Search

We present HPQCD's improved scalar, vector and tensor form factors for $B \to K$ semileptonic decays, using the heavy-HISQ formalism for more accurate normalisation of the weak currents. Working with masses close to the physical $b$ on the finest ensemble and including three ensembles with physical light quarks, we cover the full physical $q^2$ range with good precision. Our uncertainties at $q^2=0$ are a factor of three better than earlier work. We compare Standard Model observables using our form factors to experimental measurements for the rare flavour changing neutral current processes $B \to K \ell^+\ell^-$ and $B \to K \nu\bar{\nu}$ and discuss the significance of the tensions that arise., Comment: 10 pages, 6 figures. Proceedings of the 39th International Symposium on Lattice Field Theory - LATTICE2022

We use HPQCD's recent lattice QCD determination of $B \to K$ scalar, vector and tensor form factors to determine Standard Model differential branching fractions for $B \to K \ell^+\ell^-$, $B\to K \ell_1^+\ell_2^-$ and $B \to K\nu \overline{\nu}$. These form factors are calculated across the full $q^2$ range of the decay and have smaller uncertainties than previous work, particularly at low $q^2$. For $B \to K \ell^+ \ell^-$ we find the Standard Model branching fraction in the $q^2$ region below the squared $J/\psi$ mass to exceed the LHCb results, with tensions as high as $4.2\sigma$ for $B^+\to K^+\mu^+\mu^-$. For the high $q^2$ region we see $2.7\sigma$ tensions. The tensions are much reduced by applying shifts to Wilson coefficients $C_9$ and $C_{10}$ in the effective weak Hamiltonian, moving them away from their Standard Model values consistent with those indicated by other $B$ phenomenology. We also update results for lepton-flavour ratios $R^{\mu}_e$ and $R^{\tau}_{\mu}$ and the `flat term', $F_H^{\ell}$ in the differential branching fraction for $\ell\in\{e,\mu,\tau\}$. Our results for the form-factor-dependent contributions needed for searches for lepton-flavour-violating decays $B\to K\ell^-_1\ell^+_2$ achieve uncertainties of 7%. We also compute the branching fraction $\mathcal{B}(B\to K\nu\bar{\nu})$ with an uncertainty below 10%, for comparison with future experimental results., Comment: 28 pages, 38 figures. Version accepted by Physical Review D. Updated to reflect a change in the scale of alpha_EW

We present the result of lattice QCD calculation of the scalar, vector and tensor form factors for the $B\to K\ell^+\ell^-$ decay, across the full physical range of momentum transfer. We use the highly improved staggered quark (HISQ) formalism for all valence quarks on eight ensembles of gluon field configurations generated by the MILC collaboration. These include four flavours of HISQ quarks in the sea, with three ensembles having the light $u/d$ quarks at physical masses. In the first fully relativistic calculation of these form factors, we use the heavy-HISQ method. This allows us to determine the form factors as a function of heavy quark mass from the $c$ to the $b$, and so we also obtain new results for the $D\to K$ tensor form factor. The advantage of the relativistic formalism is that we can match the lattice weak currents to their continuum counterparts much more accurately than in previous calculations; our scalar and vector currents are renormalised fully nonperturbatively and we use a well-matched intermediate momentum-subtraction scheme for our tensor current. Our scalar and vector $B\to K$ form factors have uncertainties of less than 4% across the entire physical $q^2$ range and the uncertainty in our tensor form factor is less than 7%. Our heavy-HISQ method allows us to map out the dependence on heavy-quark mass of the form factors and we can also see the impact of changing spectator quark mass by comparing to earlier HPQCD results for the same quark weak transition but for heavier mesons., Comment: 30 pages, 22 figures. Version accepted by Physical Review D

