Search

We are very grateful to the Fermilab Directorate and the Fermilab Theoretical Physics Department for their financial and logistical support of the first workshop of the Muon g -2 Theory Initiative (held near Fermilab in June 2017) [123], which was crucial for its success, and indeed for the successful start of the Initiative. Financial support for this workshop was also provided by the Fermilab Distinguished Scholars program, the Universities Research Association through a URA Visiting Scholar award, the Riken Brookhaven Research Center, and the Japan Society for the Promotion of Science under Grant No. KAKEHNHI-17H02906. We thank Shoji Hashimoto, Toru Iijima, Takashi Kaneko, and Shohei Nishida for hosting the HVP workshop at KEK [124] and the KEK Theory Center and the U.S.-Japan Science and Technology Cooperation Program in High Energy Physics for providing logistical and financial support. The HLbL workshop at the University of Connecticut [125] was hosted by the University of Connecticut Physics Department. We also gratefully acknowledge support for the second plenary workshop in Mainz [126] from the Deutsche Forschungsgemeinschaft via the Cluster of Excellence "Precision Physics, Fundamental Interactions and Structure of Matter'' (PRISMA), the Collaborative Research Centre "The low-energy frontier of the Standard Model'' (SFB 1044), as well as the Helmholtz Institute Mainz. And finally, we thank the Institute for Nuclear Theory at the University of Washington for hosting the third plenary workshop [127] and for its kind hospitality and stimulating research environment. This workshop was supported in part by the U.S. Department of Energy, Office of Science, under Award Nos. DE-FG02-00ER41132, DE-SC0020106, and by the U.S.-Japan Science and Technology Cooperation Program in High Energy Physics. This review benefited from discussions with O. Cata, N. Christ, L.Y. Dai, H. Davoudiasl, S. Fayer, S. Ganguly, A. Gasparian, S. Hashimoto, T. Iijima, K. Kampf, D. Kawall, I. Larin, Z. Pagel, M. Petschlies, A. Rebhan, K. Schilcher, K. Shimomura, E. Shintani, D. Steffen, S. Tracz, C. Tu, and T. Yamazaki. The work in this paper was supported by CNRS, by Conacyt (Ciencia Basica 2015) under Grant No. 250628, by CONACyT-Mexico under Grant No. CB2014-22117, by Coordinacion de la Investigacion Cientifica (CIC-UMSNH) under Grant No. 4.10, by Danmarks Frie Forskningsfond under Grant No. 8021-00122B, by Deutsche Forschungsgemeinschaft Collaborative Research Centers CRC 1044, CRC 1044 -204404729, CRC 110, and under Grant No. HI 2048/1-1, Prisma Cluster for Excellence PRISMA+ EXC2118/1, STO/876/6-1, by European Research Council under the European Union's Horizon 2020 research and innovation programme under Grant Agreement Nos. 668679, 757646, 771971-SIMDAMA, 813942, by the European Union H2020-MSCA-COFUND2016 under Grant No. 754510, by the European Union's Horizon 2020 research and innovation programme under the Marie Sklodowska-Curie Grant Agreement No. 843134, by European Union EuroPLEx Grant H2020-MSCA-ITN-2018-813942, by European Union STRONG 2020 project under Grant Agreement No. 824093, by the Excellence Initiative of Aix-Marseille University -A*MIDEX, a French "Investissements d'Avenir" program, through the Chaire d'Excellence program and the OCEVU Laboratoire d'Excellence (ANR-11-LABX-0060), by the Fermilab Distinguished Scholars program, by Fondo SEP-Cinvestav under Grant No. 142, Fundacao para a Ciencia e a Tecnologia under Grant No. SFRH/BPD/109443/2015, by Generalitat de Catalunya under Grant No. 2017SGR1069, by the Helmholtz Association (German Federal Ministry of Education and Research), by the Helmholtz-Institut Mainz, by the Istituto Nazionale di Fisica Nucleare (INFN), by the Isaac Newton Trust, by the Japan Society for the Promotion of Science under Grant Nos. KAKENHI-15H05742, 16K05317, 16K05323, 16K05338, 17H01133, 17H02906, 18H05226, 19K21872, 20K03926, 20K03960, by Junta de Andalucia under Grant No. A-FQM-467-UGR18, by KEK, by Ministerio de Ciencia e Innovacion under Grant No. CICYTFEDER-FPA2017-86989-P, by Ministerio de Industria, Economia y Competitividad under Grant Nos. FPA2016-78220-C3-3-P, FPA2017-86989-P, PGC2018-094857-B-I00, SEV-2016-0588, SEV-2016-0597, by Laboratoires d'Excellence FIRST-TF grants, a French "Investissements d'Avenir'' program, by the Ministry of Science and Higher Education of the Russian Federation under Grant Agreement No. 14.W03.31.0026, by the National Research Foundation of South Africa, by the Natural Sciences and Engineering Research Council of Canada, by the Portuguese Science Foundation (FCT) Investigator Grant IF/00898/2015, by the Romanian Ministry of Education and Research under Grant No. PN19060101, by the Russian Science Foundation under Grant No. RSF 18-12-00128, by the Secretaria d'Universitats i Recerca del Departament d'Economia i Coneixement de la Generalitat de Catalunya under Grant No. 2017 SGR 1069, by the Swedish Research Council under Grant Nos. 2016-05996, 2019-03779, by the Swiss National Science Foundation under Grant Nos. PP00P2_176884, PCEFP2_181117, by The Leverhulme Trust under Grant No. ECF-2019-223, by the UK Science and Technology Facilities Council (STFC) under Grant Nos. ST/N504130/1, ST/P000290/1, ST/P00055X/1, ST/P000630/1, ST/P000711/1, ST/P000746/1, ST/S000879/1, ST/S000925/1, by the U.S. Department of Energy, Office of Science, Office of High Energy Physics under Award Nos. DE-SC0009919, DE-SC0009998, DE-SC0010005, DE-SC0010120, DE-SC0010339, DE-SC0012391, DE-SC0012704, DE-SC0013682, DE-SC0013895, DE-SC0015655, by the U.S. Department of Energy, Office of Science, Office of Nuclear Physics under Award Nos. DE-AC02-05CH11231, DE-FG02-00ER41132, DE-FG02-97ER41020, by the U.S.