We present progress on the calculation of scalar, vector, and tensor form factors for the following meson decays: B→π, B_s→ K, D→π and D_s→ K. This calculation uses the MILC HISQ gluon field ensembles with HISQ valence quarks. We generate ensembles of correlator data with varying lattice spacings, some as small as 0.044 fm. Some ensembles have a strange-to-light quark mass ratio of 5:1 and others use the physical light quark mass. The fully-relativistic, heavy-HISQ approach is used for the heavy quark, with simulation masses ranging from the charm to near the bottom. This heavy-HISQ approach provides nearly full coverage of the kinematic range.

We present progress on the calculation of scalar, vector, and tensor form factors for the following meson decays: $B\rightarrow\pi$, $B_s\rightarrow K$, $D\rightarrow\pi$ and $D_s\rightarrow K$. This calculation uses the MILC HISQ gluon field ensembles with HISQ valence quarks. We generate ensembles of correlator data with varying lattice spacings, some as small as 0.044 fm. Some ensembles have a strange-to-light quark mass ratio of 5:1 and others use the physical light quark mass. The fully-relativistic, heavy-HISQ approach is used for the heavy quark, with simulation masses ranging from the charm to near the bottom. This heavy-HISQ approach provides nearly full coverage of the kinematic range.

We use HPQCD's recent lattice QCD determination of $B\ensuremath{\rightarrow}K$ scalar, vector and tensor form factors to determine Standard Model differential branching fractions for $B\ensuremath{\rightarrow}K{\ensuremath{\ell}}^{+}{\ensuremath{\ell}}^{\ensuremath{-}}$, $B\ensuremath{\rightarrow}K{\ensuremath{\ell}}_{1}^{+}{\ensuremath{\ell}}_{2}^{\ensuremath{-}}$ and $B\ensuremath{\rightarrow}K\ensuremath{\nu}\overline{\ensuremath{\nu}}$. 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 $B\ensuremath{\rightarrow}K{\ensuremath{\ell}}^{+}{\ensuremath{\ell}}^{\ensuremath{-}}$ we find the Standard Model branching fraction in the ${q}^{2}$ region below the squared $J/\ensuremath{\psi}$ mass to exceed the LHCb results, with tensions as high as $4.7\ensuremath{\sigma}$ for ${B}^{+}\ensuremath{\rightarrow}{K}^{+}{\ensuremath{\mu}}^{+}{\ensuremath{\mu}}^{\ensuremath{-}}$. For the high ${q}^{2}$ region we see $3\ensuremath{\sigma}$ 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-flavor ratios ${R}_{e}^{\ensuremath{\mu}}$ and ${R}_{\ensuremath{\mu}}^{\ensuremath{\tau}}$ and the ``flat term,'' ${F}_{H}^{\ensuremath{\ell}}$ in the differential branching fraction for $\ensuremath{\ell}\ensuremath{\in}{e,\ensuremath{\mu},\ensuremath{\tau}}$. Our results for the form-factor dependent contributions needed for searches for lepton-flavor violating decays $B\ensuremath{\rightarrow}K{\ensuremath{\ell}}_{1}^{\ensuremath{-}}{\ensuremath{\ell}}_{2}^{+}$ achieve uncertainties of 7%. We also compute the branching fraction $\mathcal{B}(B\ensuremath{\rightarrow}K\ensuremath{\nu}\overline{\ensuremath{\nu}})$ with an uncertainty below 10%, for comparison with future experimental results.

The Deep Underground Neutrino Experiment (DUNE) is an upcoming neutrino oscillation experiment that is poised to answer key questions about the nature of neutrinos. Lattice QCD has the ability to make significant impact upon DUNE, beginning with computations of nucleon-neutrino interactions with weak currents. Nucleon amplitudes involving the axial form factor are part of the primary signal measurement process for DUNE, and precise calculations from LQCD can significantly reduce the uncertainty for inputs into Monte Carlo generators. Recent calculations of the nucleon axial charge have demonstrated that sub-percent precision is possible on this vital quantity. In these proceedings, we discuss preliminary results for the CalLat collaboration's calculation of the axial form factor of the nucleon. These computations are performed with M\"obius domain wall valence quarks on HISQ sea quark ensembles generated by the MILC and CalLat collaborations. The results use a variety of ensembles including several at physical pion mass.