Semileptonic $D \to{}K \ell \nu$ decays provide one angle of attack to get at the CKM matrix element $V_{cs}$, complementary to the study of leptonic $D_s$ decays. Here, HPQCD present the results of a recently published, improved determination of $V_{cs}$. We discuss a new, precise determination of $D\to K$ scalar and vector form factors from a lattice calculation on eight different $N_f=2+1+1$ MILC gluon field ensembles using the HISQ action, including three with physical light quark masses. When combined with experimental results, we are able to extract $|V_{cs}|=0.9663(80)$ to a sub percent level of precision for the first time. This is achieved using three different methods, which each combine our form factors with different sets of experimental results in different ways, with the results in very good agreement. Our primary method is to use $q^2$-binned data for the differential decay rate, but we also calculate $V_{cs}$ from the total branching fraction and from the value $|V_{cs}|f_+(0)$, which is also quoted by some experiments., Comment: 9 pages, 7 figures. Proceedings of the 38th International Symposium on Lattice Field Theory - LATTICE2021

We provide a 0.8\%-accurate determination of $V_{cs}$ from combining experimental results for the differential rate of $D \rightarrow K$ semileptonic decays with precise form factors that we determine from lattice QCD. This is the first time that $V_{cs}$ has been determined with an accuracy that allows its difference from 1 to be seen. Our lattice QCD calculation uses the Highly Improved Staggered Quark (HISQ) action for all valence quarks on gluon field configurations generated by the MILC collaboration that include the effect of $u$, $d$, $s$ and $c$ HISQ quarks in the sea. We use eight gluon field ensembles with five values of the lattice spacing ranging from 0.15 fm to 0.045 fm and include results with physical $u/d$ quarks for the first time. Our calculated form factors cover the full $q^2$ range of the physical decay process and enable a Standard Model test of the shape of the differential decay rate as well as the determination of $V_{cs}$ from a correlated weighted average over $q^2$ bins. We obtain $|V_{cs}|= 0.9663(53)_{\text{latt}}(39)_{\text{exp}}(19)_{\eta_{EW}}(40)_{\text{EM}}$, where the uncertainties come from lattice QCD, experiment, short-distance electroweak and electromagnetic corrections, respectively. This last uncertainty, neglected for $D \rightarrow K \ell \nu$ hitherto, now needs attention if the uncertainty on $V_{cs}$ is to be reduced further. We also determine $V_{cs}$ values in good agreement using the measured total branching fraction and the rates extrapolated to $q^2=0$. Our form factors enable tests of lepton flavour universality violation. We find the ratio of branching fractions for $D^0 \rightarrow K^-$ with $\mu$ and $e$ in the final state to be $R_{\mu/e}=0.9779(2)_{\text{latt}}(50)_{\mathrm{EM}}$ in the Standard Model, with the uncertainty dominated by that from electromagnetic corrections., Comment: 27 pages, 28 figures. Small changes to text to improve readability. Updated to include the BES average for the D to K branching fraction from 2104.08081

We present the results of a lattice QCD calculation of the scalar and vector form factors for the unphysical $B_s\to\eta_s$ decay, over the full physical range of $q^2$. This is a useful testing ground both for lattice QCD and for our wider understanding of the behaviour of form factors. Calculations were performed using the highly improved staggered quark (HISQ) action on $N_f = 2 + 1 + 1$ gluon ensembles generated by the MILC Collaboration with an improved gluon action and HISQ sea quarks. We use three lattice spacings and a range of heavy quark masses from that of charm to bottom, all in the HISQ formalism. This permits an extrapolation in the heavy quark mass and lattice spacing to the physical point and nonperturbative renormalisation of the vector matrix element on the lattice. We find results in good agreement with previous work using nonrelativistic QCD $b$ quarks and with reduced errors at low $q^2$, supporting the effectiveness of our heavy HISQ technique as a method for calculating form factors involving heavy quarks. A comparison with results for other decays related by SU(3) flavour symmetry shows that the impact of changing the light daughter quark is substantial but changing the spectator quark has very little effect. We also map out form factor shape parameters as a function of heavy quark mass and compare to heavy quark effective theory expectations for mass scaling at low and high recoil. This work represents an important step in the progression from previous work on heavy-to-heavy decays ($b\to c$) to the numerically more challenging heavy-to-light decays., Comment: published version; 18 pages, 14 figures

