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Register a new userThe Upsilon spectrum and m_b from full lattice QCD
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We show results for the Upsilon spectrum calculated in lattice QCD including for the first time vacuum polarization effects for light u and d quarks as well as s quarks. We use gluon field configurations generated by the MILC collaboration. The calculations compare the results for a variety of u and d quark masses, as well as making a comparison to quenched results (in which quark vacuum polarisation is ignored) and results with only u and d quarks. The b quarks in the Upsilon are treated in lattice Nonrelativistic QCD through NLO in an expansion in the velocity of the b quark. We concentrate on accurate results for orbital and radial splittings where we see clear agreement with experiment once u, d and s quark vacuum polarisation effects are included. This now allows a consistent determination of the parameters of QCD. We demonstrate this consistency through the agreement of the Upsilon and B spectrum using the same lattice bare b quark mass. A one-loop matching to continuum QCD gives a value for the b quark mass in full lattice QCD for the first time. We obtain m_b^{bar{MS}}(m_b^{bar{MS}}) = 4.4(3) GeV. We are able to give physical results for the heavy quark potential parameters, r_0 = 0.469(7) fm and r_1 = 0.321(5) fm. Results for the fine structure in the spectrum and the Upsilon leptonic width are also presented. We predict the Upsilon - eta_b splitting to be 61(14) MeV, the Upsilon^{prime} - eta_b^{prime} splitting as 30(19) MeV and the splitting between the h_b and the spin-average of the chi_b states to be less than 6 MeV. Improvements to these calculations that will be made in the near future are discussed.
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We determine the decay rate to leptons of the ground-state $Upsilon$ meson and its first radial excitation in lattice QCD for the first time. We use radiatively-improved NRQCD for the $b$ quarks and include $u$, $d$, $s$ and $c$ quarks in the sea with $u/d$ masses down to their physical values. We find $Gamma(Upsilon rightarrow e^+e^-)$ = 1.19(11) keV and $Gamma(Upsilon^{prime} rightarrow e^+e^-)$ = 0.69(9) keV, both in good agreement with experiment. The decay constants we obtain are included in a summary plot of meson decay constants from lattice QCD given in the Conclusions. We also test time-moments of the vector current-current correlator against values determined from the $b$ quark contribution to $sigma(e^+e^- rightarrow mathrm{hadrons})$ and calculate the $b$-quark piece of the hadronic vacuum polarisation contribution to the anomalous magnetic moment of the muon, $a_{mu}^b = 0.271(37) times 10^{-10}$. Finally we determine the $b$-quark mass, obtaining in the $overline{MS}$ scheme, $overline{m}_b(overline{m}_b, n_f=5)$ = 4.196(23) GeV, the most accurate result from lattice QCD to date.
Recent results from lattice QCD simulations provide a realistic picture, based upon first principles, of~$Upsilon$ physics. We combine these results with the experimentally measured mass of the $Upsilon$~meson to obtain an accurate and reliable value for the $b$-quarks pole mass. We use two different methods, each of which yields a mass consistent with $M_b = 5.0(2)$~GeV. This corresponds to a bare mass of $M_b^0 = 4.0(1)$~GeV in our lattice theory and an $msbar$~mass of $M_b^msbar(M_b)=4.0(1)$~GeV. We discuss the implications of this result for the $c$-quark mass. ******************************************************************************* THIS IS THE VERSION WHICH WILL BE PUBLISHED IN PRL. SUBSTANTIAL MATERIAL HAS BEEN ADDED, INCLUDING RESULTS WITH DYNAMICAL FERMIONS AND A CALCULATION OF THE MSBAR MASS. *******************************************************************************
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The spectrum of orbitally excited $D_s$ mesons is computed in the continuum limit of quenched lattice QCD. The results are consistent with the interpretation that the narrow resonance in the $D_s pi^0$ channel discovered by the BABAR Collaboration is a $J^P=0^+$ $cbar{s}$ meson. Furthermore, within statistical errors, the $1^+-1^-$ and the $0^+-0^-$ mass splittings are equal, in agreement with the chiral multiplet structure predicted by heavy hadron chiral effective theory. On our coarsest lattice we present results from the first study of orbitally excited $D_s$ mesons with two flavors of dynamical quarks, with mass slightly larger than the strange quark mass. These results are consistent with the quenched data.
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