Excited state contamination remains one of the most challenging sources of systematic uncertainty to control in lattice QCD calculations of nucleon matrix elements and form factors: early time separations are contaminated by excited states and late times suffer from an exponentially bad signal-to-noise problem. High-statistics calculations at large time separations $\gtrsim1$ fm are commonly used to combat these issues. In this work, focusing on $g_A$, we explore the alternative strategy of utilizing a large number of relatively low-statistics calculations at short to medium time separations (0.2--1 fm), combined with a multi-state analysis. On an ensemble with a pion mass of approximately 310 MeV and a lattice spacing of approximately 0.09 fm, we find this provides a more robust and economical method of quantifying and controlling the excited state systematic uncertainty. A quantitative separation of various types of excited states enables the identification of the transition matrix elements as the dominant contamination. The excited state contamination of the Feynman-Hellmann correlation function is found to reduce to the 1% level at approximately 1 fm while for the more standard three-point functions, this does not occur until after 2 fm. Critical to our findings is the use of a global minimization, rather than fixing the spectrum from the two-point functions and using them as input to the three-point analysis. We find that the ground state parameters determined in such a global analysis are stable against variations in the excited state model, the number of excited states, and the truncation of early-time or late-time numerical data.

We report on a subpercent scale determination using the omega baryon mass and gradient-flow methods. The calculations are performed on 22 ensembles of N-f = 2 1 1 highly improved, rooted staggered sea-quark configurations generated by the MILC and CalLat Collaborations. The valence quark action used is Mobius domain wall fermions solved on these configurations after a gradient-flow smearing is applied with a flowtime of t(gf) = 1 in lattice units. The ensembles span four lattice spacings in the range 0.06 less than or similar to a less than or similar to 0.15 fm, six pion masses in the range 130 less than or similar to m(pi) less than or similar to 400 MeV and multiple lattice volumes. On each ensemble, the gradient-flow scales t(0)/a(2) and w(0)/a and the omega baryon mass am(Omega) are computed. The dimensionless product of these quantities is then extrapolated to the continuum and infinite volume limits and interpolated to the physical light, strange and charm quark mass point in the isospin limit, resulting in the determination of root t(0) = 0.1422(14) fm and w(0) = 0.1709(11) fm with all sources of statistical and systematic uncertainty accounted for. The dominant uncertainty in both results is the stochastic uncertainty, though for root t(0 )there are comparable continuum extrapolation uncertainties. For w(0), there is a clear path for a few-per-mille uncertainty just through improved stochastic precision, as recently obtained by the Budapest-Marseille-Wuppertal Collaboration.

The nucleon axial coupling, $g_A$, is a fundamental property of protons and neutrons, dictating the strength with which the weak axial current of the Standard Model couples to nucleons, and hence, the lifetime of a free neutron. The prominence of $g_A$ in nuclear physics has made it a benchmark quantity with which to calibrate lattice QCD calculations of nucleon structure and more complex calculations of electroweak matrix elements in one and few nucleon systems. There were a number of significant challenges in determining $g_A$, notably the notorious exponentially-bad signal-to-noise problem and the requirement for hundreds of thousands of stochastic samples, that rendered this goal more difficult to obtain than originally thought. I will describe the use of an unconventional computation method, coupled with ``ludicrously'' fast GPU code, access to publicly available lattice QCD configurations from MILC and access to leadership computing that have allowed these challenges to be overcome resulting in a determination of $g_A$ with 1\% precision and all sources of systematic uncertainty controlled. I will discuss the implications of these results for the convergence of SU(2) Chiral Perturbation theory for nucleons, as well as prospects for further improvements to $g_A$ (sub-percent precision, for which we have preliminary results) which is part of a more comprehensive application of lattice QCD to nuclear physics. This is particularly exciting in light of the new CORAL supercomputers coming online, Sierra and Summit, for which our lattice QCD codes achieve a machine-to-machine speed up over Titan of an order of magnitude.

A summary of WG II of the CKM 2018 conference on semileptonic and leptonic b-hadron decays is presented. This includes discussions on the CKM matrix element magitudes |V_ub| and |V_cb|, lepton universality tests such as R(D^*) and leptonic decays. As is usual for semileptonic and leptonic decays, much discussion is devoted towards the interplay between theoretical QCD calculations and the experimental measurements.

