Lattice Nonrelativistic QCD Research Articles

Width difference in theBs−Bssystem with lattice nonrelativistic QCD

We compute the matrix element of the four-quark operator $\Op_S$ = $\bar{b}(1-\gamma_5) s \bar{b} (1-\gamma_5) s$ in the $B_s-\bar{B}_s$ mixing on the lattice using NRQCD, which gives a leading contribution in the calculation of the width difference $\Delta\Gamma_s$ in the $1/m_b$ expansion. Using the next-to-leading formula of Beneke \textit{et al.}, we obtain $(\Delta\Gamma/\Gamma)_s$ = 0.151(37)(36)(17), where the the first error reflects the uncertainty of $f_{B_s}$ = 245(30) MeV, the second error comes from our calculation of the matrix element of $\Op_S$, and the third represents unknown $1/m_b$ correction.

Scaling of the Υ spectrum in lattice nonrelativistic QCD

We present results for the spectrum of b-bbar bound states in the quenched approximation for three different values of the lattice spacing, in the range 0.05fm to 0.15fm. We find our results for spin-independent splittings in physical units to be independent of the lattice spacing, indicating the absence of systematic errors from discretisation effects. Spin-dependent splittings are more sensitive to the lattice spacing and higher order corrections to the action; we discuss the size of these effects and what can be done to arrive at a physical result.

Lattice study ofB→πsemileptonic decay using nonrelativistic lattice QCD

We present an exploratory lattice study of $\stackrel{\ensuremath{\rightarrow}}{B}\ensuremath{\pi}$ semileptonic decay form factors using nonrelativistic lattice QCD for a heavy quark with a Wilson light quark on a ${16}^{3}\ifmmode\times\else\texttimes\fi{}32$ quenched lattice at $\ensuremath{\beta}=5.8$. The matrix elements are calculated at eight values of the heavy quark mass in the range of 1.5--8 GeV and with three values of light quark mass. The ${1/m}_{B}$ corrections to the matrix elements are found to be fairly small except for the spatial component proportional to the $B$-meson momentum. We find that the ${q}^{2}$ dependence of the form factor ${f}^{+}{(q}^{2})$ near ${q}_{\mathrm{}\mathrm{max}}^{2}$ becomes much stronger for a larger heavy quark mass, which may suggest an increase in the pole contribution. We perform a model independent fit of the form factors and study whether the ${q}^{2}$ dependence is consistent with the pole contribution. Although the soft pion theorem predicts ${f}^{0}{(q}_{\mathrm{}\mathrm{max}}^{2})$ ${=f}_{B}{/f}_{\ensuremath{\pi}}$ in the chiral limit, we observe a significant violation of this relation.

Gluon excitations of the static quark potential and the hybrid quarkonium spectrum

A comprehensive determination of the rich, low-lying spectrum of gluonic excitations in the presence of a static quark-antiquark pair is presented. Our results are obtained from several simulations on anisotropic lattices using an improved action and a large set of gluonic operators. The hybrid quarkonium states are studied in the quenched approximation using the Born-Oppenheimer expansion and nonrelativistic lattice QCD.

ImprovedΥspectrum with dynamical Wilson fermions

We present results for the b \bar b spectrum obtained using an O(M_bv^6)-correct non-relativistic lattice QCD action, where M_b denotes the bare b-quark mass and v^2 is the mean squared quark velocity. Propagators are evaluated on SESAM's three sets of dynamical gauge configurations generated with two flavours of Wilson fermions at beta = 5.6. These results, the first of their kind obtained with dynamical Wilson fermions, are compared to a quenched analysis at equivalent lattice spacing, beta = 6.0. Using our three sea-quark values we perform the ``chiral'' extrapolation to m_eff = m_s/3, where m_s denotes the strange quark mass. The light quark mass dependence is found to be small in relation to the statistical errors. Comparing the full QCD result to our quenched simulation we find better agreement of our dynamical data with experimental results in the spin-independent sector but observe no unquenching effects in hyperfine-splittings. To pin down the systematic errors we have also compared quenched results in different ``tadpole'' schemes as well as using a lower order action. We find that spin-splittings with an O(M_bv^4) action are O(10%) higher compared to O(M_bv^6) results. Relative to the results obtained with the plaquette method the Landau gauge mean link tadpole scheme raises the spin splittings by about the same margin so that our two improvements are opposite in effect.

