We present results for one-loop matching coefficients between continuum fourfermion operators, de... more We present results for one-loop matching coefficients between continuum fourfermion operators, defined in the Naive Dimensional Regularization scheme, and staggered fermion operators of various types. We calculate diagrams involving gluon exchange between quark lines, and "penguin" diagrams containing quark loops. For the former we use Landau gauge operators, with and without O(a) improvement, and including the tadpole improvement suggested by Lepage and Mackenzie. For the latter we use gauge-invariant operators. Combined with existing results for two-loop anomalous dimension matrices and one-loop matching coefficients, our results allow a lattice calculation of the amplitudes for KK mixing and K → ππ decays with all corrections of O(g 2) included. We also discuss the mixing of ∆S = 1 operators with lower dimension operators, and show that, with staggered fermions, only a single lower dimension operator need be removed by non-perturbative subtraction.
We present results for the 0++ glueball mass (mo) and the string tension (o) in pure gauge lattic... more We present results for the 0++ glueball mass (mo) and the string tension (o) in pure gauge lattice QCD with a four-parameter improved action. We suggest and confirm that previous estimates for ma/v o have been too low because of the influence of the unphysical and nonuniversal phase structure in the fundamental-adjoint coupling plane. %e find that~=1200-1400 MeV using Vcr 420 MeV.
We present evidence from numerical simulations for a first-order chiral-symmetry-restoration tran... more We present evidence from numerical simulations for a first-order chiral-symmetry-restoration transition in QCD at finite temperature. The transition appears only for small quark masses. We use an exact algorithm to incorporate the dynamical quarks.
We calculate the kaon B-parameter in quenched lattice QCD at β = 6.0 using Wilson fermions at κ =... more We calculate the kaon B-parameter in quenched lattice QCD at β = 6.0 using Wilson fermions at κ = 0.154 and 0.155. We use two kinds of non-local ("smeared") sources for quark propagators to calculate the matrix elements between states of definite momentum. The use of smeared sources yields results with much smaller errors than obtained in previous calculations with Wilson fermions. By combining results for p = (0, 0, 0) and p = (0, 0, 1), we show that one can carry out the non-perturbative subtraction necessary to remove the dominant lattice artifacts induced by the chiral symmetry breaking term in the Wilson action. Our final results are in good agreement with those obtained using staggered fermions. We also present results for B-parameters of the ∆I = 3/2 part of the electromagnetic penguin operators, and preliminary results for B K in the presence of two flavors of dynamical quarks.
We investigate the use of two types of non-local (\smeared") sources for quark propagators in que... more We investigate the use of two types of non-local (\smeared") sources for quark propagators in quenched lattice QCD at = 6:0 using Wilson fermions at = 0:154 and 0:155. We present results for the hadron mass spectrum, meson decay constants, quark masses, the chiral condensate and the quark distribution amplitude of the pion. The use of smeared sources leads to a considerable improvement over previous results. We nd a disturbing discrepancy between the baryon spectra obtained using Wuppertal and wall sources. We nd good signals in the ratio of correlators used to calculate the quark mass and the chiral condensate and show that the extrapolation to the chiral limit is smooth.
Numerical lattice calculations provide strong evidence for the existence of a mass gap in pure ga... more Numerical lattice calculations provide strong evidence for the existence of a mass gap in pure gauge QCD.'Though straightforward in principle, these calculations are hampered by large statistical errors, with the problems becoming more severe as the continuum limit is ap-proached. In this paper we investigate methods to improve the signal, and givenew results for the scalar and tensor glueball masses in pure gauge QCD. Although the spectrum of pure gauge QCD cannotbe directly compared to experiment, it is important to pin it down ...
We calculate the perturbative corrections to fermion bilinears that are used in numerical simulat... more We calculate the perturbative corrections to fermion bilinears that are used in numerical simulations when extracting weak matrix elements using staggered fermions. This extends previous calculations of Golterman and Smit, and Daniel and Sheard. In particular, we calculate the corrections for non-local bilinears defined in Landau gauge with gauge links excluded. We do this for the simplest operators, i.e. those defined on a 2 4 hypercube, and for tree level improved operators which live on 4 4 hypercubes. We also consider gauge invariant operators in which the "tadpole" contributions are suppressed by projecting the sums of products of gauge links back in to the gauge group. In all cases, we find that the variation in the size of the perturbative corrections is smaller than those with the gauge invariant unimproved operators. This is most strikingly true for the smeared operators. We investigate the efficacy of the mean-field method of Lepage and Mackenzie at summing up tadpole contributions. In a companion paper we apply these results to four-fermion operators.
We show that the overrelaxed algorithm of Creutz and of Brown and Woch is the optimal local updat... more We show that the overrelaxed algorithm of Creutz and of Brown and Woch is the optimal local update algorithm for simulation of pure gauge SU(3). Our comparison criterion includes computer efficiency and decorrelation times. We also investigate the rate of decorrelation for the Hybrid Monte Carlo algorithm.
