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We present a quenched lattice calculation for the lowest lying $b bar b g$-hybrid states in the framework of NRQCD using the leading order Hamiltonian up to ${cal O}(mv^2)$. We demonstrate the existence of a nearly degenerate rotational band of states with an excitation energy approximately 1.6 GeV above the $Upsilon$ ground state. This lies around the $B bar B_J^*$-threshold but well above the $B bar B$-threshold. Therefore a heavy hybrid signal may well be detected if the centre-of-mass energy in B-factories is raised a few hundred MeV to coincide with other resonances above the 4S state. Our prediction is consistent with most phenomenological models and lattice calculations carried out in the static limit.
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We present a lattice QCD calculation of the heavy quark expansion parameters $mu_{pi}^2$ and $mu_G^2$ for heavy-light mesons and heavy-light-light baryons. The calculation is carried out on a 20$^3times$48 lattice at $beta$ = 6.0 in the quenched approximation, using the lattice NRQCD action for heavy quarks. We obtain the parameters $mu_{pi}^2$ and $mu_G^2$ in two different methods: a direct calculation of the matrix elements and an indirect calculation through the mass spectrum, and confirm that the both methods give consistent results. We also discuss an application to the lifetime ratios.
Using the lattice NRQCD action for heavy quark, we calculate the heavy quark expansion parameters $mu_{pi}^2$ and $mu_G^2$ for heavy-light mesons and heavy-light-light baryons. The results are compared with the mass differences among heavy hadrons to test the validity of HQET relations on the lattice.
We calculate semileptonic form factors for the decays $B_c to eta_c , l u$ and $B_c to J/psi , l u$ over the entire $q^2$ range, using a highly improved lattice quark action for charm at several lattice spacings down to $a=0.045$ fm. We have two ways of treating the $b$ quark: either with an $O(alpha_s)$ improved NRQCD formalism or by extrapolating a heavy mass $m_h$ to $m_b$ in the relativistic formalism. Comparison of the two approaches provides an important cross-check of methodologies in lattice QCD. Nonperturbative renormalisation of the currents in the relativistic theory also allows us then to fix NRQCD-charm normalisation for $b$ to $c$ decays such as $B to D$ and $B to D^*$.
We present a calculation of the heavy quarks self energy in moving NRQCD to one-loop in perturbation theory. Results for the energy shift and external momentum renormalisation are discussed and compared with non-perturbative results. We show that the momentum renormalisation is small, which is the result of a remnant of re-parameterisation invariance on the lattice.
The spectrum of heavy-quark hybrids is studied in the leading Born-Oppenheimer (LBO) approximation and using leading-order NRQCD simulations with an improved gluon action on anisotropic lattices. The masses of four hybrid states are obtained from our simulations for lattice spacings 0.1 fm and 0.2 fm and are compared to the LBO predictions obtained using previously-determined glue-excited static potentials. The consistency of results from the two approaches reveals a compelling physical picture for heavy-quark hybrid states.
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