-Japan Science and Technology Cooperation Program in High Energy Physics, "Incubation Platform for Intensity Frontier", by the U.S. National Science Foundation under Grant Nos. NSF-PHY-1316222, PHY14-14614, PHY17-19626, and PHY19-23131, and by the U.S. National Institute of Standards and Technology (NIST) Precision Measurement Grant Program under Award No. 60NANB16D271. This manuscript has been authored by Fermi Research Alliance, LLC under Contract No. DE-AC02-07CH11359 with the U.S. Department of Energy, Office of Science, Office of High Energy Physics., We review the present status of the Standard Model calculation of the anomalous magnetic moment of the muon. This is performed in a perturbative expansion in the fine-structure constant and is broken down into pure QED, electroweak, and hadronic contributions. The pure QED contribution is by far the largest and has been evaluated up to and including with negligible numerical uncertainty. The electroweak contribution is suppressed by and only shows up at the level of the seventh significant digit. It has been evaluated up to two loops and is known to better than one percent. Hadronic contributions are the most difficult to calculate and are responsible for almost all of the theoretical uncertainty. The leading hadronic contribution appears at and is due to hadronic vacuum polarization, whereas at the hadronic light-by-light scattering contribution appears. Given the low characteristic scale of this observable, these contributions have to be calculated with nonperturbative methods, in particular, dispersion relations and the lattice approach to QCD. The largest part of this review is dedicated to a detailed account of recent efforts to improve the calculation of these two contributions with either a data-driven, dispersive approach, or a first-principle, lattice-QCD approach. The final result reads and is smaller than the Brookhaven measurement by 3.7. The experimental uncertainty will soon be reduced by up to a factor four by the new experiment currently running at Fermilab, and also by the future J-PARC experiment. This and the prospects to further reduce the theoretical uncertainty in the near future – which are also discussed here – make this quantity one of the most promising places to look for evidence of new physics., Fermilab Directorate, Fermilab Theoretical Physics Department, Fermilab Distinguished Scholars program, Universities Research Association through a URA Visiting Scholar award, Riken Brookhaven Research Center, Ministry of Education, Culture, Sports, Science and Technology, Japan (MEXT) Japan Society for the Promotion of Science KAKEHNHI-17H02906 KAKENHI-15H05742 16K05317 16K05323 16K05338 17H01133 17H02906 18H05226 19K21872 20K03926 20K03960, High Energy Accelerator Research Organization (KEK), U.S.-Japan Science and Technology Cooperation Program in High Energy Physics, Deutsche Forschungsgemeinschaft via the Cluster of Excellence "Precision Physics, Fundamental Interactions and Structure of Matter'' (PRISMA), Collaborative Research Centre "The low-energy frontier of the Standard Model'' SFB 1044, Helmholtz Institute Mainz, United States Department of Energy (DOE) DE-FG02-00ER41132 DE-SC0020106, Centre National de la Recherche Scientifique (CNRS), Conacyt (Ciencia Basica 2015) 250628, Consejo Nacional de Ciencia y Tecnologia (CONACyT) CB2014-22117, Coordinacion de la Investigacion Cientifica (CIC-UMSNH) 4.10, Danmarks Frie Forskningsfond 8021-00122B, German Research Foundation (DFG) CRC 1044 CRC 1044 -204404729 CRC 110 HI 2048/1-1, Prisma Cluster for Excellence PRISMA+ EXC2118/1 STO/876/6-1, European Research Council (ERC) 668679 757646 771971-SIMDAMA 813942, European Union (EU) 754510, European Union (EU) 843134, European Union EuroPLEx Grant H2020-MSCA-ITN-2018-813942, European Union STRONG 2020 project 824093, French National Research Agency (ANR), OCEVU Laboratoire d'Excellence ANR-11-LABX-0060, Fondo SEP-Cinvestav 142, Portuguese Foundation for Science and Technology SFRH/BPD/109443/2015, Generalitat de Catalunya 2017SGR1069, Helmholtz Association (German Federal Ministry of Education and Research), Istituto Nazionale di Fisica Nucleare (INFN), Isaac Newton Trust, Junta de Andalucia A-FQM-467-UGR18, Instituto de Salud Carlos III Spanish Government CICYTFEDER-FPA2017-86989-P, Ministerio de Industria, Economia y Competitividad FPA2016-78220-C3-3-P FPA2017-86989-P PGC2018-094857-B-I00 SEV-2016-0588 SEV-2016-0597, Laboratoires d'Excellence FIRST-TF grants, Ministry of Science and Higher Education of the Russian Federation 14.W03.31.0026, National Research Foundation - South Africa, Natural Sciences and Engineering Research Council of Canada (NSERC) CGIAR, Portuguese Science Foundation (FCT) Investigator Grant IF/00898/2015, Romanian Ministry of Education and Research PN19060101, Russian Science Foundation (RSF) RSF 18-12-00128, Generalitat de Catalunya 2017 SGR 1069, Swedish Research Council 2016-05996 2019-03779, Swiss National Science Foundation (SNSF) PP00P2_176884 PCEFP2_181117, Leverhulme Trust ECF-2019-223, UK Research & Innovation (UKRI) Science & Technology Facilities Council (STFC) ST/N504130/1 ST/P000290/1 ST/P00055X/1 ST/P000630/1 ST/P000711/1 ST/P000746/1 ST/S000879/1 ST/S000925/1, United States Department of Energy (DOE) DE-SC0009919 DE-SC0009998 DE-SC0010005 DE-SC0010120 DE-SC0010339 DE-SC0012391 DE-SC0012704 DE-SC0013682 DE-SC0013895 DE-SC0015655, United States Department of Energy (DOE) DE-FG02-00ER41132 DE-AC02-05CH11231 DE-FG02-97ER41020 DE-AC02-07CH11359, U.S.-Japan Science and Technology Cooperation Program in High Energy Physics, "Incubation Platform for Intensity Frontier", National Science Foundation (NSF) NSF-PHY-1316222 PHY14-14614 PHY17-19626 PHY19-23131, U.S. National Institute of Standards and Technology (NIST) Precision Measurement Grant 60NANB16D271