Precision experimental tests of the Standard Model of particle physics (SM) are one of our best hopes for discovering what new physics lies beyond the SM (BSM). Key in the search for new physics is the connection between theory and experiment. Forging this connection for searches involving low-energy hadronic or nuclear environments requires the use of a non-perturbative theoretical tool, lattice QCD. We present two recent lattice QCD calculations by the CalLat collaboration relevant for new physics searches: the nucleon axial coupling, $g_A$, whose precise value as predicted by the SM could help point to new physics contributions to the so-called "neutron lifetime puzzle", and hadronic matrix elements of short-ranged operators relevant for neutrinoless double beta decay searches., Comment: Plenary talk presented CIPANP2018. 11 pages, 3 figures

Using the MILC 2+1 flavor asqtad quark action ensembles, we are calculating the form factors $f_0$ and $f_+$ for the semileptonic $B_s \rightarrow K \ell\nu$ decay. A total of six ensembles with lattice spacing from $\approx0.12$ to 0.06 fm are being used. At the coarsest and finest lattice spacings, the light quark mass $m'_l$ is one-tenth the strange quark mass $m'_s$. At the intermediate lattice spacing, the ratio $m'_l/m'_s$ ranges from 0.05 to 0.2. The valence $b$ quark is treated using the Sheikholeslami-Wohlert Wilson-clover action with the Fermilab interpretation. The other valence quarks use the asqtad action. When combined with (future) measurements from the LHCb and Belle II experiments, these calculations will provide an alternate determination of the CKM matrix element $|V_{ub}|$., Comment: 8 pages, 6 figures, to appear in the Proceedings of Lattice 2017, June 18-24, Granada, Spain

We calculate in three-flavor lattice QCD the short-distance hadronic matrix elements of all five $\Delta C=2$ four-fermion operators that contribute to neutral $D$-meson mixing both in and beyond the Standard Model. We use the MILC Collaboration's $N_f = 2+1$ 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 $M_\pi \approx 180$ MeV and lattice spacings as fine as $a\approx 0.045$ fm, thereby enabling good control over the extrapolation to the physical pion mass and continuum limit. We obtain for the matrix elements in the $\overline{\text{MS}}$-NDR scheme using the choice of evanescent operators proposed by Beneke \emph{et al.}, evaluated at 3 GeV, $\langle D^0|\mathcal{O}_i|\bar{D}^0 \rangle = \{0.0805(55)(16), -0.1561(70)(31), 0.0464(31)(9), 0.2747(129)(55), 0.1035(71)(21)\}~\text{GeV}^4$ ($i=1$--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 $D^0$~mixing, finding lower limits of about 10--50$\times 10^3$ TeV for couplings of $\mathrm{O}(1)$. 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., Comment: Published version, 42 pages, 18 figures

We present results for neutral D-meson mixing in 2+1-flavor lattice QCD. We compute the matrix elements for all five operators that contribute to D mixing at short distances, including those that only arise beyond the Standard Model. Our results have an uncertainty similar to those of the ETM collaboration (with 2 and with 2+1+1 flavors). This work shares many features with a recent publication on B mixing and with ongoing work on heavy-light decay constants from the Fermilab Lattice and MILC Collaborations., Comment: 6+1 pp., presented at Lattice 2016

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 $|V_{td}| = 8.00(34)(8) \times 10^{-3}$, $|V_{ts}| = 39.0(1.2)(0.4) \times 10^{-3}$, and $|V_{td}/V_{ts}| = 0.2052(31)(10)$, 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., Comment: 75 pp, 17 figs. Ver 2 fixes typos; corrects mistakes resulting in slight changes to results, correlation matrices; updates decay constants to agree with recent PDG update; corrects uncertainties for tree-level CKM matrix elements used in comparison, slightly reducing tensions; includes additional analyses that support mostly-nonperturbative matching; expands discussion of isospin-breaking effects