Description/Abstract We present results for the hadron spectrum of quenched lattice QCD on an 18/... more Description/Abstract We present results for the hadron spectrum of quenched lattice QCD on an 18/sup 3/x 42 lattice at.. beta..= 6.2. We compare r=(1/2 Wilson fermions with quark masses in the range m/sub q//m/sub s/= 1 to 5 to staggered fermions with m/sub q//m/sub s/=(1/3 to 2. In the overlap region we find that the spectra agree, and that both yield a/sup-1/approx.= 2.5 GeV, if we use m/sub rho/to set the scale. We also find that the flavor symmetry of the staggered fermions is restored to a greater degree than at lower.. beta... ...
We present preliminary results for BK calculated using improved staggered fermions with a mixed a... more We present preliminary results for BK calculated using improved staggered fermions with a mixed action (HYP-smeared staggered valence quarks and AsqTad st aggered sea quarks). We investigate the effect of non-degenerate quarks on BK and attempt to estimate the O(a2) effect due to nonGoldstone pions in loops. We fit the data to continuum partial ly quenched chiral perturbation theory. We find that the quality of fit for BK improves if we include non-degenerate quark mass combinations. We also observe, however, that the fitting cur ve deviates from the data points in the light quark mass region. This may indicate the need to inc lude taste-breaking in pion loops.
We present results for one-loop matching coefficients between continuum fourfermion operators, de... more We present results for one-loop matching coefficients between continuum fourfermion operators, defined in the Naive Dimensional Regularization scheme, and staggered fermion operators of various types. We calculate diagrams involving gluon exchange between quark lines, and “penguin” diagrams containing quark loops. For the former we use Landau gauge operators, with and without O(a) improvement, and including the tadpole improvement suggested by Lepage and Mackenzie. For the latter we use gauge-invariant operators. Combined with existing results for two-loop anomalous dimension matrices and one-loop matching coefficients, our results allow a lattice calculation of the amplitudes for KK mixing and K → ππ decays with all corrections of O(g) included. We also discuss the mixing of ∆S = 1 operators with lower dimension operators, and show that, with staggered fermions, only a single lower dimension operator need be removed by non-perturbative subtraction. October 1993 Email: sharpe@galile...
A brief overview of the status of lattice QCD is given, with emphasis on topics relevant to pheno... more A brief overview of the status of lattice QCD is given, with emphasis on topics relevant to phenomenology. The calculation of the light quark spectrum, the lattice prediction of [alpha] [sub [ovr MS]] (M [sub Z]), and the calculation of f[sub B] are discussed. 3 figs., 3 tabs., 40 refs.
We present results for one-loop matching coefficients between continuum fourfermion operators, de... more We present results for one-loop matching coefficients between continuum fourfermion operators, defined in the Naive Dimensional Regularization scheme, and staggered fermion operators of various types. We calculate diagrams involving gluon exchange between quark lines, and "penguin" diagrams containing quark loops. For the former we use Landau gauge operators, with and without O(a) improvement, and including the tadpole improvement suggested by Lepage and Mackenzie. For the latter we use gauge-invariant operators. Combined with existing results for two-loop anomalous dimension matrices and one-loop matching coefficients, our results allow a lattice calculation of the amplitudes for KK mixing and K → ππ decays with all corrections of O(g 2) included. We also discuss the mixing of ∆S = 1 operators with lower dimension operators, and show that, with staggered fermions, only a single lower dimension operator need be removed by non-perturbative subtraction.
We present results for the 0++ glueball mass (mo) and the string tension (o) in pure gauge lattic... more We present results for the 0++ glueball mass (mo) and the string tension (o) in pure gauge lattice QCD with a four-parameter improved action. We suggest and confirm that previous estimates for ma/v o have been too low because of the influence of the unphysical and nonuniversal phase structure in the fundamental-adjoint coupling plane. %e find that~=1200-1400 MeV using Vcr 420 MeV.
We present evidence from numerical simulations for a first-order chiral-symmetry-restoration tran... more We present evidence from numerical simulations for a first-order chiral-symmetry-restoration transition in QCD at finite temperature. The transition appears only for small quark masses. We use an exact algorithm to incorporate the dynamical quarks.
We calculate the kaon B-parameter in quenched lattice QCD at β = 6.0 using Wilson fermions at κ =... more We calculate the kaon B-parameter in quenched lattice QCD at β = 6.0 using Wilson fermions at κ = 0.154 and 0.155. We use two kinds of non-local ("smeared") sources for quark propagators to calculate the matrix elements between states of definite momentum. The use of smeared sources yields results with much smaller errors than obtained in previous calculations with Wilson fermions. By combining results for p = (0, 0, 0) and p = (0, 0, 1), we show that one can carry out the non-perturbative subtraction necessary to remove the dominant lattice artifacts induced by the chiral symmetry breaking term in the Wilson action. Our final results are in good agreement with those obtained using staggered fermions. We also present results for B-parameters of the ∆I = 3/2 part of the electromagnetic penguin operators, and preliminary results for B K in the presence of two flavors of dynamical quarks.