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 $a \approx 0.06$ to~0.15~fm. The up- and down-quark masses in our simulations have equal masses $m_l$. We obtain, in this world where all pions have the mass of the $\pi^0$, $10^{10} a_\mu^{ll}({\rm conn.}) = 637.8\,(8.8)$, 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 $\mathcal{O}(\alpha^2)$ hadronic vacuum polarization to the muon's anomalous magnetic moment is~$10^{10}a_\mu^{\rm HVP,LO} = 699(15)_{u,d}(1)_{s,c,b}$, where the errors are from the light-quark and heavy-quark contributions, respectively. Our result agrees with both {\it ab-initio} lattice-QCD calculations and phenomenological determinations from experimental $e^+e^-$-scattering data. It is $1.3\sigma$ below the "no new physics" value of the hadronic-vacuum-polarization contribution inferred from combining the BNL E821 measurement of $a_\mu$ with theoretical calculations of the other contributions., Comment: 19 pages, 12 figures, 6 tables; updated to correct a small mistake in the finite volume correction resulting in small changes to the results, matches published version

We review lattice results related to pion, kaon,D-meson,B-meson, and nucleon physics with the aim of making them easily accessible to the nuclear and particle physics communities. More specifically, we report on the determination of the light-quark masses, the form factor$$f_+(0)$$f+(0)arising in the semileptonic$$K \rightarrow \pi $$K→πtransition at zero momentum transfer, as well as the decay constant ratio$$f_K/f_\pi $$fK/fπand its consequences for the CKM matrix elements$$V_{us}$$Vusand$$V_{ud}$$Vud. Furthermore, we describe the results obtained on the lattice for some of the low-energy constants of$$SU(2)_L\times SU(2)_R$$SU(2)L×SU(2)Rand$$SU(3)_L\times SU(3)_R$$SU(3)L×SU(3)RChiral Perturbation Theory. We review the determination of the$$B_K$$BKparameter of neutral kaon mixing as well as the additional fourBparameters that arise in theories of physics beyond the Standard Model. For the heavy-quark sector, we provide results for$$m_c$$mcand$$m_b$$mbas well as those forD- andB-meson decay constants, form factors, and mixing parameters. These are the heavy-quark quantities most relevant for the determination of CKM matrix elements and the global CKM unitarity-triangle fit. We review the status of lattice determinations of the strong coupling constant$$\alpha _s$$αs. Finally, in this review we have added a new section reviewing results for nucleon matrix elements of the axial, scalar and tensor bilinears, both isovector and flavor diagonal.

We report updates to an ongoing lattice-QCD calculation of the form factors for the semileptonic decays $B \to \pi \ell \nu$, $B_s \to K \ell \nu$, $B \to \pi \ell^+ \ell^-$, and $B \to K \ell^+ \ell^-$. The tree-level decays $B_{(s)} \to \pi (K) \ell \nu$ enable precise determinations of the CKM matrix element $|V_{ub}|$, while the flavor-changing neutral-current interactions $B \to \pi (K) \ell^+ \ell^-$ are sensitive to contributions from new physics. This work uses MILC's (2+1+1)-flavor HISQ ensembles at approximate lattice spacings between $0.057$ and $0.15$ fm, with physical sea-quark masses on four out of the seven ensembles. The valence sector is comprised of a clover $b$ quark (in the Fermilab interpretation) and HISQ light and $s$ quarks. We present preliminary results for the form factors $f_0$, $f_+$, and $f_T$, including studies of systematic errors.

We present an update on the ongoing calculations by the Fermilab Lattice, HPQCD, and MILC Collaboration of the leading-order (in electromagnetism) hadronic vacuum polarization contribution to the anomalous magnetic moment of the muon. Our project employs ensembles with four flavors of highly improved staggered fermions, physical light-quark masses, and four lattice spacings ranging from $a \approx 0.06$ to 0.15 fm for most of the results thus far.

Using highly improved staggered quark (HISQ) ${N}_{f}=2+1+1$ 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 $K\ensuremath{\rightarrow}\ensuremath{\pi}\ensuremath{\ell}\ensuremath{\nu}$ vector form factor at zero momentum transfer, ${f}_{+}^{{K}^{0}{\ensuremath{\pi}}^{\ensuremath{-}}}(0)=0.9696(15{)}_{\mathrm{stat}}(12{)}_{\mathrm{syst}}$. 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 $|{V}_{us}|=0.22333(44{)}_{{f}_{+}(0)}(42{)}_{\mathrm{exp}}$, 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 ${f}_{{K}^{+}}/{f}_{{\ensuremath{\pi}}^{+}}$, which uses $|{V}_{ud}|$ as input. Our value of $|{V}_{us}|$ is in tension at the $2--2.6\ensuremath{\sigma}$ 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 $|{V}_{ud}|$, although a recent determination of the nucleus-independent radiative corrections to superallowed nuclear $\ensuremath{\beta}$ decays could reduce the $|{V}_{ud}{|}^{2}$ uncertainty nearly to that of $|{V}_{us}{|}^{2}$. 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 ${f}_{+}^{K\ensuremath{\pi}}(0)$ 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 $[{C}_{12}^{r}+{C}_{34}^{r}\ensuremath{-}({L}_{5}^{r}{)}^{2}]({M}_{\ensuremath{\rho}})=(2.92\ifmmode\pm\else\textpm\fi{}0.31)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}6}$.

We discuss preliminary results for the vector form factors $f_+^{\{\pi,K\}}$ at zero-momentum transfer for the decays $D\to\pi\ell\nu$ and $D\to K \ell\nu$ using MILC's $N_f = 2+1+1$ HISQ ensembles at four lattice spacings, $a \approx 0.042, 0.06, 0.09$, and 0.12 fm, and various HISQ quark masses down to the (degenerate) physical light quark mass. We use the kinematic constraint $f_+(q^2)= f_0(q^2)$ at $q^2 = 0$ to determine the vector form factor from our study of the scalar current, which yields $f_0(0)$. Results are extrapolated to the continuum physical point in the framework of hard pion/kaon SU(3) heavy-meson-staggered $\chi$PT and Symanzik effective theory. Our calculation improves upon the precision achieved in existing lattice-QCD calculations of the vector form factors at $q^2=0$. We show the values of the CKM matrix elements $|V_{cs}|$ and $|V_{cd}|$ that we would obtain using our preliminary results for the form factors together with recent experimental results, and discuss the implications of these values for the second row CKM unitarity.