We give a progress report on a project aimed at a high-precision calculation of the decay constants $f_B$ and $f_{B_s}$ from simulations with HISQ heavy and light valence and sea quarks. Calculations are carried out with several heavy valence-quark masses on ensembles with 2+1+1 flavors of HISQ sea quarks at five lattice spacings and several light sea-quark mass ratios $m_{ud}/m_s$, including approximately physical sea-quark masses. This range of parameters provides excellent control of the continuum limit and of heavy-quark discretization errors. We present a preliminary error budget with projected uncertainties of 2.2~MeV and 1.5~MeV for $f_B$ and $f_{B_s}$, respectively., Comment: 7 pages, 6 figures, Lattice 2015

We compute the form factors for the $B \to Kl^+l^-$ 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 $f_+(q^2)$, $f_0(q^2)$, and $f_T(q^2)$, 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 $q^2$. We also compare a Standard-Model calculation of the branching ratio for $B \to Kl^+l^-$ with experimental data., Comment: V2: Fig.7 added. Typos text corrected. Reference added. Version published in Phys. Rev. D

The rare decay $B\to\pi\ell^+\ell^-$ arises from $b\to d$ 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 $B\to\pi$ tensor form factor $f_T$. Together with the vector and scalar form factors $f_+$ and $f_0$ from our companion work [J. A. Bailey $et~al.$, Phys. Rev. D 92, 014024 (2015)], these parameterize the hadronic contribution to $B\to\pi$ semileptonic decays in any extension of the Standard Model. We obtain the total branching ratio ${\text{BR}}(B^+\to\pi^+\mu^+\mu^-)=20.4(2.1)\times10^{-9}$ 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 $et~al.$, JHEP 1212, 125 (2012)]. Note added: after this paper was submitted for publication, LHCb announced a new measurement of the differential decay rate for this process [T. Tekampe, talk at DPF 2015], which we now compare to the shape and normalization of the Standard-Model prediction., Comment: V3: Corrected errors in results for Standard-Model differential and total decay rates in abstract, Fig. 3, Table IV, and outlook. Added new preliminary LHCb data to Fig. 3 and brief discussion after outlook. Replaced outdated correlation matrix in Table III with correct final version. Other minor wording changes and references added. 7 pages, 4 tables, 3 figures

We present a lattice-QCD calculation of the $B\to\pi\ell\nu$ semileptonic form factors and a new determination of the CKM matrix element $|V_{ub}|$. 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 $z$ parameterization 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 $|V_{ub}|$, we simultaneously fit the experimental data for the $B\to\pi\ell\nu$ differential decay rate obtained by the BaBar and Belle collaborations together with our lattice form-factor results. We find $|V_{ub}|=(3.72\pm 0.16)\times 10^{-3}$ 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 $|V_{ub}|$ to the same level as the experimental error. We also provide results for the $B\to\pi\ell\nu$ 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., Comment: 63 pages, 48 figures; v2: minor changes in Sec. IV, Table X, modified Fig.14,16, results unchanged

We present the first unquenched lattice-QCD calculation of the hadronic form factors for the exclusive decay $\overline{B} \rightarrow D \ell \overline{\nu}$ at nonzero recoil. We carry out numerical simulations on fourteen 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 parameterize 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 form-factor data jointly with the experimentally measured differential decay rate from BaBar to determine the CKM matrix element, $|V_{cb}|=(39.6 \pm 1.7_{\rm QCD+exp} \pm 0.2_{\rm QED})\times 10^{-3}$. 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 $R(D) = 0.299(11)$., Comment: 47 pages, 32 figures

