PHYSICAL REVIEW D 98, 074512 (2018) B- and D-meson leptonic decay constants from four-flavor lattice QCD A. Bazavov,1 C. Bernard,2,* N. Brown,2 C. DeTar,3 A. X. El-Khadra,4,5 E. Gámiz,6 Steven Gottlieb,7 U. M. Heller,8 † ‡ J. Komijani,9,10,11, A. S. Kronfeld,5,10, J. Laiho,12 P. B. Mackenzie,5 E. T. Neil,13,14 J. N. Simone,5 R. L. Sugar,15 ∥ D. Toussaint,16,§ and R. S. Van de Water5, (Fermilab Lattice and MILC Collaborations) 1Department of Computational Mathematics, Science and Engineering, and Department of Physics and Astronomy, Michigan State University, East Lansing, Michigan 48824, USA 2Department of Physics, Washington University, St. Louis, Missouri 63130, USA 3Department of Physics and Astronomy, University of Utah, Salt Lake City, Utah 84112, USA 4Department of Physics, University of Illinois, Urbana, Illinois 61801, USA 5Fermi National Accelerator Laboratory, Batavia, Illinois 60510, USA 6CAFPE and Departamento de Física Teórica y del Cosmos, Universidad de Granada, E-18071 Granada, Spain 7Department of Physics, Indiana University, Bloomington, Indiana 47405, USA 8American Physical Society, One Research Road, Ridge, New York 11961, USA 9Physik-Department, Technische Universität München, 85748 Garching, Germany 10Institute for Advanced Study, Technische Universität München, 85748 Garching, Germany 11School of Physics and Astronomy, University of Glasgow, Glasgow G12 8QQ, United Kingdom 12Department of Physics, Syracuse University, Syracuse, New York 13244, USA 13Department of Physics, University of Colorado, Boulder, Colorado 80309, USA 14RIKEN-BNL Research Center, Brookhaven National Laboratory, Upton, New York 11973, USA 15Department of Physics, University of California, Santa Barbara, California 93106, USA 16Physics Department, University of Arizona, Tucson, Arizona 85721, USA (Received 30 December 2017; published 29 October 2018) We calculate the leptonic decay constants of heavy-light pseudoscalar mesons with charm and bottom quarks in lattice quantum chromodynamics on four-flavor QCD gauge-field configurations with dynamical u, d, s,andc quarks. We analyze over twenty isospin-symmetric ensembles with six lattice spacings down to 1 a ≈ 0.03 fm and several values of the light-quark mass down to the physical value 2 ðmu þ mdÞ. We employ the highly-improved staggered-quark (HISQ) action for the sea and valence quarks; on the finest lattice spacings, discretization errors are sufficiently small that we can calculate the B-meson decay constants with the HISQ action for the first time directly at the physical b-quark mass. We obtain the most precise determinations to-date þ 212 7 0 6 249 9 0 4 of the D-andB-meson decay constants and their ratios, fD ¼ . ð . Þ MeV, fDs ¼ . ð . Þ MeV, þ 1 1749 16 þ 189 4 1 4 230 7 1 3 þ 1 2180 47 fDs =fD ¼ . ð Þ, fB ¼ . ð . Þ MeV, fBs ¼ . ð . Þ MeV, fBs =fB ¼ . ð Þ,where the errors include statistical and all systematic uncertainties. Our results for the B-meson decay constants are three times more precise than the previous best lattice-QCD calculations, and bring the QCD errors in the ¯ þ − −9 ¯ 0 þ − standard model predictions for the rare leptonic decays BðBs →μ μ Þ¼3.64ð11Þ×10 , BðB →μ μ Þ¼ −11 ¯ 0 þ − ¯ þ − 1.00ð3Þ×10 ,andBðB → μ μ Þ=BðBs → μ μ Þ¼0.00264ð8Þ to well below other sources of uncertainty. As a byproduct of our analysis, we also update our previously published results for the light- quark-mass ratios and the scale-setting quantities fp4s, Mp4s,andRp4s. Weobtain the most precise lattice-QCD þ16 determination to date of the ratio fKþ =fπþ ¼ 1.1950ð −23 Þ MeV. DOI: 10.1103/PhysRevD.98.074512 *[email protected] † [email protected] ‡ [email protected] §[email protected] ∥ [email protected] Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Funded by SCOAP3. 2470-0010=2018=98(7)=074512(36) 074512-1 Published by the American Physical Society A. BAZAVOV et al. PHYS. REV. D 98, 074512 (2018) I. INTRODUCTION actions are available [16–28], with uncertainties ranging from ∼0.5%–5% and ∼2%–8% for the D and B Leptonic decays of B and D mesons are important probes ðsÞ ðsÞ systems, respectively. The most precise results for f and of heavy-to-light quark flavor-changing interactions. The D f f þ þ þ þ Ds have been obtained by us [23], and for Bs by the charged-current decays H → l νl (H ¼ D ;Ds;B ; l μ τ HPQCD Collaboration [17], in both cases using improved ¼ e, , ) proceed at tree level in the standard model “ A ≡ ¯ γ γ staggered sea quarks and the highly-improved staggered via the axial-vector current μ Q 5 μq, where Q is the quark” (HISQ) action [29] for the valence light and heavy heavy charm or bottom quark and q is the light quark in the quarks. The HISQ action makes possible this high precision pseudoscalar meson. When