We introduce a new method for calculating the ${\rm O}(\alpha^3)$ 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 $\hat\Pi(q^2)$, 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 $\hat\Pi(q^2)$ that were obtained on four-flavor QCD gauge-field configurations with physical light-quark masses. We obtain $10^{10} a_\mu^{\rm HVP,HO} = -9.3(1.3)$, in agreement with, but with a larger uncertainty than, determinations from $e^+e^- \to {\rm hadrons}$ data plus dispersion relations., Comment: Expanded and clarified discussion and revised Figure 4. Results unchanged. 11 pages, 5 tables, 5 figures. Version accepted to Physical Review D

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 $a\approx0.15$~fm 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 $\overline{\text{MS}}$-renormalized masses are $m_u(2~\text{GeV}) = 2.130(41)$~MeV, $m_d(2~\text{GeV}) = 4.675(56)$~MeV, $m_s(2~\text{GeV}) = 92.47(69)$~MeV, $m_c(3~\text{GeV}) = 983.7(5.6)$~MeV, and $m_c(m_c) = 1273(10)$~MeV, with four active flavors; and $m_b(m_b) = 4195(14)$~MeV with five active flavors. We also obtain ratios of quark masses $m_c/m_s = 11.783(25)$, $m_b/m_s = 53.94(12)$, and $m_b/m_c = 4.578(8)$. The result for $m_c$ 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 $\alpha_s^4$. As byproducts of our method, we obtain the matrix elements of HQET operators with dimension 4 and 5: $\overline{\Lambda}_\text{MRS}=555(31)$~MeV in the minimal renormalon-subtracted (MRS) scheme, $\mu_\pi^2 = 0.05(22)~\text{GeV}^2$, and $\mu_G^2(m_b)=0.38(2)~\text{GeV}^2$. The MRS scheme [Phys. Rev. D97, 034503 (2018), arXiv:1712.04983 [hep-ph]] is the key new aspect of our method., Comment: The published version; 32 pages and 7 figures

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 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.

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 $\approx 0.12$ fm to $\approx 0.045$ fm. We compute the quantity $\epsilon$, which parameterizes the corrections to Dashen's theorem for the $K^+$-$K^0$ EM mass splitting, as well as $\epsilon_{K^0}$, which parameterizes the EM contribution to the mass of the $K^0$ 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 $\epsilon$, they are estimated only qualitatively for $\epsilon_{K^0}$, and constitute one of the largest sources of uncertainty for that quantity. We find $\epsilon = 0.78(1)_{\rm stat}({}^{+\phantom{1}8}_{-11})_{\rm syst}$ and $\epsilon_{K^0}=0.035(3)_{\rm stat}(20)_{\rm syst}$. We then use these results on 2+1+1 flavor pure QCD HISQ ensembles and find $m_u/m_d = 0.4529(48)_{\rm stat}( {}_{-\phantom{1}67}^{+150})_{\rm syst}$., Comment: Version published in Phys. Rev. D. Compared to v1, more discussion of nonperturbative EM renormalization scheme, of statistical errors (with 3 added figures), and of choice QED_{TL} in finite volume. 87 pages, 35 figures

All lattice-QCD calculations of the hadronic-vacuum-polarization contribution to the muon's anomalous magnetic moment to-date have been performed with degenerate up- and down-quark masses. Here we calculate directly the strong-isospin-breaking correction to aHVPμ for the first time with physical values of mu and md and dynamical u, d, s, and c quarks, thereby removing this important source of systematic uncertainty. We obtain a relative shift to be applied to lattice-QCD results obtained with degenerate light-quark masses of δaHVP,mu≠mdμ= +1.5(7)%, in agreement with estimates from phenomenology and a recent lattice-QCD calculation with unphysically heavy pions., We thank John Campbell, Vera Gülpers, Fred Jegerlehner, Laurent Lellouch, and Silvano Simula for useful discussions. Computations for this work were carried out with resources provided by the USQCD Collaboration, the National Energy Research Scientific Computing Center and the Argonne Leadership Computing Facility, which are funded by the Office of Science of the U.S. Department of Energy; and with resources provided by the National Institute for Computational Science and the Texas Advanced Computing Center, which are funded through the National Science Foundation’s Teragrid/XSEDE Program. Computations were also carried out on the Darwin Supercomputer at the DiRAC facility, which is jointly funded by the U.K. Science and Technology Facility Council, the U.K. Department for Business, Innovation and Skills, and the Universities of Cambridge and Glasgow. This work utilized the RMACC Summit supercomputer, which is supported by the National Science Foundation (Grants No. ACI-1532235 and No. ACI-1532236), the University of Colorado Boulder, and Colorado State University. The Summit supercomputer is a joint effort of the University of Colorado Boulder and Colorado State University. This research is part of the Blue Waters sustained-petascale computing project, which is supported by the National Science Foundation (Grants No. OCI- 0725070 and No. ACI-1238993) and the state of Illinois. Blue Waters is a joint effort of the University of Illinois at Urbana-Champaign and its National Center for Supercomputing Applications. This work was supported in part by the U.S. Department of Energy under Grants No. DE-AC05-06OR23177 (B. C.), No. DE-SC0010120 (S. G.), No. DE-SC0015655 (A. X. K.), No. DESC0009998 (J. L.), No. DE-SC0010005 (E. T. N.), No. DE-FG02-13ER41976 (D. T.), by the U.S. National Science Foundation under Grants No. PHY14-17805 (J. L.), No. PHY14-14614 (C. D., A. V.), No. PHY13- 16222 (G. P. L.), No. PHY12-12389 (Y. L.), and No. PHY13-16748 and No. PHY16-20625 (R. S.); by the Royal Society, STFC and Wolfson Foundation (C. T. H. D., D. H., J. K.); by the MINECO (Spain) under Grants No. FPA2013-47836-C-1-P and No. FPA2016- 78220-C3-3-P (E. G.); by the Junta de Andalucía (Spain) under Grant No. FQM-101 (E. G.) by the Fermilab Distinguished Scholars Program (A. X. K.); by the German Excellence Initiative and the European Union Seventh Framework Program under grant agreement No. 291763 as well as the European Union’s Marie Curie COFUND program (A. S. K.); by the Blue Waters PAID program (Y. L.); and by the U.K. STFC under Grants No. ST/N005872/1 and ST/P00055X/1 (C.M.). Brookhaven National Laboratory is supported by the U.S. Department of Energy under Contract No. DESC0012704. Fermilab is operated by Fermi Research Alliance, LLC, under Contract No. DE-AC02- 07CH11359 with the United States Department of Energy, Office of Science, Office of High Energy Physics. The U.S. Government retains and the publisher, by accepting the article for publication, acknowledges that the U.S. Government retains a non-exclusive, paid-up, irrevocable, worldwide license to publish or reproduce the published form of this manuscript, or allow others to do so, for U.S. Government purposes.

