We give results for the Upsilon spectrum from lattice QCD using an improved version of the NRQCD action for b quarks which includes radiative corrections to kinetic terms at O(v 4 ) in the velocity expansion. We also include for the first time the effect of up, down, strange and charm quarks in the sea using 'second generation' gluon field configurations from the MILC collaboration. Using the Υ 2S − 1S splitting to determine the lattice spacing, we are able to obtain the 1P − 1S splitting to 1.4% and the 3S − 1S splitting to 2.4%. Our improved result for M (Υ) − M (η b ) is 70(9) MeV and we predict M (Υ ) − M (η b ) = 35(3) MeV. We also calculate π, K and ηs correlators using the Highly Improved Staggered Quark action and perform a chiral and continuum extrapolation to give values for Mη s (0.6893(12) GeV) and fη s (0.1819(5) GeV) that allow us to tune the strange quark mass as well as providing an independent and consistent determination of the lattice spacing. Combining the NRQCD and HISQ analyses gives m b /ms = 54.7(2.5) and a value for the heavy quark potential parameter of r1 = 0.3209(26) fm.

The rare decays B 0 → K Ã0 μ þ μ − and B s → ϕμ þ μ − are now being observed with enough precision to test Standard Model predictions. A full understanding of these decays requires accurate determinations of the corresponding hadronic form factors. Here we present results of lattice QCD calculations of the B → K Ã and B s → ϕ form factors. We also determine the form factors relevant for the decays B s → K Ã lν and B s →K Ã0 l þ l − . We use full-QCD configurations including 2 þ 1 flavors of sea quarks using an improved staggered action, and we employ lattice nonrelativistic QCD to describe the bottom quark.

We present improved results for the B and D meson spectrum from lattice QCD including the effect of u=d, s and c quarks in the sea. For the B mesons the highly improved staggered quark action is used for the sea and light valence quarks and nonrelativistic QCD for the b quark including Oð s Þ radiative corrections to many of the Wilson coefficients for the first time. The D mesons use the highly improved staggered quark action for both valence quarks on the same sea. We find M B s À M B ¼ 84ð2Þ MeV, M B s ¼ 5:366ð8Þ GeV, M B c ¼ 6:278ð9Þ GeV, M D s ¼ 1:9697ð33Þ GeV, and M D s À M D ¼ 101ð3Þ MeV. Our results for the B meson hyperfine splittings are M B Ã À M B ¼ 50ð3Þ MeV, M B Ã s À M B s ¼ 52ð3Þ MeV, in good agreement with existing experimental results. This demonstrates that our perturbative improvement of the nonrelativistic QCD chromomagnetic coupling works for both heavyonium and heavylight mesons. We predict M B Ã c À M B c ¼ 54ð3Þ MeV. We also present first results for the radially excited B c states as well as the orbitally excited scalar B Ã c0 and axial-vector B c1 mesons.

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We calculate the differential branching fractions and angular distributions of the rare decays B 0 → K Ã0 μ þ μ − and B 0 s → ϕμ þ μ − , using for the first time form factors from unquenched lattice QCD. We focus on the kinematic region where the K Ã or ϕ recoils softly; there, the newly available form factors are most precise and the nonlocal matrix elements can be included via an operator product expansion. Our results for the differential branching fractions calculated in the standard model are higher than the experimental data. We consider the possibility that the deviations are caused by new physics and perform a fit of the Wilson coefficients C 9 and C 0 9 to the experimental data for multipleIn agreement with recent results from complementary studies, we obtain C 9 − C SM 9 ¼ −1.0 AE 0.6 and C Decays involving the transition of a bottom quark to a strange quark are highly suppressed in the standard model. Contributions from nonstandard interactions could therefore be significant, causing observable changes in the decay rates and angular distributions. The search for such discrepancies is one of the most important routes to discovering what might lie beyond our current model of fundamental particle physics, and complements efforts to directly produce nonstandard particles. Because of quark confinement, the b → s transitions are being observed with hadronic initial and final states. Among the cases that have been measured experimentally [1], the decaywhere l is an electron or muon) is proving to be particularly powerful in looking for physics beyond the standard model [2][3][4][5][6][7][8][9][10][11][12][13].The LHCb Collaboration recently published new precision measurements of the decay B → K Ã μ þ μ − , and one of the observables shows a significant deviation from the standard model predictions [14]. There is currently an intense effort to understand this discrepancy, which could be a manifestation of new physics [15][16][17][18][19][20][21][22]. Previous calculations of the matrix elements that relate the underlying b → s interactions and the hadronic observables are reliable only in the kinematic region of high recoil (large K Ã momentum in the B rest frame), and consequently it was in this region that a discrepancy was found. In the low-recoil region, numerical lattice QCD computations must be performed. We recently completed the first unquenched lattice QCD calculation of the form factors that parametrize the hadronic matrix elements relevant forIn this Letter, we investigate the consequences of using these results in combination with experimental data. We find that hints of deviations from the standard model are present also in the lowrecoil region, and a better fit of the data is obtained by allowing nonstandard interactions consistent with those suggested to explain the aforementioned anomaly at high recoil.At hadronic energy scales, b → sγ and b → sl þ l − transitions can be described using an effective Hamiltonian of the form [24-31]where O 9 ¼ e 2 =ð16π 2 Þsγ μ P LðRÞ blγ μ l;10 ¼ e 2 =ð16π 2 Þ...