. Our calculation uses six MILC asqtad 2 + 1 flavor gauge-field ensembles with three lattice spacings. At the smallest and largest lattice spacing the light-quark sea mass is set to 1 / 10 the strange-quark mass. At the intermediate lattice spacing, we use four values for the light-quark sea mass ranging from 1/5 to 1/20 of the strange-quark mass. We use the asqtad improved staggered action for the light valence quarks, and the clover action with the Fermilab interpolation for the heavy valence bottom quark. We use SU(2) hard-kaon heavy-meson rooted staggered chiral perturbation theory to take the chiral-continuum limit. A functional z expansion is used to extend the form factors to the full kinematic range. We present predictions for the differential decay rate for both Bs → Kμν and Bs → Kτν. We also present results for the forward-backward asymmetry, the lepton polarization asymmetry, ratios of the scalar and vector form factors for the decays Bs → Kℓν and Bs → Dsℓν. Our results, together with future experimental measurements, can be used to determine the magnitude of the Cabibbo-Kobayashi-Maskawa matrix element |Vub|. [ABSTRACT FROM AUTHOR]

Using highly improved staggered quark (HISQ) Nf = 2 + 1 + 1 MILC ensembles with five different values of the lattice spacing, including four ensembles with physical quark masses, we perform the most precise computation to date of the K → πℓν vector form factor at zero momentum transfer, f+K0π- (0) = 0.9696 (15)stat (12)syst. This is the first calculation that includes the dominant finite-volume effects, as calculated in chiral perturbation theory at next-to-leading order. Our result for the form factor provides a direct determination of the Cabibbo-Kobayashi-Maskawa (CKM) matrix element |Vus| = 0.22333(44)f+(0) (42)exp, with a theory error that is, for the first time, at the same level as the experimental error. The uncertainty of the semileptonic determination is now similar to that from leptonic decays and the ratio fK+/fπ+, which uses |Vud| as input. Our value of |Vus| is in tension at the 2-2.6σ level both with the determinations from leptonic decays and with the unitarity of the CKM matrix. In the test of CKM unitarity in the first row, the current limiting factor is the error in |Vud|, although a recent determination of the nucleus-independent radiative corrections to superallowed nuclear β decays could reduce the |Vud|² uncertainty nearly to that of |Vus|². Alternative unitarity tests using only kaon decays, for which improvements in the theory and experimental inputs are likely in the next few years, reveal similar tensions and could be further improved by taking correlations between the theory inputs. As part of our analysis, we calculated the correction to f+Kπ(0) due to nonequilibrated topological charge at leading order in chiral perturbation theory, for both the full-QCD and the partially quenched cases. We also obtain the combination of low-energy constants in the chiral effective Lagrangian [C12r + C34r - (L5r)²] (Mρ) = (2.92 ± 0.31) × 10-6. [ABSTRACT FROM AUTHOR]

We present a lattice calculation of the electromagnetic (EM) effects on the masses of light pseudoscalar mesons. The simulations employ 2+1 dynamical flavors of asqtad QCD quarks and quenched photons. Lattice spacings vary from ≈0.12 fm to ≈0.045 fm. We compute the quantity ε, which parametrizes the corrections to Dashen's theorem for the K+-K0 EM mass splitting, as well as εK0, which parametrizes the EM contribution to the mass of the K0 itself. An extension of the nonperturbative EM renormalization scheme introduced by the BMW group is used in separating EM effects from isospin-violating quark mass effects. We correct for leading finite-volume effects in our realization of lattice electrodynamics in chiral perturbation theory, and remaining finite-volume errors are relatively small. While electroquenched effects are under control for ε, they are estimated only qualitatively for εK0 and constitute one of the largest sources of uncertainty for that quantity. We find ε=0.78(1)stat(+8-11)syst and εK0=0.035(3)stat(20)syst. We then use these results on 2+1+1 flavor pure QCD highly improved staggered quark (HISQ) ensembles and find mu/md=0.4529(48)stat(+150-67)syst. [ABSTRACT FROM AUTHOR]

We introduce a new method for calculating the O(α³) hadronic-vacuum-polarization contribution to the muon anomalous magnetic moment from ab initio lattice QCD. We first derive expressions suitable for computing the higher-order contributions either from the renormalized vacuum polarization function Π(q²) or directly from the lattice vector-current correlator in Euclidean space. We then demonstrate the approach using previously published results for the Taylor coefficients of Π(q²) that were obtained on four-flavor QCD gauge-field configurations with physical light-quark masses. We obtain 1010αμHVP,HO=-9.3(1.3) in agreement with, but with a larger uncertainty than, determinations from e+e-→hadrons data plus dispersion relations. [ABSTRACT FROM AUTHOR]