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 8

We report on the status of our calculation of the hadronic matrix elements for neutral $B$-meson mixing with asqtad sea and valence light quarks and using the Wilson clover action with the Fermilab interpretation for the $b$ quark. We calculate the matrix elements of all five local operators that contribute to neutral $B$-meson mixing both in and beyond the Standard Model. We use MILC ensembles with $N_f=2+1$ dynamical flavors at four different lattice spacings in the range $a \approx 0.045$--$0.12$~fm, and with light sea-quark masses as low as 0.05 times the physical strange quark mass. We perform a combined chiral-continuum extrapolation including the so-called wrong-spin contributions in simultaneous fits to the matrix elements of the five operators. We present a complete systematic error budget and conclude with an outlook for obtaining final results from this analysis., Comment: 7 pages, 4 figures, presented at the 32nd International Symposium on Lattice Field Theory (Lattice 2014), 23-28 June, 2014, Columbia University, New York, NY

We present an update on our calculation of the short-distance $D^0$-meson mixing hadronic matrix elements. The analysis is performed on the MILC collaboration's $N_f=2+1$ asqtad configurations. We use asqtad light valence quarks and the Sheikoleslami-Wohlert action with the Fermilab interpretation for the valence charm quark. SU(3), partially quenched, rooted, staggered heavy-meson chiral perturbation theory is used to extrapolate to the chiral-continuum limit. Systematic errors arising from the chiral-continuum extrapolation, heavy-quark discretization, and quark-mass uncertainties are folded into the statistical errors from the chiral-continuum fits with methods of Bayesian inference. A preliminary error budget for all five operators is presented., Comment: 7 pages, 1 figure, LATTICE2014 proceedings

We compute the $B\to\pi\ell\nu$ semileptonic form factors and update the determination of the CKM matrix element $|V_{ub}|$. We use the MILC asqtad ensembles with $N_f=2+1$ sea quarks at four different lattice spacings in the range $a \approx 0.045$~fm to $0.12$~fm. The lattice form factors are extrapolated to the continuum limit using SU(2) staggered chiral perturbation theory in the hard pion limit, followed by an extrapolation in $q^2$ to the full kinematic range using a functional $z$-parameterization. The extrapolation is combined with the experimental measurements of the partial branching fraction to extract $|V_{ub}|$. Our preliminary result is $|V_{ub}|=(3.72\pm 0.14)\times 10^{-3}$, where the error reflects both the lattice and experimental uncertainties, which are now on par with each other., Comment: 7 pages, 4 figures; talk presented at Lattice 2014. the 32nd International Symposium on Lattice Field Theory, 23-28 June, 2014, Columbia University New York, NY

We compute the leptonic decay constants $f_{D^+}$, $f_{D_s}$, and $f_{K^+}$, and the quark-mass ratios $m_c/m_s$ and $m_s/m_l$ in unquenched lattice QCD. We use the MILC highly improved staggered quark (HISQ) ensembles with four dynamical quark flavors. Our primary results are $f_{D^+} = 212.6(0.4)({}^{+1.0}_{-1.2})\ \mathrm{MeV}$, $f_{D_s} = 249.0(0.3)({}^{+1.1}_{-1.5})\ \mathrm{MeV}$, and $f_{D_s}/f_{D^+} = 1.1712(10)({}^{+29}_{-32})$, where the errors are statistical and total systematic, respectively. We also obtain $f_{K^+}/f_{\pi^+} = 1.1956(10)({}^{+26}_{-18})$, updating our previous result, and determine the quark-mass ratios $m_s/m_l = 27.35(5)({}^{+10}_{-7})$ and $m_c/m_s = 11.747(19)({}^{+59}_{-43})$. When combined with experimental measurements of the decay rates, our results lead to precise determinations of the CKM matrix elements $|V_{us}| = 0.22487(51) (29)(20)(5)$, $|V_{cd}|=0.217(1) (5)(1)$ and $|V_{cs}|= 1.010(5)(18)(6)$, 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 $|V_{us}|$, the uncertainty in $|V_{ud}|$, respectively., Comment: 7 pages, 1 figure. Proceedings of the 32nd International Symposium on Lattice Field Theory; 23-28 June, 2014, Columbia University, New York

