Application of heavy-quark effective theory to lattice QCD: III. Radiative corrections to heavy-heavy currents

We apply heavy-quark effective theory (HQET) to separate long- and short-distance effects of heavy quarks in lattice gauge theory. In this paper we focus on flavor-changing currents that mediate transitions from one heavy flavor to another. We stress differences in the formalism for heavy-light currents, which are discussed in a companion paper, showing how HQET provides a systematic matching procedure. We obtain one-loop results for the matching factors of lattice currents, needed for heavy-quark phenomenology, such as the calculation of zero-recoil form factors for the semileptonic decays $B\to D^{(*)}l\nu$. Results for the Brodsky-Lepage-Mackenzie scale $q^*$ are also given.Comment: 35 pages, 17 figures. Program LatHQ2QCD to compute matching one-loop coefficients available at http://theory.fnal.gov/people/kronfeld/LatHQ2QCD

Semileptonic Decays of D and B Mesons

We report results of our ongoing investigation concerning semileptonic decays of heavy pseudoscalar mesons into pseudoscalar and vector mesons. Particular attention is paid to uncertainties in the $q^2$ and the heavy quark mass dependence of formfactors. Moreover we present a non-perturbative test to the LMK current renormalization scheme for vector current transition matrix elements and find remarkable agreement.Comment: 3 pages, uuencoded, contribution to Lat 9

Dual vortices in Abelian projected SU(2) in the Polyakov gauge

We study dual Abrikosov vortices in Abelian projected SU(2) gauge theory in the Polyakov gauge. We show that vortices are present in this gauge but they are suppressed with respect to the maximal Abelian gauge. We interpret this difference in terms of the shielding of the electric charge by the charged coset fields.Comment: Talk presented at LATTICE96(topology), 3 pages, latex, 4 eps figures, uses epsfig and espcrc2.sty (included

Semileptonic Decays of Heavy Mesons: A Status Report

We present intermediate results on our ongoing investigation concerning semileptonic decays of heavy pseudoscalar mesons into pseudoscalar and vector mesons. The corresponding formfactors are evaluated at several momenta and appropriate combinations of four light and four heavy quarks, which are chosen to allow for an extrapolation into the B Meson region. In order to obtain clear groundstate signals we apply gauge invariant ``Wuppertal'' smearing to the quarks. The analysis is based on 32 quenched gauge configurations of size $24^3 \times 64$ at $\beta=6.3$, with Wilson fermions.Comment: 3 pages, uuencoded, contribution to Lat 9

New lattice action for heavy quarks

We extend the Fermilab method for heavy quarks to include interactions of dimensions 6 and 7 in the action. There are, in general, many new interactions, but we carry out the calculations needed to match the lattice action to continuum QCD at the tree level, finding six non-zero couplings. Using the heavy-quark theory of cutoff effects, we estimate how large the remaining discretization errors are. We find that our tree-level matching, augmented with one-loop matching of the dimension-five interactions, can bring these errors below 1%, at currently available lattice spacings.Comment: 43 pp; v2 conforms with PRD version, improving plots and many minor thing

Heavy and Light Quarks with Lattice Chiral Fermions

The feasibility of using lattice chiral fermions which are free of $O(a)$ errors for both the heavy and light quarks is examined. The fact that the effective quark propagators in these fermions have the same form as that in the continuum with the quark mass being only an additive parameter to a chirally symmetric antihermitian Dirac operator is highlighted. This implies that there is no distinction between the heavy and light quarks and no mass dependent tuning of the action or operators as long as the discretization error $O(m^2 a^2)$ is negligible. Using the overlap fermion, we find that the $O(m^2a^2)$ (and $O(ma^2)$) errors in the dispersion relations of the pseudoscalar and vector mesons and the renormalization of the axial-vector current and scalar density are small. This suggests that the applicable range of $ma$ may be extended to $\sim 0.56$ with only 5% error, which is a factor of $\sim 2.4$ larger than that of the improved Wilson action. We show that the generalized Gell-Mann-Oakes-Renner relation with unequal masses can be utilized to determine the finite $ma$ errors in the renormalization of the matrix elements for the heavy-light decay constants and semileptonic decay constants of the B/D meson.Comment: final version to appear in Int. Jou. Mod. Phys.

Finite ma corrections for sea quark matrix elements

We discuss the finite $ma$ corrections associated with the computation of sea quark matrix elements. We find them to differ from the standard normalization used for valence quarks and to depend strongly on the Lorentz structure of the current under consideration. Phenomenological implications of these results are briefly discussed in two examples. We also mention how the magnitude of the correction factors can be reduced by using a 2-link improved action.Comment: 3 pages, contribution to LATTICE'94, uuencoded compressed tar file (square root removed in equation (1)

Quark Confinement in the Deconfined Phase

In cylindrical volumes with C-periodic boundary conditions in the long direction, static quarks are confined even in the gluon plasma phase due to the presence of interfaces separating the three distinct high-temperature phases. An effective "string tension" is computed analytically using a dilute gas of interfaces. At T_c, the deconfined-deconfined interfaces are completely wet by the confined phase and the high-temperature "string tension" turns into the usual string tension below T_c. Finite size formulae are derived, which allow to extract interface and string tensions from the expectation value of a single Polyakov loop. A cluster algorithm is built for the 3-d three-state Potts model and an improved estimator for the Polyakov loop is constructed, based on the number of clusters wrapping around the C-periodic direction of the cluster.Comment: 3 pages, Latex, talk presented at Lattice '97, to appear in Nucl. Phys. B (Proc. Suppl.), uses espcrc2.st

Application of heavy-quark effective theory to lattice QCD: II. Radiative corrections to heavy-light currents

We apply heavy-quark effective theory to separate long- and short-distance effects of heavy quarks in lattice gauge theory. In this approach, the inverse heavy-quark mass and the lattice spacing are treated as short distances, and their effects are lumped into short-distance coefficients. We show how to use this formalism to match lattice gauge theory to continuum QCD, order by order in the heavy-quark expansion. In this paper, we focus on heavy-light currents. In particular, we obtain one-loop results for the matching factors of lattice currents, needed for heavy-quark phenomenology, such as the calculation of heavy-light decay constants, and heavy-to-light transition form factors. Results for the Brodsky-Lepage-Mackenzie scale $q^*$ are also given.Comment: 32 pages, 8 figures. v2 corrects Eqs. (4.9) and (4.10) and adds a reference. Program LatHQ2QCD to compute matching one-loop coefficients available at http://theory.fnal.gov/people/kronfeld/LatHQ2QCD

Quark Confinement Physics in Quantum Chromodynamics

We study abelian dominance and monopole condensation for the quark confinement physics using the lattice QCD simulations in the MA gauge. These phenomena are closely related to the dual superconductor picture of the QCD vacuum, and enable us to construct the dual Ginzburg-Landau (DGL) theory as an useful effective theory of nonperturbative QCD. We then apply the DGL theory to the studies of the low-lying hadron structure and the scalar glueball properties.Comment: Talk given at 15th International Conference on Particle and Nuclei (PANIC 99), Uppsala, Sweden, 10-16 Jun 1999, 4 page