We report the status of an ongoing lattice-QCD calculation of form factors for exclusive semileptonic decays of $B$ mesons with both charged currents ($B\to\pi\ell\nu$, $B_s\to K\ell\nu$) and neutral currents ($B\to\pi\ell^+\ell^-$, $B\to K\ell^+\ell^-$). The results are important for constraining or revealing physics beyond the Standard Model. This work uses MILC's (2+1+1)-flavor ensembles with the HISQ action for the sea and light valence quarks and the clover action in the Fermilab interpretation for the $b$ quark. Simulations are carried out at three lattice spacings down to $0.088$ fm, with both physical and unphysical sea-quark masses. We present preliminary results for correlation-function fits., Comment: 8 pages, 3 figures; presented at the 35th International Symposium on Lattice Field Theory, 18-24 June 2017, Granada, Spain

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./Users/ask/TeX/confs/lat16/307/lat-16-307.pdf

We present a calculation of the form factors of the D $\rightarrow$ Klν and D $\rightarrow$ $\pi$lν semileptonic decays at zero momentum transfer, ultimately for the purpose of determining the Cabibbo-KobayashiMaskawa (CKM) matrix elements |Vcs| and |Vcd|. This work uses MILC Nf = 2+1+1 configurations with the HISQ action for both sea quarks and valence quarks, including several physical mass ensembles and lattice spacings down to 0.042 fm. The calculation is done directly at q 2 = 0 by employing twisted boundary conditions to tune the child particle momenta. Results at the physical point and in the continuum limit will be achieved in the final analysis through the use of Heavy-Meson Staggered $\chi$PT. Here we present our expected error budget and compare with the error of prior calculations

We discuss the reduction of errors in the calculation of the form factor $$f_+^{K \pi}(0)$$ with HISQ fermions on the $$N_f=2+1+1$$ MILC configurations from increased statistics on some key ensembles, new data on ensembles with lattice spacings down to 0.042 fm and the study of finite-volume effects within staggered ChPT. We also study the implications for the unitarity of the CKM matrix in the first row and for current tensions with leptonic determinations of $$\vert V_{us}\vert$$.

We present a progress report on our calculation of the decay constants $f_B$ and $f_{B_s}$ from lattice-QCD simulations with highly-improved staggered quarks. Simulations are carried out with several heavy valence-quark masses on $(2+1+1)$-flavor ensembles that include charm sea quarks. We include data at six lattice spacings and several light sea-quark masses, including an approximately physical-mass ensemble at all but the smallest lattice spacing, 0.03 fm. This range of parameters provides excellent control of the continuum extrapolation to zero lattice spacing and of heavy-quark discretization errors. Finally, using the heavy-quark effective theory expansion we present a method of extracting from the same correlation functions the charm- and bottom-quark masses as well as some low-energy constants appearing in the heavy-quark expansion.

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.

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 $\ensuremath{\xi}=1.206(18)(6)$, 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 $|{V}_{td}|=8.00(34)(8)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}3}$, $|{V}_{ts}|=39.0(1.2)(0.4)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}3}$, and $|{V}_{td}/{V}_{ts}|=0.2052(31)(10)$, which differ from CKM-unitarity expectations by about $2\ensuremath{\sigma}$. 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.

We compute the form factors for the $B\ensuremath{\rightarrow}K{l}^{+}{l}^{\ensuremath{-}}$ 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 study the exclusive semileptonic $B$-meson decays $B\to K(\pi)\ell^+\ell^-$, $B\to K(\pi)\nu\bar\nu$, and $B\to\pi\tau\nu$, computing observables in the Standard model using the recent lattice-QCD results for the underlying form factors from the Fermilab Lattice and MILC Collaborations. These processes provide theoretically clean windows into physics beyond the Standard Model because the hadronic uncertainties are now under good control for suitably binned observables. For example, the resulting partially integrated branching fractions for $B\to\pi\mu^+\mu^-$ and $B\to K\mu^+\mu^-$ outside the charmonium resonance region are 1-2$\sigma$ higher than the LHCb Collaboration's recent measurements, where the theoretical and experimental errors are commensurate. The combined tension is 1.7$\sigma$. Combining the Standard-Model rates with LHCb's measurements yields values for the Cabibbo-Kobayashi-Maskawa (CKM) matrix elements $|V_{td}|=7.45{(69)}\times10^{-3}$, $|V_{ts}|=35.7(1.5)\times10^{-3}$, and $|V_{td}/V_{ts}|=0.201{(20)}$, which are compatible with the values obtained from neutral $B_{(s)}$-meson oscillations and have competitive uncertainties. Alternatively, taking the CKM matrix elements from unitarity, we constrain new-physics contributions at the electroweak scale. The constraints on the Wilson coefficients ${\rm Re}(C_9)$ and ${\rm Re}(C_{10})$ from $B\to\pi\mu^+\mu^-$ and $B\to K\mu^+\mu^-$ are competitive with those from $B\to K^* \mu^+\mu^-$, and display a 2.0$\sigma$ tension with the Standard Model. Our predictions for $B\to K(\pi)\nu\bar\nu$ and $B\to\pi\tau\nu$ are close to the current experimental limits., Comment: V3: Typos in Eq. (5.13) and text corrected. Reference added. Version published in Phys. Rev. D