We compute the leptonic decay constants $f_{D^+}$, $f_{D_s}$, and $f_{K^+}$, and the quark-mass ratios $m_c/m_s$ and $m_s/m_l$ in unquenched lattice QCD using the experimentally determined value of $f_{\pi^+}$ for normalization. We use the MILC highly improved staggered quark (HISQ) 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 $a\approx 0.06$ fm to $0.15$ fm are included in the analysis to control the extrapolation to the continuum limit. Our primary results are $f_{D^+} = 212.6(0.4)({}^{+1.0}_{-1.2})\ \mathrm{MeV}$, $f_{D_s} = 249.0(0.3)({}^{+1.1}_{-1.5})\ \mathrm{MeV}$, and $f_{D_s}/f_{D^+} = 1.1712(10)({}^{+29}_{-32})$, where the errors are statistical and total systematic, respectively. The errors on our results for the charm decay constants and their ratio are approximately two to four times smaller than those of the most precise previous lattice calculations. We also obtain $f_{K^+}/f_{\pi^+} = 1.1956(10)({}^{+26}_{-18})$, updating our previous result, and determine the quark-mass ratios $m_s/m_l = 27.35(5)({}^{+10}_{-7})$ and $m_c/m_s = 11.747(19)({}^{+59}_{-43})$. When combined with experimental measurements of the decay rates, our results lead to precise determinations of the CKM matrix elements $|V_{us}| = 0.22487(51) (29)(20)(5)$, $|V_{cd}|=0.217(1) (5)(1)$ and $|V_{cs}|= 1.010(5)(18)(6)$, 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 $|V_{us}|$, the uncertainty in $|V_{ud}|$, respectively., Comment: v2: minor clarifications and additions; version published in Phys. Rev. D. (73 pages, 26 figures.)

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 version

We present a study of the $D$ and $B$ leptonic decay constants on the MILC $N_f=2+1$ asqtad gauge ensembles using asqtad-improved staggered light quarks and clover heavy quarks in the Fermilab interpretation. Our previous analysis \cite{Bazavov:2011aa} computed the decay constants at lattice spacings $a \approx 0.14, 0.11$ and $0.083$ fm. We have extended the simulations to finer $a \approx 0.058$ and $0.043$ fm lattice spacings, and have also increased statistics; this allows us to address many important sources of uncertainty. Technical advances include a two-step two-point fit procedure, better tuning of the heavy quark masses and a better determination of the axial-vector current matching. The present analysis remains blinded, so here we focus on the improvements and their predicted impact on the error budget compared to the prior analysis., Comment: LATTICE 2013; added missing .bbl file

We compute the zero-recoil form factor for the semileptonic decay $\bar{B}^0\to D^{*+}\ell^-\bar{\nu}$ (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 $D_s$ and $B_s$ hyperfine splittings with few-MeV accuracy. For the zero-recoil form factor, we obtain $\mathcal{F}(1)=0.906(4)(12)$, where the first error is statistical and the second is the sum in quadrature of all systematic errors. With the latest HFAG average of experimental results and a cautious treatment of QED effects, we find $|V_{cb}| = (39.04 \pm 0.49_\text{expt} \pm 0.53_\text{QCD} \pm 0.19_\text{QED})\times10^{-3}$. The QCD error is now commensurate with the experimental error., Comment: 53 pages, 12 figures; expanded discussion of correlator fits, typos corrected, conforms to version published in PRD

We calculate the form factors for the semileptonic decays $B_s\to K\ell\nu$ and $B\to K\ell\ell$ with lattice QCD. We work at several lattice spacings and a range of light quark masses, using the MILC 2+1-flavor asqtad ensembles. We use the Fermilab method for the $b$ quark. We obtain chiral-continuum extrapolations for $E_K$ up to $\sim1.2$ GeV and then extend to the entire kinematic range with the model-independent $z$ expansion., Comment: 7. pp, 6 figs. Presented at the 31st International Symposium on Lattice Field Theory - LATTICE 2013, July 29 - August 3, 2013, Mainz, Germany