Bottomonium from NRQCD with dynamical Wilson Fermions

We present results for the b b spectrum obtained using an O ( M bv 6)-correct non-relativistic lattice QCD action. Propagators are evaluated on SESAM's three sets of dynamical gauge configurations generated with two flavours of Wilson fermions at β = 5.6. Compared to a quenched simulation at equivalent lattice spacing we find better agreement of our dynamical data with experimental results in the spin-independent sector but observe no unquenching effects in hyperfine-splittings. To pin down the systematic errors we have also compared quenched results in different “tadpole” schemes and used a lower order action.

Precision Upsilon spectroscopy from nonrelativistic lattice QCD.

The spectrum of the Upsilon system is investigated using the Nonrelativistic Lattice QCD approach to heavy quarks and ignoring light quark vacuum polarization. We find good agreement with experiment for the Upsilon(1S), Upsilon(2S), Upsilon(3S) and for the center of mass and fine structure of the chi_b states. The lattice calculations predict b-bbar D-states with center of mass at (10.20 +/- 0.07 +/- 0.03)GeV. Fitting procedures aimed at extracting both ground and excited state energies are developed. We calculate a nonperturbative dispersion mass for the Upsilon(1S) and compare with tadpole-improved lattice perturbation theory.

Radiative corrections to the kinetic couplings in nonrelativistic lattice QCD.

The heavy-quark mass and wave function renormalizations, energy shift, and radiative corrections to two important couplings, the so-called kinetic couplings, in nonrelativistic lattice QCD are determined to leading order in tadpole-improved perturbation theory. The scales at which to evaluate the running QCD coupling for these quantities, except the wave function renormalization, are obtained using the Lepage-Mackenzie prescription. When the bare quark mass is greater than the inverse lattice spacing, the kinetic coupling corrections are roughly 10\% of the tree-level coupling strengths; these corrections grow quickly as the bare quark mass becomes small. A need for computing the two-loop corrections to the energy shift and mass renormalization is demonstrated.

Computation of the heavy-light decay constant using nonrelativistic lattice QCD.

We report results on a lattice calculation of the heavy-light meson decay constant employing the non-relativistic QCD approach for heavy quark and Wilson action for light quark. Simulations are carried out at $\beta=6.0$ on a $16^3\times 48$ lattice. Signal to noise ratio for the ground state is significantly improved compared to simulations in the static approximation, enabling us to extract the decay constant reliably. We compute the heavy-light decay constant for several values of heavy quark mass and estimate the magnitude of the deviation from the heavy mass scaling law $f_{P} \sqrt{m_{P}} = const$. For the $B$ meson we find $f_{B} = 171\pm 22^{+19}_{-45}$ MeV, while an extrapolation to the static limit yields $f_{B}^{static}$ = $297\pm 36^{+15}_{-30}$ MeV.

The improvement program in nonrelativistic lattice QCD

Progress in the improvement program in nonrelativistic lattice QCD is outlined. The leading radiative corrections to the heavy-quark mass renormalization, energy shift, and two important kinetic coupling coefficients are presented. The reliability of tadpole-improved perturbation theory in determining the energy shift and mass renormalization is demonstrated.

Heavy-quark self-energy in nonrelativistic lattice QCD.

The heavy quark self-energy in nonrelativistic lattice QCD is calculated to $O(\alpha_s)$ in perturbation theory. An action which includes all spin-independent relativistic corrections to order $v^2$, where $v$ is the typical heavy quark velocity, and all spin-dependent corrections to order $v^4$ is used. The standard Wilson action and an improved multi-plaquette action are used for the gluons. Results for the mass renormalization, wavefunction renormalization, and energy shift are given; tadpole contributions are found to be large. A tadpole improvement scheme in which all link variables are rescaled by a mean-field factor is also studied. The effectiveness of this scheme in offsetting the large tadpole contributions to the heavy quark renormalization parameters is demonstrated.

Instantaneous potentials in nonrelativistic lattice QCD

The validity of instantaneous potential ideas in heavy-quark bound-state problems is examined with the aid of a suitable lattice potential model. The model is also used as a testing ground for a multistate smearing method.