combined with a nonperturba- because it has both small discretization errors, even tive lattice-QCD calculation of the decay constant fHþ ,an at relatively large lattice spacings, and an absolutely- experimental measurement of the leptonic decay width normalized axial current. Our previous calculation [23] of allows the determination of the corresponding Cabibbo- the DðsÞ-meson decay constants employed physical-mass Kobayashi-Maskawa (CKM) quark-mixing matrix element light and charm quarks and gauge-field configurations with 0 → lþl− 0 0 jVQqj. Because the decays H (H ¼ D ;B ;Bs) lattice spacings down to a ≈ 0.06 fm; the dominant con- proceed via a flavor-changing-neutral-current interaction, tribution to the errors on fD and fDs came from the and are forbidden at tree level in the standard model, these ’ continuum extrapolation. HPQCD s calculation of fBs with processes may be especially sensitive to (tree-level) con- the HISQ action for the b quark employed five three-flavor tributions of new heavy particles. Both the standard model ensembles of gauge-field configurations from the MILC and new-physics predictions for the rare-decay branching Collaboration [30–32] with lattice spacings as fine as ratios depend upon the decay constants fH0 . a ≈ 0.045 fm, enabling them to simulate with heavy-quark Leptonic B-meson decays, in particular, make possible masses close to the physical bottom-quark mass. The several interesting tests of the standard model and prom- statistical errors dominate in their calculation due to the ising new-physics searches. The determination of jVubj comparatively small number of configurations per ensemble þ þ from B → τ ντ decay can play an important role in (roughly 200 on their finest up to 600 on their coarsest). resolving the 2 − 3σ tension between the values of jVubj Other important sources of uncertainty are from the extrapo- obtained from inclusive and exclusive semileptonic B- lation in heavy-quark mass up to mb and from the extrapo- meson decays (see the recent reviews [1,2] and references lation to zero lattice spacing. þ þ therein). Alternatively, the decay B → τ ντ, because of In this paper, we present a new calculation of the leptonic the large τ-lepton mass, may receive observable contribu- decay constants of heavy-light mesons containing bottom tions from new heavy particles such as charged Higgs and charm quarks that improves upon prior works in several 0 → bosons or leptoquarks [3,4]. The branching ratios for B ways. As in our previous calculation of fD and fDs [23],we þ − þ − l l and Bs → l l can be enhanced with respect to the employ the four-flavor QCD gauge-field configurations standard model rates in new-physics scenarios with tree- generated by the MILC Collaboration with HISQ up, down, level flavor-changing-neutral currents, such as in fourth- strange, and charm quarks [33]; we also use the HISQ generation models [5,6]. action for the light and heavy valence quarks. We now Lattice-QCD calculations of the B-meson decay constants employ three new ensembles with finer lattice spacings of are especially timely given the wealth of leptonic B-decay a ≈ 0.042 and a ≈ 0.03 fm, and also increase statistics on measurements from the B-factories and, more recently, by the a ≈ 0.06 fm ensemble with physical-mass light quarks. hadron-collider experiments at the LHC. The branching Altogether, we analyze 24 ensembles, most of which have þ þ ratio for the charged-current decay B → τ ντ has been approximately 1000 configurations. We also calculate the measured by the BABAR and Belle experiments to about Bþ- and B0-meson decay constant with HISQ b quarks on þ − 20% precision [7–10]. The rare decay Bs → μ μ has now the HISQ ensembles for the first time. been independently observed by the ATLAS, CMS, and We fit our lattice data for the heavy-light meson decay LHCb experiments with errors on the measured branching constants to a functional form that combines information on ratio ranging from around 20%–100% [11–13]; these works the heavy-quark mass dependence from heavy-quark have also set limits on the process B0 → μþμ−. Precise effective theory, on the light-quark mass dependence from þ 0 determinations of fB , fB , and fBs are needed to interpret chiral perturbation theory, and on discretization effects these results. Such determinations are also necessary to fully from Symanzik effective theory. This allows us to exploit exploit coming measurements by Belle II [14], which will our wide range of simulation parameters by including begin running at the Super-KEKb facility next year, as well multiple lattice spacings and heavy- and light-quark mass as future measurements by ATLAS, CMS, and LHCb after values in a single effective-field-theory (EFT) fit.