We calculate the kaon semileptonic form factor $f_+(0)$ from lattice QCD, working, for the first time, at the physical light-quark masses. We use gauge configurations generated by the MILC collaboration with $N_f=2+1+1$ flavors of sea quarks, which incorporate the effects of dynamical charm quarks as well as those of up, down, and strange. We employ data at three lattice spacings to extrapolate to the continuum limit. Our result, $f_+(0) = 0.9704(32)$, where the error is the total statistical plus systematic uncertainty added in quadrature, is the most precise determination to date. Combining our result with the latest experimental measurements of $K$ semileptonic decays, one obtains the Cabibbo-Kobayashi-Maskawa matrix element $|V_{us}|=0.22290(74)(52)$, where the first error is from $f_+(0)$ and the second one is from experiment. In the first-row test of Cabibbo-Kobayashi-Maskawa unitarity, the error stemming from $|V_{us}|$ is now comparable to that from $|V_{ud}|$., Comment: 6 pages, 2 figures; version published in PRL

We update our determinations of $f_{D^+}$, $f_{D_s}$, $f_K$, and quark mass ratios from simulations with four flavors of HISQ dynamical quarks. The availability of ensembles with light quarks near their physical mass means that we can extract physical results with only small corrections for valence- and sea-quark mass mistunings instead of a chiral extrapolation. The adjusted valence-quark masses and lattice spacings may be determined from an ensemble-by-ensemble analysis, and the results for the quark mass ratios then extrapolated to the continuum limit. Our central values of the charmed meson decay constants, however, come from an alternative analysis, which uses staggered chiral perturbation theory for the heavy-light mesons, and allows us to incorporate data at unphysical quark masses where statistical errors are often smaller. A jackknife analysis propagated through all of these steps takes account of the correlations among all the quantities used in the analysis. Systematic errors from the finite spatial size and EM effects are estimated by varying the parameters in the analysis, and systematic errors from the assumptions in the continuum extrapolation are estimated from the spread of values from different extrapolations., Comment: presented at Lattice 2013, Mainz, Germany, July 29 - August 3, 2013. 14 pages, 7 figures

We present results for the form factor $f_+^{K \pi}(0)$, needed to extract the CKM matrix element $|V_{us}|$ from experimental data on semileptonic $K$ decays, on the HISQ $N_f=2+1+1$ MILC configurations. The HISQ action is also used for the valence sector. The data set used for our final result includes three different values of the lattice spacing and data at the physical light quark masses. We discuss the error budget and how this calculation improves on our previous determination of $f_+^{K \pi}(0)$ on the asqtad $N_f=2+1$ MILC configurations., Comment: 7 pages, 1 figure, presented at the 31st International Symposium on Lattice Field Theory (Lattice 2013), 29 July - 3 August 2013, Mainz, Germany; v2: minor changes

We present the status of our calculation of hadronic matrix elements for $D$- and $B$-meson mixing. We use a large set of the MILC collaboration's $N_f=2+1$ asqtad ensembles, which includes lattice spacings in the range $a\approx0.12$-0.045 fm, and up/down to strange quark mass ratios as low as 0.05. The asqtad action is also employed for the light valence quarks. For the heavy quarks we use the Sheikholeslami-Wohlert action with the Fermilab interpretation. Our calculation covers the complete set of five local operators needed to describe $B$-meson mixing in the Standard Model and Beyond. In the charm sector, our calculation of local mixing matrix elements may be used to constrain new physics models. We present final correlator fit results on the full data set for the $B$-meson mixing project and preliminary fit results for the $D$-meson mixing project., Comment: 7 pages, 4 figures, Lattice 2013 proceedings