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 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 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 $\overline{B}\ensuremath{\rightarrow}D\ensuremath{\ell}\overline{\ensuremath{\nu}}$ 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 form-factor data jointly with the experimentally measured differential decay rate from BABAR to determine the CKM matrix element, $|{V}_{cb}|=(39.6\ifmmode\pm\else\textpm\fi{}1.{7}_{\mathrm{QCD}+\mathrm{exp}}\ifmmode\pm\else\textpm\fi{}0.{2}_{\mathrm{QED}})\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}3}$. 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 $B\ensuremath{\rightarrow}\ensuremath{\pi}\ensuremath{\ell}\ensuremath{\nu}$ 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 $z$ 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 $|{V}_{ub}|$, we simultaneously fit the experimental data for the $B\ensuremath{\rightarrow}\ensuremath{\pi}\ensuremath{\ell}\ensuremath{\nu}$ differential decay rate obtained by the BABAR and Belle collaborations together with our lattice form-factor results. We find $|{V}_{ub}|=(3.72\ifmmode\pm\else\textpm\fi{}0.16)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}3}$, 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 $B\ensuremath{\rightarrow}\ensuremath{\pi}\ensuremath{\ell}\ensuremath{\nu}$ 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.

We report on the MILC Collaboration calculation of electromagnetic effects on light pseudoscalar mesons. The simulations employ asqtad staggered dynamical quarks in QCD plus quenched photons, with lattice spacings varying from 0.12 to 0.06 fm. Finite volume corrections for the MILC realization of lattice electrodynamics have been calculated in chiral perturbation theory and applied to the lattice data. These corrections differ from those calculated by Hayakawa and Uno because our treatment of zero modes differs from theirs. Updated results for the corrections to “Dashen’s theorem” are presented.

We calculate the $B$-meson decay constants ${f}_{B}$, ${f}_{{B}_{s}}$, and their ratio in unquenched lattice QCD using domain-wall light quarks and relativistic $b$ quarks. We use gauge-field ensembles generated by the RBC and UKQCD collaborations using the domain-wall fermion action and Iwasaki gauge action with three flavors of light dynamical quarks. We analyze data at two lattice spacings of $a\ensuremath{\approx}0.11$, 0.086 fm with unitary pion masses as light as ${M}_{\ensuremath{\pi}}\ensuremath{\approx}290\text{ }\text{ }\mathrm{MeV}$; this enables us to control the extrapolation to the physical light-quark masses and continuum. For the $b$ quarks we use the anisotropic clover action with the relativistic heavy-quark interpretation, such that discretization errors from the heavy-quark action are of the same size as from the light-quark sector. We renormalize the lattice heavy-light axial-vector current using a mostly nonperturbative method in which we compute the bulk of the matching factor nonperturbatively, with a small correction, that is close to unity, in lattice perturbation theory. We also improve the lattice heavy-light current through $\mathcal{O}({\ensuremath{\alpha}}_{s}a)$. We extrapolate our results to the physical light-quark masses and continuum using SU(2) heavy-meson chiral perturbation theory, and provide a complete systematic error budget. We obtain ${f}_{{B}^{0}}=199.5(12.6)\text{ }\text{ }\mathrm{MeV}$, ${f}_{{B}^{+}}=195.6(14.9)\text{ }\text{ }\mathrm{MeV}$, ${f}_{{B}_{s}}=235.4(12.2)\text{ }\text{ }\mathrm{MeV}$, ${f}_{{B}_{s}}/{f}_{{B}^{0}}=1.197(50)$, and ${f}_{{B}_{s}}/{f}_{{B}^{+}}=1.223(71)$, where the errors are statistical and total systematic added in quadrature. These results are in good agreement with other published results and provide an important independent cross-check of other three-flavor determinations of $B$-meson decay constants using staggered light quarks.

We report on a scale determination with gradient-flow techniques on the $N_f=2+1+1$ highly improved staggered quark ensembles generated by the MILC Collaboration. The ensembles include four lattice spacings, ranging from approximately 0.15 to 0.06 fm, and both physical and unphysical values of the quark masses. The scales $\sqrt{t_0}/a$ and $w_0/a$ and their tree-level improvements, $\sqrt{t_{0,{\rm imp}}}$ and $w_{0,{\rm imp}}$, are computed on each ensemble using Symanzik flow and the cloverleaf definition of the energy density $E$. Using a combination of continuum chiral-perturbation theory and a Taylor-series ansatz for the lattice-spacing and strong-coupling dependence, the results are simultaneously extrapolated to the continuum and interpolated to physical quark masses. We determine the scales $\sqrt{t_0} = 0.1416({}_{-5}^{+8})$ fm and $w_0 = 0.1714({}_{-12}^{+15})$ fm, where the errors are sums, in quadrature, of statistical and all systematic errors. The precision of $w_0$ and $\sqrt{t_0}$ is comparable to or more precise than the best previous estimates, respectively. We then find the continuum mass dependence of $\sqrt{t_0}$ and $w_0$, which will be useful for estimating the scales of new ensembles. We also estimate the integrated autocorrelation length of $\langle E(t) \rangle$. For long flow times, the autocorrelation length of $\langle E \rangle$ appears to be comparable to that of the topological charge., 50 pages, 12 pdf figures, 10 tables, v2: Figure 11 and Table 9 updated to include additional results by other groups, v3: official PRD release with revised charm mass dependence, autocorrelation sections, and other miscellaneous changes, v4: fixed one typo

Using the MILC 2+1 flavor asqtad quark action ensembles, we are calculating the form factors f0 and f+ for the semileptonic Bs → Kℓv decay. A total of six ensembles with lattice spacing from ≈ 0.12 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 |Vub|.

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 compute the zero-recoil form factor for the semileptonic decay ${\overline{B}}^{0}\ensuremath{\rightarrow}{D}^{*+}{\ensuremath{\ell}}^{\ensuremath{-}}\overline{\ensuremath{\nu}}$ (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 Heavy Flavor Averaging Group average of experimental results and a cautious treatment of QED effects, we find $|{V}_{cb}|=(39.04\ifmmode\pm\else\textpm\fi{}0.4{9}_{\text{expt}}\ifmmode\pm\else\textpm\fi{}0.5{3}_{\mathrm{QCD}}\ifmmode\pm\else\textpm\fi{}0.1{9}_{\mathrm{QED}})\ifmmode\times\else\texttimes\fi{}1{0}^{\ensuremath{-}3}$. The QCD error is now commensurate with the experimental error.

