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

BRST symmetry of SU(2) Yang-Mills theory in Cho--Faddeev--Niemi decomposition

We determine the nilpotent BRST and anti-BRST transformations for the Cho--Faddeev-Niemi variables for the SU(2) Yang-Mills theory based on the new interpretation given in the previous paper of the Cho--Faddeev-Niemi decomposition. This gives a firm ground for performing the BRST quantization of the Yang--Mills theory written in terms of the Cho--Faddeev-Niemi variables. We propose also a modified version of the new Maximal Abelian gauge which could play an important role in the reduction to the original Yang-Mills theory.Comment: 11 pages, no figure; Introduction improved, 3 references adde

Remarks on abelian dominance

We used a renormalisation group based smoothing to address two questions related to abelian dominance. Smoothing drastically reduces short distance fluctuations but it preserves the long distance physical properties of the SU(2) configurations. This enabled us to extract the abelian heavy-quark potential from time-like Wilson loops on Polyakov gauge projected configurations. We obtained a very small string tension which is inconsistent with the string tension extracted from Polyakov loop correlators. This shows that the Polyakov gauge projected abelian configurations do not have a consistent physical meaning. We also applied the smoothing on SU(2) configurations to test how sensitive abelian dominance in the maximal abelian gauge is to the short distance fluctuations. We found that on smoothed SU(2) configurations the abelian string tension was about 30% smaller than the SU(2) string tension which was unaffected by smoothing. This suggests that the approximate abelian dominance found with the Wilson action is probably an accident and it has no fundamental physical relevance.Comment: 13 pages, LaTeX, 3 eps figure

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

Abelian Dominance of Chiral Symmetry Breaking in Lattice QCD

Calculations of the chiral condensate on the lattice using staggered fermions and the Lanczos algorithm are presented. Four gauge fields are considered: the quenched non-Abelian field, an Abelian projected field, and monopole and photon fields further decomposed from the Abelian field. Abelian projection is performed in maximal Abelian gauge and in Polyakov gauge. The results show that monopoles in maximal Abelian gauge largely reproduce the chiral condensate values of the full non-Abelian theory, in both SU(2) and SU(3) color.Comment: 13 pages in RevTex including 6 figures, uucompressed, self-extractin

Temperature Dependence of Extended and Fractional SU(3) Monopole Currents

We examine in pure SU(3) the dependence of extended monopole current k and cross-species extended monopole current k^{cross} on temperature t, monopole size L, and fractional monopole charge 1/q. We find that features of both k and k^{cross} are sensitive to t for a range of L and q. In particular, the spatial-temporal asymmetry ratios of both k and k^{cross} are sensitive over a range of L and q to the SU(3) deconfinement transition. The motivation for studying cross, extended, and fractional monopoles in SU(3) is given.Comment: 15 pages (archiving final publication version; very minor revisions

Towards an Abelian Formulation of Lattice QCD Confinement

We probe for operators occurring in the APQCD(``abelian-projected QCD'') action by evaluating abelian-projected $1$-plaquette spectral densities in pure gauge $SU(3)$ fixed to maximal abelian gauge. Couplings $B_{APQCD}(q,L)$ are extracted from the spectral densities for each representation $q$, $L\times L$ plaquette. While APQCD is dominated by a $q=L=1$ resonance, we also find evidence for weakly coupled $L=2$ plaquettes. Moreover, since $B_{APQCD}(1,1) > B_{QED}(1,1)$ even if $\beta_{QED} > \beta_c$, $L>1$ plaquettes must be significant since APQCD is confining.Comment: 1+11 pages, fixed minor postscript erro

The Perturbative Pole Mass in QCD

It is widely believed that the pole mass of a quark is infrared-finite and gauge-independent to all orders in perturbation theory. This seems not to have been proved in the literature. A proof is provided here.Comment: 12 pages REVTeX with 2 figures; archiving published version with note and references added. If you thought this was proven long ago see http://www-theory.fnal.gov/people/ask/TeX/mPole

Abelian Monopoles in SU(2) Lattice Gauge Theory as Physical Objects

By numerical calculations we show that the abelian monopole currents are locally correlated with the density of SU(2) lattice action. The correlations are larger by the order of magnitude in the maximal abelian projection than in the projections which correspond to the diagonalization of Polyakov line and to the diagonalization of the plaquette. These facts show that (at least) in the maximal abelian projection the monopoles are the physical objects, they carry the SU(2) action. The larger value of \beta, the larger the relative action carried by monopole. Calculations on the asymmetric lattice show that this correlation exists also in the deconfinement phase of gluodynamics.Comment: 6 pages, RevTeX, 3 figures, uses epsf.sty; to be published in Phys.Rev.Lett., replaced to match version accepted for publicatio

Effective Monopole Potential for SU(2) Lattice Gluodynamics in Spatial Maximal Abelian Gauge

We investigate the dual superconductor hypothesis in finite-temperature SU(2) lattice gluodynamics in the Spatial Maximal Abelian gauge. This gauge is more physical than the ordinary Maximal Abelian gauge due to absence of non-localities in temporal direction. We show numerically that in the Spatial Maximal Abelian gauge the probability distribution of the abelian monopole field is consistent with the dual superconductor mechanism of confinement: the abelian condensate vanishes in the deconfinement phase and is not zero in the confinement phase.Comment: LaTeX2e, 8 pages with 3 EPS figures, uses epsf.st