We investigate the use of two types of non-local (\smeared") sources for quark propagators in que... more We investigate the use of two types of non-local (\smeared") sources for quark propagators in quenched lattice QCD at = 6:0 using Wilson fermions at = 0:154 and 0:155. We present results for the hadron mass spectrum, meson decay constants, quark masses, the chiral condensate and the quark distribution amplitude of the pion. The use of smeared sources leads to a considerable improvement over previous results. We nd a disturbing discrepancy between the baryon spectra obtained using Wuppertal and wall sources. We nd good signals in the ratio of correlators used to calculate the quark mass and the chiral condensate and show that the extrapolation to the chiral limit is smooth.
Numerical lattice calculations provide strong evidence for the existence of a mass gap in pure ga... more Numerical lattice calculations provide strong evidence for the existence of a mass gap in pure gauge QCD.'Though straightforward in principle, these calculations are hampered by large statistical errors, with the problems becoming more severe as the continuum limit is ap-proached. In this paper we investigate methods to improve the signal, and givenew results for the scalar and tensor glueball masses in pure gauge QCD. Although the spectrum of pure gauge QCD cannotbe directly compared to experiment, it is important to pin it down ...
We calculate the perturbative corrections to fermion bilinears that are used in numerical simulat... more We calculate the perturbative corrections to fermion bilinears that are used in numerical simulations when extracting weak matrix elements using staggered fermions. This extends previous calculations of Golterman and Smit, and Daniel and Sheard. In particular, we calculate the corrections for non-local bilinears defined in Landau gauge with gauge links excluded. We do this for the simplest operators, i.e. those defined on a 2 4 hypercube, and for tree level improved operators which live on 4 4 hypercubes. We also consider gauge invariant operators in which the "tadpole" contributions are suppressed by projecting the sums of products of gauge links back in to the gauge group. In all cases, we find that the variation in the size of the perturbative corrections is smaller than those with the gauge invariant unimproved operators. This is most strikingly true for the smeared operators. We investigate the efficacy of the mean-field method of Lepage and Mackenzie at summing up tadpole contributions. In a companion paper we apply these results to four-fermion operators.
We show that the overrelaxed algorithm of Creutz and of Brown and Woch is the optimal local updat... more We show that the overrelaxed algorithm of Creutz and of Brown and Woch is the optimal local update algorithm for simulation of pure gauge SU(3). Our comparison criterion includes computer efficiency and decorrelation times. We also investigate the rate of decorrelation for the Hybrid Monte Carlo algorithm.
Description/Abstract We present results for the hadron spectrum of quenched lattice QCD on an 18/... more Description/Abstract We present results for the hadron spectrum of quenched lattice QCD on an 18/sup 3/x 42 lattice at.. beta..= 6.2. We compare r=(1/2 Wilson fermions with quark masses in the range m/sub q//m/sub s/= 1 to 5 to staggered fermions with m/sub q//m/sub s/=(1/3 to 2. In the overlap region we find that the spectra agree, and that both yield a/sup-1/approx.= 2.5 GeV, if we use m/sub rho/to set the scale. We also find that the flavor symmetry of the staggered fermions is restored to a greater degree than at lower.. beta... ...
We present preliminary results for BK calculated using improved staggered fermions with a mixed a... more We present preliminary results for BK calculated using improved staggered fermions with a mixed action (HYP-smeared staggered valence quarks and AsqTad st aggered sea quarks). We investigate the effect of non-degenerate quarks on BK and attempt to estimate the O(a2) effect due to nonGoldstone pions in loops. We fit the data to continuum partial ly quenched chiral perturbation theory. We find that the quality of fit for BK improves if we include non-degenerate quark mass combinations. We also observe, however, that the fitting cur ve deviates from the data points in the light quark mass region. This may indicate the need to inc lude taste-breaking in pion loops.
We present results for one-loop matching coefficients between continuum fourfermion operators, de... more We present results for one-loop matching coefficients between continuum fourfermion operators, defined in the Naive Dimensional Regularization scheme, and staggered fermion operators of various types. We calculate diagrams involving gluon exchange between quark lines, and “penguin” diagrams containing quark loops. For the former we use Landau gauge operators, with and without O(a) improvement, and including the tadpole improvement suggested by Lepage and Mackenzie. For the latter we use gauge-invariant operators. Combined with existing results for two-loop anomalous dimension matrices and one-loop matching coefficients, our results allow a lattice calculation of the amplitudes for KK mixing and K → ππ decays with all corrections of O(g) included. We also discuss the mixing of ∆S = 1 operators with lower dimension operators, and show that, with staggered fermions, only a single lower dimension operator need be removed by non-perturbative subtraction. October 1993 Email: sharpe@galile...
A brief overview of the status of lattice QCD is given, with emphasis on topics relevant to pheno... more A brief overview of the status of lattice QCD is given, with emphasis on topics relevant to phenomenology. The calculation of the light quark spectrum, the lattice prediction of [alpha] [sub [ovr MS]] (M [sub Z]), and the calculation of f[sub B] are discussed. 3 figs., 3 tabs., 40 refs.
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Papers by Stephen Sharpe