We present recent results on the QCD equation of state with 2+1+1 flavors of highly improved staggered quarks (HISQ). We focus on three sets of ensembles with temporal extent 6, 8 and 10, that reach up to temperatures of 967, 725 and 580 MeV, respectively. The strange and charm quark masses are tuned to the physical values and the light quarks mass is set to one fifth of the strange. This corresponds to a Goldstone pion of about 300 MeV.

We update our determinations of fD+, fDs , fK, 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 valencequark 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.

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 Nf = 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)|.

We report on a calculation of the $B^*B\pi$ coupling in lattice QCD. The strong matrix element $\langle B \pi | B^*\rangle$ is directly related to the leading order low-energy constant in heavy meson chiral perturbation theory (HM$\chi$PT) for $B$-mesons. We carry out our calculation directly at the $b$-quark mass using a non-perturbatively tuned clover action that controls discretisation effects of order $|\vec{p}a|$ and $(ma)^n$ for all $n$. Our analysis is performed on RBC/UKQCD gauge configurations using domain wall fermions and the Iwasaki gauge action at two lattice spacings of $a^{-1}=1.73(3)$ GeV, $a^{-1}=2.28(3)$ GeV, and unitary pion masses down to 290 MeV. We achieve good statistical precision and control all systematic uncertainties, giving a final result for the HM$\chi$PT coupling $g_b = 0.569(48)_{stat}(59)_{sys}$ in the continuum and at the physical light-quark masses. This is the first calculation performed directly at the physical $b$-quark mass and lies in the region one would expect from carrying out an interpolation between previous results at the charm mass and at the static point., Comment: 7 pages, 2 figures, presented at the 31st International Symposium on Lattice Field Theory (Lattice 2013), 29 July - 3 August 2013, Mainz, Germany

A calculation of the ratio of leptonic decay constants ${f}_{{K}^{+}}/{f}_{{\ensuremath{\pi}}^{+}}$ makes possible a precise determination of the ratio of Cabibbo-Kobayashi-Maskawa (CKM) matrix elements $|{V}_{\mathrm{us}}|/|{V}_{\mathrm{ud}}|$ in the standard model, and places a stringent constraint on the scale of new physics that would lead to deviations from unitarity in the first row of the CKM matrix. We compute ${f}_{{K}^{+}}/{f}_{{\ensuremath{\pi}}^{+}}$ numerically in unquenched lattice QCD using gauge-field ensembles recently generated that include four flavors of dynamical quarks: up, down, strange, and charm. We analyze data at four lattice spacings $a\ensuremath{\approx}0.06$, 0.09, 0.12, and 0.15 fm with simulated pion masses down to the physical value 135 MeV. We obtain ${f}_{{K}^{+}}/{f}_{{\ensuremath{\pi}}^{+}}=1.1947(26)(37)$, where the errors are statistical and total systematic, respectively. This is our first physics result from our ${N}_{f}=2+1+1$ ensembles, and the first calculation of ${f}_{{K}^{+}}/{f}_{{\ensuremath{\pi}}^{+}}$ from lattice-QCD simulations at the physical point. Our result is the most precise lattice-QCD determination of ${f}_{{K}^{+}}/{f}_{{\ensuremath{\pi}}^{+}}$, with an error comparable to the current world average. When combined with experimental measurements of the leptonic branching fractions, it leads to a precise determination of $|{V}_{\mathrm{us}}|/|{V}_{\mathrm{ud}}|=0.2309(9)(4)$ where the errors are theoretical and experimental, respectively.

Using staggered fermions and partially 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 Nf = 2 + 1 configurations). For the chiral and continuum extrapolation we use two-loop continuum χPT, supplemented by partially quenched staggered χPT at one loop. Our result is f Kπ + (0) = 0.9667 ±

E.D. Freeland∗ a C.M. Bouchard b, C. Bernard c, A.X. El-Khadra d , E. Gamiz e, A.S. Kronfeld f , J. Laiho g, and R.S. Van de Water f aDepartment of Physics, Benedictine University, Lisle, IL 60532, USA bDepartment of Physics, The Ohio State University, Columbus, OH 43210, USA cDepartment of Physics, Washington University, St. Louis, MO 63130, USA dPhysics Department, University of Illinois, Urbana, IL 61801, USA eCAFPE and Departamento de Fisica Teorica y del Cosmos, Universidad de Granada, E-18002 Granada, Spain f Theoretical Physics Department, Fermi National Accelerator Laboratory, Batavia, IL 60510, USA gSUPA, School of Physics and Astronomy, University of Glasgow, Glasgow, G12 8QQ, UK

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 fD, fDs , fDs = fD, and ratios

By combining experimentally measured partial branching fractions for the semileptonic decays D→Klν and D→ πlν with lattice calculations of the form factors f D→K + (q2) and f D→π + (q2), one can extract the CKM matrix elements |Vcs| and |Vcd |. We are calculating the form factors by using Fermilab charm and asqtad staggered light and strange quarks on 2+1 flavor asqtad staggered ensembles generated by the MILC Collaboration. We vary the light valence quark masses from 0.4ms to 0.05ms (ms is the strange sea-quark mass), and the lattice spacings, from about 0.12 fm to about 0.045 fm. We extrapolate to the physical light-quark mass and the continuum limit using heavy-light meson staggered chiral perturbation theory about the SU(2) and SU(3) limits, compare the resulting (preliminary) form factor shapes with experiment, and discuss our errors.

