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We have developed two methods for handling $b$ quarks in lattice QCD. One uses NRQCD (now improved to include radiative corrections) and the other uses Highly Improved Staggered Quarks (HISQ), extrapolating to the $b$ quark from lighter masses and using multiple lattice spacings to control discretisation errors. Comparison of results for the two different methods gives confidence in estimates of lattice QCD systematic errors, since they are very different in these two cases. Here we show results for heavyonium hyperfine splittings and vector current-current correlator moments using HISQ quarks, to add to earlier results testing the heavy HISQ method with pseudoscalar mesons. We also show the form factor for $B rightarrow pi l u$ decay at zero recoil using NRQCD $b$ quarks and $u/d$ quarks with physical masses. This allows us to test the soft pion theorem relation ($f_0(q^2_{max})=f_B/f_{pi}$) accurately and we find good agreement as $M_{pi} rightarrow 0$. }
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We calculate the mass difference between the $Upsilon$ and $eta_b$ and the $Upsilon$ leptonic width from lattice QCD using the Highly Improved Staggered Quark formalism for the $b$ quark and including $u$, $d$, $s$ and $c$ quarks in the sea. We have results for lattices with lattice spacing as low as 0.03 fm and multiple heavy quark masses, enabling us to map out the heavy quark mass dependence and determine values at the $b$ quark mass. Our results are: $M_{Upsilon} -M_{eta_b} = 57.5(2.3)(1.0) ,mathrm{MeV}$ (where the second uncertainty comes from neglect of quark-line disconnected correlation functions) and decay constants, $f_{eta_b}=724(12)$ MeV and $f_{Upsilon} =677.2(9.7)$ MeV, giving $Gamma(Upsilon rightarrow e^+e^-) = 1.292(37)(3) ,mathrm{keV}$. The hyperfine splitting and leptonic width are both in good agreement with experiment, and provide the most accurate lattice QCD results to date for these quantities by some margin. At the same time results for the time moments of the vector-vector correlation function can be compared to values for the $b$ quark contribution to $sigma(e^+e^- rightarrow mathrm{hadrons})$ determined from experiment. Moments 4--10 provide a 2% test of QCD and yield a $b$ quark contribution to the anomalous magnetic moment of the muon of 0.300(15)$times 10^{-10}$. Our results, covering a range of heavy quark masses, may also be useful to constrain QCD-like composite theories for beyond the Standard Model physics.
We calculate the bag parameters for neutral $B$-meson mixing in and beyond the Standard Model, in full four-flavour lattice QCD for the first time. We work on gluon field configurations that include the effect of $u$, $d$, $s$ and $c$ sea quarks with the Highly Improved Staggered Quark (HISQ) action at three values of the lattice spacing and with three $u/d$ quark masses going down to the physical value. The valence $b$ quarks use the improved NRQCD action and the valence light quarks, the HISQ action. Our analysis was blinded. Our results for the bag parameters for all five operators are the most accurate to date. For the Standard Model operator between $B_s$ and $B_d$ mesons we find: $hat{B}_{B_s}=1.232(53)$, $hat{B}_{B_d}=1.222(61)$. Combining our results with lattice QCD calculations of the decay constants using HISQ quarks from the Fermilab/MILC collaboration and with experimental values for $B_s$ and $B_d$ oscillation frequencies allows determination of the CKM elements $V_{ts}$ and $V_{td}$. We find $V_{ts} = 0.04189(93)$, $V_{td} = 0.00867(23)$ and $V_{ts}/V_{td} = 0.2071(27)$. Our results agree well (within $2sigma$) with values determined from CKM unitarity constraints based on tree-level processes (only). Using a ratio to $Delta M$ in which CKM elements cancel in the Standard Model, we determine the branching fractions ${text{Br}}(B_srightarrow mu^+mu^-) = 3.81(18) times 10^{-9}$ and ${text{Br}}(B_drightarrow mu^+mu^-) = 1.031(54) times 10^{-10}$. We also give results for matrix elements of the operators $R_0$, $R_1$ and $tilde{R}_1$ that contribute to neutral $B$-meson width differences.
We extend the picture of $B$-meson decay constants obtained in lattice QCD beyond those of the $B$, $B_s$ and $B_c$ to give the first full lattice QCD results for the $B^*$, $B^*_s$ and $B^*_c$. We use improved NonRelativistic QCD for the valence $b$ quark and the Highly Improved Staggered Quark (HISQ) action for the lighter quarks on gluon field configurations that include the effect of $u/d$, $s$ and $c$ quarks in the sea with $u/d$ quark masses going down to physical values. For the ratio of vector to pseudoscalar decay constants, we find $f_{B^*}/f_B$ = 0.941(26), $f_{B^*_s}/f_{B_s}$ = 0.953(23) (both $2sigma$ less than 1.0) and $f_{B^*_c}/f_{B_c}$ = 0.988(27). Taking correlated uncertainties into account we see clear indications that the ratio increases as the mass of the lighter quark increases. We compare our results to those using the HISQ formalism for all quarks and find good agreement both on decay constant values when the heaviest quark is a $b$ and on the dependence on the mass of the heaviest quark in the region of the $b$. Finally, we give an overview plot of decay constants for gold-plated mesons, the most complete picture of these hadronic parameters to date.
We study $I=0$ quarkonium resonances decaying into pairs of heavy-light mesons using static-static-light-light potentials from lattice QCD. To this end, we solve a coupled channel Schrodinger equation with a confined quarkonium channel and channels with a heavy-light meson pair to compute phase shifts and $mbox{T}$ matrix poles for the lightest decay channel. We discuss our results for $S$, $P$, $D$ and $F$ wave states in the context of corresponding experimental results, in particular for $Upsilon(10753)$ and $Upsilon(10860)$.
We study the temperature dependence of bottomonium for temperatures in the range $0.4 T_c < T < 2.1 T_c$, using nonrelativistic dynamics for the bottom quark and full relativistic lattice QCD simulations for $N_f=2$ light flavors on a highly anisotropic lattice. We find that the $Upsilon$ is insensitive to the temperature in this range, while the $chi_b$ propagators show a crossover from the exponential decay characterizing the hadronic phase to a power-law behaviour consistent with nearly-free dynamics at $T simeq 2 T_c$.
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