The nucleon axial coupling, g_A, is a fundamental property of protons and neutrons, dictating the strength with which the weak axial current of the Standard Model couples to nucleons, and hence, the lifetime of a free neutron. The prominence of g_A in nuclear physics has made it a benchmark quantity with which to calibrate lattice QCD calculations of nucleon structure and more complex calculations of electroweak matrix elements in one and few nucleon systems. There were a number of significant challenges in determining g_A, notably the notorious exponentially-bad signal-to-noise problem and the requirement for hundreds of thousands of stochastic samples, that rendered this goal more difficult to obtain than originally thought. I will describe the use of an unconventional computation method, coupled with "ludicrously'" fast GPU code, access to publicly available lattice QCD configurations from MILC and access to leadership computing that have allowed these challenges to be overcome resulting in a determination of g_A with 1 precision and all sources of systematic uncertainty controlled. I will discuss the implications of these results for the convergence of SU(2) Chiral Perturbation theory for nucleons, as well as prospects for further improvements to g_A (sub-percent precision, for which we have preliminary results) which is part of a more comprehensive application of lattice QCD to nuclear physics. This is particularly exciting in light of the new CORAL supercomputers coming online, Sierra and Summit, for which our lattice QCD codes achieve a machine-to-machine speed up over Titan of an order of magnitude.

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 approximate to 180 MeV and lattice spacings as fine as a approximate to 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, < D-0 vertical bar O-i vertical bar(D) over bar (0)> = {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 D-0 mixing, finding lower limits of about 10-50 x 10(3) 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.

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 present a lattice quantum chromodynamics determination of the ratio of the scalar and vector form factors for two semileptonic decays of the B-s meson: B-s -> Kl nu and B-s -> D(s)l nu In conjunction with future experimental data, our results for these correlated form factors will provide a new method to extract vertical bar V-ub/V-cb vertical bar which may elucidate the current tension between exclusive and inclusive determinations of these Cabibbo-Kobayashi-Maskawa mixing matrix parameters. In addition to the form factor results, we determine the ratio of the differential decay rates, and forward-backward and polarization asymmetries, for the two decays.

We present state-of-the-art results from a lattice QCD calculation of the nucleon axial coupling, $g_A$, using M\obius Domain-Wall fermions solved on the dynamical $N_f = 2 + 1 + 1$ HISQ ensembles after they are smeared using the gradient-flow algorithm. Relevant three-point correlation functions are calculated using a method inspired by the Feynman-Hellmann theorem, and demonstrate significant improvement in signal for fixed stochastic samples. The calculation is performed at five pion masses of $m_\pi\sim \{400, 350, 310, 220, 130\}$~MeV, three lattice spacings of $a\sim\{0.15, 0.12, 0.09\}$~fm, and we do a dedicated volume study with $m_\pi L\sim\{3.22, 4.29, 5.36\}$. Control over all relevant sources of systematic uncertainty are demonstrated and quantified. We achieve a preliminary value of $g_A = 1.285(17)$, with a relative uncertainty of 1.33\%.

Jon A. Bailey ∗a†, A. Bazavov b, C. Bernard c, C. Bouchard e, C. DeTard, A.X. El-Khadra e, E.D. Freeland c, W. Freeman b, E. Gamiza,e, Steven Gottlieb e, f ,g, U.M. Heller h, J.E. Hetrick i, A.S. Kronfeld a, J. Laiho c, L. Levkova d, P.B. Mackenzie a, M.B. Oktay d, M. Di Pierro j , J.N. Simone a, R. Sugar k, D. Toussaint b, and R.S. Van de Water l aTheoretical Physics Department, Fermilab, Batavia, IL 605 1 , USA bDepartment of Physics, University of Arizona, Tucson, AZ 85 721, USA cDepartment of Physics, Washington University, St. Louis, M O 63130, USA dPhysics Department, University of Utah, Salt Lake City, UT 8 4112, USA ePhysics Department, University of Illinois, Urbana, IL 618 01, USA f Department of Physics, Indiana University, Bloomington, I N 47405, USA gNational Center for Supercomputing Applications, Univers ity of Illinois, Urbana, IL 61801, USA hAmerican Physical Society, One Research Road, Ridge, NY 119 61, USA iPhysics Department, University of the Pacific, Stockton, CA 95211, USA jSchool of Computing, DePaul University, Chicago, IL 60604, USA kDepartment of Physics, University of California, Santa Bar bara, CA 93106, USA l Department of Physics, Brookhaven National Laboratory, Up ton, NY 11973, USA

Institute for Nuclear Theory, University of Washington, Seattle, Washington 98195-1550, USA School of Physics and Astronomy, University of Glasgow, Glasgow G12 8QQ, United Kingdom Laboratory of Elementary Particle Physics, Cornell University, Ithaca, New York 14853, USA Ohio Supercomputer Center, 1224 Kinnear Road, Columbus, Ohio 43212, USA Department of Physics, The Ohio State University, Columbus, Ohio 43210, USA

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.