We calculate the leptonic decay constants of heavy-light pseudoscalar mesons with charm and bottom quarks in lattice quantum chromodynamics on four-flavor QCD gauge-field configurations with dynamical u, d, s, and c quarks. We analyze over twenty isospin-symmetric ensembles with six lattice spacings down to a≈0.03 fm and several values of the light-quark mass down to the physical value 1/2(mu+md). We employ the highly-improved staggered-quark (HISQ) action for the sea and valence quarks; on the finest lattice spacings, discretization errors are sufficiently small that we can calculate the B-meson decay constants with the HISQ action for the first time directly at the physical b-quark mass. We obtain the most precise determinations to-date of the D- and B-meson decay constants and their ratios, fD+=212.7(0.6) MeV, fDs=249.9(0.4) MeV, fDs/fD+=1.1749(16), fB+=189.4(1.4) MeV, fBs=230.7(1.3) MeV, fBs/fB+=1.2180(47), where the errors include statistical and all systematic uncertainties. Our results for the B¯meson decay constants are three times more precise than the previous best lattice-QCD calculations, and bring the QCD errors in the standard model predictions for the rare leptonic decays ¯B(Bs→μ+μ-)=3.64(11)×10-9, ¯B(B0→μ+μ-)=1.00(3)×10-11, and ¯B(B0→μ+μ-)/¯B(Bs→μ+μ-)=0.00264(8) to well below other sources of uncertainty. As a byproduct of our analysis, we also update our previously published results for the light-quark-mass ratios and the scale-setting quantities fp4s, Mp4s, and Rp4s. We obtain the most precise lattice-QCD determination to date of the ratio fK+/fπ+=1.1950(+16-23) MeV. [ABSTRACT FROM AUTHOR]

We calculate the up-, down-, strange-, charm-, and bottom-quark masses using the MILC highly improved staggered-quark ensembles with four flavors of dynamical quarks. We use ensembles at six lattice spacings ranging from a≈0.15 to 0.03 fm and with both physical and unphysical values of the two light and the strange sea-quark masses. We use a new method based on heavy-quark effective theory (HQET) to extract quark masses from heavy-light pseudoscalar meson masses. Combining our analysis with our separate determination of ratios of light-quark masses we present masses of the up, down, strange, charm, and bottom quarks. Our results for the MS-renormalized masses are mu(2 GeV)=2.130(41) MeV, md(2 GeV)=4.675(56) MeV, ms(2 GeV)=92.47(69) MeV, mc(3 GeV)=983.7(5.6) MeV, and mc(mc)=1273(10) MeV, with four active flavors; and mb(mb)=4195(14) MeV with five active flavors. We also obtain ratios of quark masses mc/ms=11.783(25), mb/ms=53.94(12), and mb/mc=4.578(8). The result for mc matches the precision of the most precise calculation to date, and the other masses and all quoted ratios are the most precise to date. Moreover, these results are the first with a perturbative accuracy of α4s. As byproducts of our method, we obtain the matrix elements of HQET operators with dimension 4 and 5: ΛMRS=555(31) MeV in the minimal renormalon-subtracted (MRS) scheme, μ²π=0.05(22) GeV², and μ²G(mb)=0.38(2) GeV². The MRS scheme [Phys. Rev. D 97, 034503 (2018)] is the key new aspect of our method. [ABSTRACT FROM AUTHOR]

We calculate in three-flavor lattice QCD the short-distance hadronic matrix elements of all five ΔC=2 four-fermion operators that contribute to neutral D-meson mixing both in and beyond the Standard Model. We use the MILC Collaboration's Nf=2+1 lattice gauge-field configurations generated with asqtad-improved staggered sea quarks. We also employ the asqtad action for the valence light quarks and use the clover action with the Fermilab interpretation for the charm quark. We analyze a large set of ensembles with pions as light as Mπ≈180 MeV and lattice spacings as fine as a≈0.045 fm, thereby enabling good control over the extrapolation to the physical pion mass and continuum limit. We obtain for the matrix elements in the MS-NDR scheme using the choice of evanescent operators proposed by Beneke et al., evaluated at 3 GeV, ⟨D0|Oi|D0⟩={0.0805(55)(16),-0.1561(70)(31),0.0464(31)(9),0.2747(129)(55),0.1035(71)(21)} GeV4 (i=1-5). The errors shown are from statistics and lattice systematics, and the omission of charmed sea quarks, respectively. To illustrate the utility of our matrix-element results, we place bounds on the scale of CP-violating new physics in D0 mixing, finding lower limits of about 10-50×10³ TeV for couplings of O(1). To enable our results to be employed in more sophisticated or model-specific phenomenological studies, we provide the correlations among our matrix-element results. For convenience, we also present numerical results in the other commonly used scheme of Buras, Misiak, and Urban. [ABSTRACT FROM AUTHOR]

We determine the contribution to the anomalous magnetic moment of the muon from the aQED² hadronic vacuum polarization diagram using full lattice QCD and including u/d quarks with physical masses for the first time. We use gluon field configurations that include u, d, s and c quarks in the sea at multiple values of the lattice spacing, multiple u/d masses and multiple volumes that allow us to include an analysis of finite-volume effects. We obtain a result for aμHVP,LO of 667(6)(12)×10-10, where the first error is from the lattice calculation and the second includes systematic errors from missing QED and isospin-breaking effects and from quark-line disconnected diagrams. Our result implies a discrepancy between the experimental determination of aμ and and the Standard Model of 3σ. [ABSTRACT FROM AUTHOR]