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., Proceedings of Lattice 2012 Int. Symposium

We study $SU(3)$-breaking effects in the neutral ${B}_{d}$-${\overline{B}}_{d}$ and ${B}_{s}$-${\overline{B}}_{s}$ systems with unquenched ${N}_{f}=2+1$ lattice quantum chromodynamics (QCD). We calculate the relevant matrix elements on the MILC collaboration's gauge configurations with asqtad-improved staggered sea quarks. For the valence light-quarks ($u$, $d$, and $s$) we use the asqtad action, while for $b$ quarks we use the Fermilab action. We obtain $\ensuremath{\xi}={f}_{{B}_{s}}\sqrt{{B}_{{B}_{s}}}/{f}_{{B}_{d}}\sqrt{{B}_{{B}_{d}}}=1.268\ifmmode\pm\else\textpm\fi{}0.063$. We also present results for the ratio of bag parameters ${B}_{{B}_{s}}/{B}_{{B}_{d}}$ and the ratio of Cabibbo-Kobayashi-Maskawa matrix elements $|{V}_{td}|/|{V}_{ts}|$. Although we focus on the calculation of $\ensuremath{\xi}$, the strategy and techniques described here will be employed in future extended studies of the $B$ mixing parameters $\ensuremath{\Delta}{M}_{d,s}$ and $\ensuremath{\Delta}{\ensuremath{\Gamma}}_{d,s}$ in the standard model and beyond.

We calculate form-factor ratios between the semileptonic decays {bar B}{sup 0} {yields} D{sup +} {ell}{sup -}{bar {nu}} and {bar B}{sub s}{sup 0} {yields} D{sub s}{sup +}{ell}{sup -}{bar {nu}} with lattice QCD. These ratios are a key theoretical input in a new strategy to determine the fragmentation fractions of the neutral B decays, which are needed for measurements of BR(B{sub s}{sup 0} {yields} {mu}{sup +}{mu}{sup -}). They use the MILC ensembles of gauge configurations with 2 + 1 flavors of sea quarks at two lattice spacings of approximately 0.12 fm and 0.09 fm. We use the model-independent z parametrization to extrapolate their simulation results at small recoil toward maximum recoil. The results for the form-factor ratios are {line_integral}{sub 0}{sup (s)} (M{sub {pi}}{sup 2})/{line_integral}{sub 0}{sup (d)} (M{sub K}{sup 2}) = 1.046(44){sub stat.}(15){sub syst.} and {line_integral}{sub 0}{sup (s)} (M{sub {pi}}{sup 2})/{line_integral}{sub 0}{sup (d)} (M{sub {pi}}{sup 2}) = 1.054(47){sub stat.}(17){sub syst.}. In contrast to a QCD sum-rule calculation, no significant departure from U-spin (d {leftrightarrow} s) symmetry is observed.

We fit lattice-QCD data for light-pseudoscalar masses and decay constants, from HISQ configurations generated by MILC, to SU(3) staggered chiral perturbation theory. At present such fits have rather high values of χ2/d.o.f., possibly due to the lack of ensembles with lighter-than-physical sea strange-quark masses. We propose solutions to this problem for future work. We also perform simple linear interpolations near the physical point on two ensembles with different lattice spacings, and obtain the preliminary result ( fK/ fπ) = 1.1872(41) in the continuum limit. XXIX International Symposium on Lattice Field Theory July 10 16 2011 Squaw Valley, Lake Tahoe, California

The semileptonic decay channel $B\ensuremath{\rightarrow}D\ensuremath{\tau}\ensuremath{\nu}$ is sensitive to the presence of a scalar current, such as that mediated by a charged-Higgs boson. Recently, the BABAR experiment reported the first observation of the exclusive semileptonic decay $B\ensuremath{\rightarrow}D{\ensuremath{\tau}}^{\ensuremath{-}}\overline{\ensuremath{\nu}}$, finding an approximately $2\ensuremath{\sigma}$ disagreement with the standard-model prediction for the ratio $R(D)=\mathrm{BR}(B\ensuremath{\rightarrow}D\ensuremath{\tau}\ensuremath{\nu})/\mathrm{BR}(B\ensuremath{\rightarrow}D\ensuremath{\ell}\ensuremath{\nu})$, where $\ensuremath{\ell}=e,\ensuremath{\mu}$. We compute this ratio of branching fractions using hadronic form factors computed in unquenched lattice QCD and obtain $R(D)=0.316(12)(7)$, where the errors are statistical and total systematic, respectively. This result is the first standard-model calculation of $R(D)$ from ab initio full QCD. Its error is smaller than that of previous estimates, primarily due to the reduced uncertainty in the scalar form factor ${f}_{0}({q}^{2})$. Our determination of $R(D)$ is approximately $1\ensuremath{\sigma}$ higher than previous estimates and, thus, reduces the tension with experiment. We also compute $R(D)$ in models with electrically charged scalar exchange, such as the type-II two-Higgs-doublet model. Once again, our result is consistent with, but approximately $1\ensuremath{\sigma}$ higher than, previous estimates for phenomenologically relevant values of the scalar coupling in the type-II model. As a by-product of our calculation, we also present the standard-model prediction for the longitudinal-polarization ratio ${P}_{L}(D)=0.325(4)(3)$.

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 ~ 0.086 fm). 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 B_s and B_s* heavy-light meson states. The masses and mass-splittings of the low-lying bottomonium states (such as the eta_b and Upsilon) 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 ~35-45%; 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., 30 pages, 14 figures, 14 tables

We calculate the leptonic decay constants of B_{(s)} and D_{(s)} mesons in lattice QCD using staggered light quarks and Fermilab bottom and charm quarks. We compute the heavy-light meson correlation functions on the MILC asqtad-improved staggered gauge configurations which include the effects of three light dynamical sea quarks. We simulate with several values of the light valence- and sea-quark masses (down to ~m_s/10) and at three lattice spacings (a ~ 0.15, 0.12, and 0.09 fm) and extrapolate to the physical up and down quark masses and the continuum using expressions derived in heavy-light meson staggered chiral perturbation theory. We renormalize the heavy-light axial current using a mostly nonperturbative method such that only a small correction to unity must be computed in lattice perturbation theory and higher-order terms are expected to be small. We obtain f_{B^+} = 196.9(8.9) MeV, f_{B_s} = 242.0(9.5) MeV, f_{D^+} = 218.9(11.3) MeV, f_{D_s} = 260.1(10.8) MeV, and the SU(3) flavor-breaking ratios f_{B_s}/f_{B} = 1.229(26) and f_{D_s}/f_{D} = 1.188(25), where the numbers in parentheses are the total statistical and systematic uncertainties added in quadrature.