We report on salient features of a mixed lattice QCD action using valence Mobius domain-wall fermions solved on the dynamical N-f = 2 + 1 + 1 highly improved staggered quark sea- quark ensembles generated by the MILC Collaboration. The approximate chiral symmetry properties of the valence fermions are shown to be significantly improved by utilizing the gradient- flow scheme to first smear the highly improved staggered quark configurations. The greater numerical cost of the Mobius domain- wall inversions is mitigated by the highly efficient QUDA library optimized for NVIDIA GPU accelerated compute nodes. We have created an interface to this optimized QUDA solver in CHROMA. We provide tuned parameters of the action and performance of QUDA using ensembles with the lattice spacings a similar or equal to {0.15; 0.12; 0.09} fm and pion masses m(pi) similar or equal to {310; 220; 130} MeV. We have additionally generated two new ensembles with a similar to 0.12 fm and m(pi) similar to {400; 350} MeV. With a fixed flow time of t(gf) = 1 in lattice units, the residual chiral symmetry breaking of the valence fermions is kept below 10% of the light quark mass on all ensembles, m(res) less than or similar to 0.1 x m(l), with moderate values of the fifth dimension L-5 and a domain- wall height M-5 <= 1.3. As a benchmark calculation, we perform a continuum, infinite volume, physical pion and kaon mass extrapolation of F-K +/-/F-pi +/- and demonstrate our results are independent of flow time and consistent with the FLAG determination of this quantity at the level of less than one standard deviation.

We present a lattice quantum chromodynamics determination of the scalar and vector form factors for the B-s -> D(s)l. decay over the full physical range of momentum transfer. In conjunction with future experimental data, our results will provide a new method to extract vertical bar V-cb vertical bar, which may elucidate the current tension between exclusive and inclusive determinations of this parameter. Combining the form factor results at nonzero recoil with recent HPQCD results for the B -> Dl(v) form factors, we determine the ratios f(0)(Bs -> Ds) (M-pi(2))/f(0)(B -> D) (M-K(2))=1.000(62) and f(0)(Bs -> Ds) (M-pi(2))/f(0)(B -> D)(M-pi(2))=1.006(62). These results give the fragmentation fraction ratios f(s)/f(d) = 0.310(30)(stat)(21)(syst)(6)(theor)(38)(latt) and f(s)/f(d) = 0.307(16)(stat)(21)(syst)(23)(theor)(44)(latt), respectively. The fragmentation fraction ratio is an important ingredient in experimental determinations of Bs meson branching fractions at hadron colliders, in particular for the rare decay B(B-s ->mu(+)mu(-). In addition to the form factor results, we make the first prediction of the branching fraction ratio R(D-s) = B(B-s -> D-s tau nu)/B(B-s -> D-s tau nu)= 0.301(6), where l is an electron or muon. Current experimental measurements of the corresponding ratio for the semileptonic decays of B mesons disagree with Standard Model expectations at the level of nearly four standard deviations. Future experimental measurements of R(D-s) may help understand this discrepancy.

Chia Cheng Changabc∗, C. M. Bouchardc†, A. X. El-Khadraab, E. Freelandd , E. Gámize, A. S. Kronfeld‡b f , J. W. Laihog, E. T. Neilhi, J. N. Simoneb, and R. S. Van de Waterb aDepartment of Physics, University of Illinois, Urbana, Illinois, 61801, USA bFermi National Accelerator Laboratory, Batavia, Illinois, 60510, USA cPhysics Department, The College of William and Mary, Williamsburg, Virginia, 23185, USA dLiberal Arts Department, School of the Art Institute of Chicago, Chicago, Illinois, 60603, USA eCAFPE and Departamento de Física Teórica y del Cosmos, Universidad de Granada,