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, Germany

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, 2013

We present an update of the Fermilab-MILC Collaboration's calculation of hadronic matrix elements for B^0-\bar{B^0} mixing. This work is a more extended analysis than our recent publication of the SU(3)-breaking ratio xi [arXiv:1205.7013]. We use the asqtad staggered action for light valence quarks in combination with the Fermilab interpretation of the Sheikoleslami-Wohlert action for heavy quarks. The calculations use MILC's 2+1 flavor asqtad ensembles. Ensembles include four lattice spacings from approximately 0.125 fm to 0.045 fm and up/down to strange quark mass ratios as low as 0.05. Our calculation covers the complete set of five operators needed to describe B mixing in the Standard Model and beyond. In addition to an update including a fuller set of analyzed data, we comment on the form of the staggered ChPT extrapolation function., Comment: 7 pages, 2 figures; Proceedings of the 30th International Symposium on Lattice Field Theory, June 24-29, 2012, Cairns, Australia

Using staggered fermions and twisted boundary conditions, we calculate the K meson semileptonic decay vector form factor at zero momentum transfer. The HISQ formulation is used for the valence quarks, while the sea quarks are simulated with the asqtad action (MILC N_f=2+1 configurations). For the chiral and continuum extrapolation we use two-loop continuum CHPT, supplemented by partially quenched staggered CHPT at one loop. Our result is f_+^{K\pi}(0) = 0.9667+-0.0023+-0.0033, where the first error is statistical and the second is the sum in quadrature of the systematic uncertainties. This result is the first N_f=2+1 calculation with two lattice spacings and a controlled continuum extrapolation. It is also the most precise result to date for the vector form factor and, although the central value is larger than previous unquenched lattice calculations, it is compatible with them within errors. Combining our value for f_+^{K\pi}(0) with the latest experimental measurements of K semileptonic decays, we obtain |V_{us}| = 0.2238+-0.0009+-0.0005, where the first error is from f_+^{K\pi}(0) and the second one is experimental. As a byproduct of our calculation, we obtain the combination of low-energy constants [C_{12}^r+C_{34}^r-(L_5^r)^2](M_\rho) = (3.62+-1.00)x10^{-6}., Comment: 28 pages, 6 figures

We present our methods to fit the two point correlators for light, strange, and charmed pseudoscalar meson physics with the highly improved staggered quark (HISQ) action. We make use of the least-squares fit including the full covariance matrix of the correlators and including Gaussian constraints on some parameters. We fit the correlators on a variety of the HISQ ensembles. The lattice spacing ranges from 0.15 fm down to 0.06 fm. The light sea quark mass ranges from 0.2 times the strange quark mass down to the physical light quark mass. The HISQ ensembles also include lattices with different volumes and with unphysical values of the strange quark mass. We use the results from this work to obtain our preliminary results of $f_D$, $f_{D_s}$, $f_{D_s}/f_{D}$, and ratios of quark masses presented in another talk [1]., Comment: Proceedings of Lattice 2012 Int. Symposium

We report on the status of our kaon semileptonic form factor calculations using the highly-improved staggered quark (HISQ) formulation to simulate the valence fermions. We present results for the form factor f_+^{K \pi}(0) on the asqtad N_f=2+1 MILC configurations, discuss the chiral-continuum extrapolation, and give a preliminary estimate of the total error. We also present a more preliminary set of results for the same form factor but with the sea quarks also simulated with the HISQ action; these results include data at the physical light quark masses. The improvements that we expect to achieve with the use of the HISQ configurations and simulations at the physical quark masses are briefly discussed., Comment: Proceedings of Lattice 2012 International Symposium, 7 pages, 4 figures

We present preliminary results for light, strange and charmed pseudoscalar meson physics from simulations using four flavors of dynamical quarks with the highly improved staggered quark (HISQ) action. These simulations include lattice spacings ranging from 0.15 to 0.06 fm, and sea-quark masses both above and at their physical value. The major results are charm meson decay constants f_D, f_{D_s} and f_{D_s}/f_D and ratios of quark masses. This talk will focus on our procedures for finding the decay constants on each ensemble, the continuum extrapolation, and estimates of systematic error., Comment: Proceedings of Lattice 2012 Int. Symposium