arXiv subjects
Publications and source records attributed to Claude Bernard.
I review recent developments in lattice weak matrix element calculations. I focus on on $f_B$ (both with propagating quarks and in the static limit for the $b$ quark), semi-leptonic form factors for $D$ meson decay, form factors for $B \to K^* γ$, and $B_K$. [Review presented at Lattice '93]
We describe a series of simulations of high temperature QCD with two flavors of Wilson quarks aimed at clarifying the nature of the high temperature phase found in current simulations. Most of our work is with four time slices, although we include some runs with six and eight time slices for comparison. In addition to the usual thermodynamic observables we study the quark mass defined by the divergence of the axial current and the quark propagator in the Landau gauge. We find that the sharpness of the $N_t=4$ thermal transition has a maximum around $κ=0.19$ and $6/g^2=4.8$.
As part of an ongoing effort to characterize the high temperature phase of QCD, in a numerical simulation using the staggered fermion scheme, we measure the quark baryon density in the vicinity of a fixed test quark at high temperature and compare it with similar measurements at low temperature and at the crossover temperature. We find an extremely weak correlation at high temperature, suggesting that small color singlet clusters are unimportant in the thermal ensemble. We also find that at $T = 0.75\ T_c$ the total induced quark number shows a surprisingly large component attributable to baryonic screening. A companion simulation of a simple flux tube model produces similar results and also suggests a plausible phenomenological scenario: As the crossover temperature is approached from below, baryonic states proliferate. Above the crossover temperature the mean size of color singlet clusters grows explosively, resulting in an effective electrostatic deconfinement.
A lattice calculation of the pseudoscalar decay constant of heavy-light mesons is reported. Results are obtained (in the quenched approximation) from lattices at $β=6.3$ through a procedure that interpolates between the static approximation of Eichten and the conventional ("heavy" Wilson fermion) method. The previously observed discrepancy between these two approaches has been resolved: we find the scaling quantity $f\sqrt{M}$ to be significantly smaller than previous calculations had indicated ({\it e.g.} at $β=6.0$); in addition, we discuss a modification which is required in normalizing the conventional amplitude to correct for large-$am$ lattice errors. This change guarantees that $f\sqrt{M}$ will smoothly approach its value in the static limit. From the numerical interpolation of the static and intermediate-mass results, we find, in units of MeV, $f_B=187(10)\pm34\pm15$, $f_{B_s}=207(9)\pm34\pm22$, $f_D=208(9)\pm35\pm12$ and $f_{D_s}=230(7)\pm30\pm18$, where the first error is statistical and the second two are estimates of systematics due to 1) fitting and large-$am$ effects and 2) scaling. In addition, using lattices at $β=6.3$, $β=6.0$ and $β=5.7$ and extrapolating to the limit of zero lattice spacing, we have computed $f_K/f_π= 1.08\pm.03\pm.08$ in the quenched approximation.
We extend our lagrangian technique for chiral perturbation theory for quenched QCD to include theories in which only some of the quarks are quenched. We discuss the relationship between the partially quenched theory and a theory in which only the unquenched quarks are present. We also investigate the peculiar infrared divergences associated with the $η'$ in the quenched approximation, and find the conditions under which such divergences can appear in a partially quenched theory. We then apply our results to staggered fermion QCD in which the square root of the fermion determinant is taken, using the observation that this should correspond to a theory with four quarks, two of which are quenched. [Uses harvmac macro package. No postscipt for the figures is available (sorry), but the figures are simple and we include do-it-yourself instructions for drawing them.]
We calculate the Isgur-Wise function by measuring the heavy-heavy meson transition matrix element on the lattice. The standard Wilson action is used for both the heavy and light quarks. Our first numerical results are presented.
We have computed the decay constants for the $B$ and $D$ mesons, using quenched lattices at $β=6.3$, by interpolating between the static approximation of Eichten and the conventional (``heavy'' Wilson fermion) method. A more careful treatment of the static result using better sources with longer time-displacements and a modification to the Wilson quark normalization to correct approximately for lattice effects in the large-$am$ regime have led to the elimination of the large discrepancy between the two methods which had been previously observed. We report final results, with estimates of various systematic errors.
We present results for physical quantities computed in quenched chiral perturbation theory and compare them with the corresponding unquenched expressions. We also point out an apparent theoretical problem of the quenched approximation. latex, file espcrc2.sty needed (appended at the end: search for espcrc2.sty).
This talk was presented to a non-lattice audience at the June, 1992 Paris Workshop on QCD Vacuum Structure. We report on the status of quark and gluon propagators in quenched, gaugefixed lattice QCD. In Landau gauge we find that the effective quark mass in the chiral limit is $M_q \sim 350(40)MeV$. Quark and gluon propagators, the slope of the quark dispersion relation, and effective masses all appear to depend on gauge. A link-chain picture of lattice gaugefixing in the color $N\to\infty$ and strong coupling limit, where the system becomes almost solvable, supports the gauge variance of these numerical results. Subscribers will be given one Postscript file, the Figure included. Latex and Axis versions available from KY at kyee@rouge.phys.lsu.edu on request.
We report on a study of hadron thermodynamics with two flavors of Wilson quarks on 12^3x6 lattices. We have studied the crossover between the high and low temperature regimes for three values of the hopping parameter, kappa=0.16, 0.17, and 0.18. At each of these values of kappa we have carried out spectrum calculations on 12^3x24 lattices for two values of the gauge coupling in the vicinity of the crossover in order to set an energy scale for our thermodynamics calculations and to determine the critical value of the gauge coupling for which the pion and quark masses vanish. For kappa=0.17 and 0.18 we find coexistence between the high and low temperature regimes over 1,000 simulation time units indicating either that the equilibration time is extremely long or that there is a possibility of a first order phase transition. The pion mass is large at the crossover values of the gauge coupling, but the crossover curve has moved closer to the critical curve along which the pion and quark masses vanish, than it was on lattices with four time slices. In addition, values of the dimensionless quantity T_c/m_rho are in closer agreement with those for staggered quarks than was the case at N_t=4. (A POSTSCRIPT VERSION OF THIS PAPER IS AVAILABLE BY ANONYMOUS FTP FROM sarek.physics.ucsb.edu (128.111.8.250) IN THE FILE pub/wilson_thermo.ps)
[This version is a minor revision of a previously submitted preprint. Only references have been changed.] We describe a technique for constructing the effective chiral theory for quenched QCD. The effective theory which results is a lagrangian one, with a graded symmetry group which mixes Goldstone bosons and fermions, and with a definite (though slightly peculiar) set of Feynman rules. The straightforward application of these rules gives automatic cancellation of diagrams which would arise from virtual quark loops. The techniques are used to calculate chiral logarithms in $f_K/f_π$, $m_π$, $m_K$, and the ratio of $\langle{\bar s}s\rangle$ to $\langle{\bar u}u\rangle$. The leading finite-volume corrections to these quantities are also computed. Problems for future study are described.