K.C. Bowler

Hadron Mass Calculations With Susskind and Wilson Fermions in the Fundamental Adjoint Plane

Abstract We report the results of hadron mass calculations in the valence (quenched) approximation, on an 8 3 × 16 lattice. For Wilson fermions with the standard Wilson action we find good agreement with results form the hopping parameter expansion on a 16 4 lattice at β = 5.7, with only a small finite size effect in the anticipated direction. The proton-to-rho mass ration is however too high by 60% and the delta-proton mass difference is too small. We have repeated these calculations at two points of the same string tension in the plane of the fundamental and adjoint couplings, in an attempt to avoid the unphysical critical point there; within statistical errors the meson masses remain the same, there is an improvement in the delta-proton splitting and the proton mass decreases slightly, but not enough to produce agreement with experiment. The estimates of lines of constant string tension obtained as a preliminary to the mass calculation are in good agreement with weak coupling expansions at the larger β values and cross over towards strong coupling predictions around β = 5.7. Also, crude estimates reveal the disappearance of the specific heat peak as one moves away from the unphysical singularity. For Susskind fermions we find some measure of agreement with other results form a 10 3 × 16 lattice, but large, apparently finite size, effects in the rho mass at low quark mass. Meson masses in lattice units disagree with the Wilson fermion results by as much as a factor of 2. This disagreement persists in the fundamental-adjoint plane, suggesting the importance of studying improved fermion actions. At β = 6.0, Wilson fermion results show clear finite size effects on the 8 3 × 16 lattice.

Phase diagrams of U(1) lattice Higgs models

Abstract Phase diagrams for charge-one and charge-two scalar particles in compact QED are constructed using Monte Carlo methods on the ICL DAP computer. The results are in agreement with the features predicted by Fradkin and Shenker and with known and new limiting cases.

Large scale applications of transputers in HEP: The Edinburgh concurrent supercomputer project

Abstract The Edinburgh Concurrent Supercomputer Project is built around a Meiko Computing Surface, with presently some 400 floating-point transputers and 1.6 Gbytes of memory. The first part of this paper gives a brief overview of the projects origins and status. In the second part we review the results of applications in high energy physics, including lattice gauge theory and Monte Carlo event simulation.

Quenched heavy-light decay constants

We present results for heavy-light decay constants, using both propagating quarks and the static approximation, in O(a)-improved, quenched lattice QCD. At beta=6.2 on a 24^3x48 lattice we find f_D=185 +4-3(stat)+42-7(syst) MeV, f_B=160 +6-6 +53-19 MeV, f_{D_s}/f_D=1.18 +2-2 and f_{B_s}/f_B=1.22 +4-3, in good agreement with earlier studies. From the static theory we obtain f_B^stat=253 +16-15 +105-14 MeV. We also present results from a simulation at beta=6.0 on a 16^3x48 lattice, which are consistent with those at beta=6.2. In order to study the effects of improvement, we present a direct comparison of the results using both the Wilson and the improved action at beta=6.0.

Hadron mass calculations using susskind fermions at β = 5.7 and 6.0

Abstract Hadron masses are calculated in quenched quantum chromodynamics (QCD) using pure gauge configurations on 16 4 lattices, periodically extended in time where necessary. We use the Susskind formulation of lattice fermions and construct the propagators for hadrons created by local lattice operators. The inversion of the fermion matrix is accomplished using either the even/odd partitioned conjugate gradient algorithm, or block successive over-relaxation, depending on lattice size. Low statistics results at β = 5.7 confirm the high value of the nucleon-to-rho mass ratio found on smaller lattices. Together with the absence of flavour symmetry in the meson spectrum, this leads us to conclude that continuum behaviour is not observed at this coupling. Higher statistics results at β = 6.0 give a nucleon-to-rho mass ratio of approximately 1.5 and satisfy flavour symmetry in the meson sector to within 10%. We observe two baryon timeslice propagators which become increasingly different as the quark mass is decreased. This effect appears to be exaggerated by our choice of antiperiodic boundary conditions in space and is interpreted as a finite size effect.

Exploiting Highly Concurrent Computers for Physics

Computational physics—that is, the use of computers to solve problems by simulating theoretical models—is part of a new methodology that has taken its place alongside theory and experiment during the last 50 years or so. Computer simulations permit one to study microscopic properties and their macroscopic consequences in a host of problems that may be inaccessible to direct experimental study or too complex for theoretical analysis. Thus computers have become laboratories for experimenting with theories. The growth of computational physics has been fueled by the explosion in the availability of relatively cheap and powerful computers—and, for just that reason, the field is utterly dependent for its good health on continued advances in computer technology.

Monte Carlo algorithms for gauge fields in quenched lattice QCD

Abstract We present the results of a comparative study of the properties of SU(3) gauge field configurations generated by the Metropolis algorithm and by a modified heat-bath algorithm. Measurement of the average plaquette and of the Wilson line for ensembles of configurations generated by the two methods are compared and suggest that the modified heat-bath algorithm is significantly better at avoiding persistence of metastable states. We also report the result of a recomputation of the pion propagator on an 83 × 16 lattice at g2 = 1.0 using an ensemble of 40 configurations generated by the modified heat-bath algorithm. We find that correlations between particle masses and Wilson line expectation values are reduced and we estimate the critical value of the hopping parameter Kc = 0.156±0.001.

Quenched hadron mass calculations using staggerred fermions at β = 6.15 and 6.3

Abstract We report results of quenched hadron mass calculations using 16 3 × 24 lattices, extending our earlier work to higher values of β. We continue to use staggered fermions and local lattice hadron operators. At β = 6.15, there is good flavour symmetry in the meson sector and indications that finite-size effects are small for quark masses between 0.01 and 0.16 in lattice units. Although there is some indication of crossover from the heavy- to the light-quark regime in the nucleon-to-rho mass ratio, finite-size effects prevent us making measurements at quark masses for which the pion is significantly less than half the mass of the rho. At 0β = 6.3 the finite-size effects appear to be substantially worse.

Concurrency and parallelism in MC and MD simulations in physics

Abstract Certain problems lend themselves admirably to SIMD architecture computers. A number of such problems in physics will be discussed and their implementation on the ICL DAP analyzed. Monte Carlo (MC) problems such as the 3-D Ising model and quantum chromodynamics (QCD) calculations need care and attention with respect to maintaining detailed balance on a SIMD architecture, whereas molecular dynamics (MD) problems do not pose such problems. The efficient use of a DAP requires the development of parallel algorithms designed to make use of the particular architecture and size of the machine, though further software developments must be made which remove the user one stage farther from the particular details of the computer. Experience on the DAP, especially those with only 2 Mbytes of store such as the Edinburgh DAPs, has led to thought about the detailed precisions necessary for the various calculations being done—many computers operate at an accuracy which is in excess of requirement whereas the bit-serial DAP can have its program finely tuned in accuracy. The present DAPs are far from the modern state of the art in fabrication, and future engines of similar design could be made with present technology with a rating well over a Gflop, providing very cost-effective computing.

Nucleon wave functions from lattice-gauge theories: Measurements of baryonic operators

Abstract We present measurements of the matrix elements of certain 3-quark operators that govern the short-distance and light-cone properties of the proton wave function obtained on an 8 3 × 16 lattice at β = 5.7 with Wilson fermions. Using these measurements we find the proton lifetime in the minimal SU(5) grand unified theory to be incompatible with the current experimental limits, in accord with another recent lattice calculation.