Soft Covariant Gauges on the Lattice

We present an exploratory study of a one-parameter family of covariant, non-perturbative lattice gauge-fixing conditions, that can be implemented through a simple Monte Carlo algorithm. We demonstrate that at the numerical level the procedure is feasible, and as a first application we examine the gauge dependence of the gluon propagator.Comment: 11 pages, Latex, epsf.sty included + 5 PostScript picture

Asymptotic scaling of the gluon propagtor on the lattice

We pursue the study of the high energy behaviour of the gluon propagator on the lattice in the Landau gauge in the flavorless case (n_f=0). It was shown in a precedin g paper that the gluon propagator did not reach three-loop asymptotic scaling at an energy scale as high as 5 GeV. Our present high statistics analysis includes also a simulation at $\beta=6.8$ ($a\simeq 0.03$ fm), which allows to reach $\mu \simeq 10$ GeV. Special care has been devoted to the finite lattice-spacing artifacts as well as to the finite volume effects, the latter being acute at $\beta=6.8$ where the volume is bounded by technical limits. Our main conclusion is a strong evidence that the gluon propagator has reached three-loop asymptotic scaling, at $\mu$ ranging from 5.6 GeV to 9.5 GeV. We buttress up this conclusion on several demanding criteria of asymptoticity, including scheme independence. Our fit in the 5.6 GeV to 9.5 GeV window yields $\Lambda^{\bar{{\rm MS}}} = 319 \pm 14 ^{+10}_{-20}$ MeV, in good agreement with our previous result, $\Lambda^{\bar{{\rm MS}}} = 295 \pm 20$ MeV, obtained from the three gluon vertex, but it is significantly above the Schr\"odinger functional method estimate : $238 \pm 19$ MeV. The latter difference is not understood. Confirming our previous paper, we show that a fourth loop is necessary to fit the whole ($2.8 \div 9.5$) GeV energy window.Comment: latex-file, 19 pgs., 6 fig

Off-diagonal Gluon Mass Generation and Infrared Abelian Dominance in the Maximally Abelian Gauge in Lattice QCD

We study effective mass generation of off-diagonal gluons and infrared abelian dominance in the maximally abelian (MA) gauge. Using the SU(2) lattice QCD, we investigate the propagator and the effective mass of the gluon field in the MA gauge with the U(1)$_3$ Landau gauge fixing. The Monte Carlo simulation is performed on the $12^3 \times 24$ lattice with $2.2 \le \beta \le 2.4$, and also on the $16^4$ and $20^4$ lattices with $2.3 \le \beta \le 2.4$. In the MA gauge, the diagonal gluon component $A_\mu^3$ shows long-range propagation, and infrared abelian dominance is found for the gluon propagator. In the MA gauge, the off-diagonal gluon component $A_\mu^\pm$ behaves as a massive vector boson with the effective mass $M_{\rm off} \simeq 1.2$ GeV in the region of r \gsim 0.2 fm, and its propagation is limited within short range. We conjecture that infrared abelian dominance can be interpreted as infrared inactivity of the off-diagonal gluon due to its large mass generation induced by the MA gauge fixing.Comment: 31 pages, 7 figures and 2 tables included, changed title, corrected typos and updated reference, accepted for publication in Physical Review

Heavy Baryon Specroscopy from the Lattice

The results of an exploratory lattice study of heavy baryon spectroscopy are presented. We have computed the full spectrum of the eight baryons containing a single heavy quark, on a $24^3\times 48$ lattice at $\beta=6.2$, using an $O(a)$-improved fermion action. We discuss the lattice baryon operators and give a method for isolating the contributions of the spin doublets $(\Sigma,\Sigma^*)$, $(\Xi',\Xi^*)$ and $(\Omega,\Omega^*)$ to the correlation function of the relevant operator. We compare our results with the available experimental data and find good agreement in both the charm and the beauty sectors, despite the long extrapolation in the heavy quark mass needed in the latter case. We also predict the masses of several undiscovered baryons. We compute the \Lambda-\mbox{pseudoscalar meson} and $\Sigma-\Lambda$ mass splittings. Our results, which have errors in the range $10-30\%$, are in good agreement with the experimental numbers. For the $\Sigma^*-\Sigma$ mass splitting, we find results considerably smaller than the experimental values for both the charm and the beauty baryons, although in the latter case the experimental results are still preliminary. This is also the case for the lattice results for the hyperfine splitting for the heavy mesons.Comment: 31 pages LaTex, with postscript figures include

Problems in Lattice Gauge Fixing

We review many topics and results about numeric gauge fixing in lattice QCD.Comment: 47 pages, 16 eps figures. Review article sent to IJMP

Inhomogeneous Field Configurations and the Electroweak Phase Transition

We investigate the effects of inhomogeneous scalar field configurations on the electroweak phase transition. For this purpose we calculate the leading perturbative correction to the wave function correction term Z(\vph,T), i.e., the kinetic term in the effective action, for the electroweak Standard Model at finite temperature and the top quark self--mass. Our finding for the fermionic contribution to Z(\vph,T) is infra--red finite and disagrees with other recent results. In general, neither the order of the phase transition nor the temperature at which it occurs change, once Z(\vph,T) is included. But a non--vanishing, positive (negative) Z(\vph,T) enhances (decreases) the critical droplet surface tension and the strength of the phase transition. We find that in the range of parameter space, which allows for a first--order phase transition, the wave function correction term is negative --- indicating a weaker phase transition --- and especially for small field values so large that perturbation theory becomes unreliable.Comment: 23 pages of LaTeX + 3 PostScript figures included in uuencoded form, FERMI-PUB-93/253-

The Infrared Behaviour of the Pure Yang-Mills Green Functions

We review the infrared properties of the pure Yang-Mills correlators and discuss recent results concerning the two classes of low-momentum solutions for them reported in literature; i.e. decoupling and scaling solutions. We will mainly focuss on the Landau gauge and pay special attention to the results inferred from the analysis of the Dyson-Schwinger equations of the theory and from "{\it quenched}" lattice QCD. The results obtained from properly interplaying both approaches are strongly emphasized.Comment: Final version to be published in FBS (54 pgs., 11 figs., 4 tabs

Optimization of R(e+e-) and "Freezing" of the QCD Couplant at Low Energies

The new result for the third-order QCD corrections to R_{e^+e^-}, unlike the old, incorrect result, is nicely compatible with the principle-of-minimal-sensitivity optimization method. Moreover, it leads to infrared fixed-point behaviour: the optimized couplant, alpha_s/pi, for R(e+e-) does not diverge at low energies, but "freezes" to a value 0.26 below about 300 MeV. This provides some direct theoretical evidence, purely from perturbation theory, for the "freezing" of the couplant -- an idea that has long been a popular and successful phenomenological hypothesis. We use the "smearing" method of Poggio, Quinn, and Weinberg to compare the resulting theoretical prediction for R(e+e-) with experimental data down to the lowest energies, and find excellent agreement.Comment: 27 pages, LaTeX, 8 uuencoded figures, DE-FG05-92ER40717-