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C. Michael

Publications and source records attributed to C. Michael.

At least 109 records · Page 6Linked to original sources
arXiv1995

A Study of Degenerate Four-quark states in SU(2) Lattice Monte Carlo

The energies of four-quark states are calculated for geometries in which the quarks are situated on the corners of a series of tetrahedra and also for geometries that correspond to gradually distorting these tetrahedra into a plane. The interest in tetrahedra arises because they are composed of {\bf three } degenerate partitions of the four quarks into two two-quark colour singlets. This is an extension of earlier work showing that geometries with {\bf two} degenerate partitions (e.g.\ squares) experience a large binding energy. It is now found that even larger binding energies do not result, but that for the tetrahedra the ground and first excited states become degenerate in energy. The calculation is carried out using SU(2) for static quarks in the quenched approximation with $β=2.4$ on a $16^3\times 32$ lattice. The results are analysed using the correlation matrix between different euclidean times and the implications of these results are discussed for a model based on two-quark potentials.

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arXiv1995

Is the Quenched Spectrum in agreement with Experiment?

We analyse the meson spectrum in quenched QCD using lattice gauge theory. By studying hadron propagation with a variety of operators (both smeared and local), we are able to extract the ground state and first excited state masses with confidence. We pay attention to the correlations among the data used in the fits to extract these masses and couplings. We compare the resulting hadron spectrum with experiment and find evidence for a significant departure in the pseudoscalar and vector meson masses.

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arXiv1995

Cooling and the SU(2) Instanton Vaccuum

We present results of an investigation into the nature of instantons in 4-dimensional pure gauge lattice $SU(2)$\ obtained from configurations which have been cooled using an under-relaxed cooling algorithm. We discuss ways of calibrating the cooling and the effects of different degrees of cooling, and compare our data for the shapes, sizes and locations of instantons with continuum results. In this paper we extend the ideas and techniques developed by us for use in $O(3)$, and compare the results with those obtained by other groups.

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arXiv1994

Fitting Correlated Hadron Mass Spectrum Data

We discuss fitting hadronic Green functions versus time $t$ to extract mass values in quenched lattice QCD. These data are themselves strongly correlated in $t$. With only a limited number of data samples, the method of minimising correlated $χ^2$ is unreliable. We explore several methods of modelling the correlations among the data set by a few parameters which then give a stable and sensible fit even if the data sample is small. In particular these models give a reliable estimate of the goodness of fit.

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arXiv1994

Efficient Hadronic Operators in Lattice Gauge Theory

We study operators to create hadronic states made of light quarks in quenched lattice gauge theory. We construct non-local gauge-invariant operators which provide information about the spatial extent of the ground state and excited states. The efficiency of the operators is shown by looking at the wave function of the first excited state, which has a node as a function of the spatial extent of the operator. This allows one to obtain an uncontaminated ground state for hadrons.

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arXiv1994

Instanton size distributions from calibrated cooling

Using an under-relaxed cooling algorithm we investigated the vacuum in the $2d\ O(3)$ model and $4d$ pure gauge $SU(2)$. We calibrated the amount of cooling performed to have similar physical effect at different lattice spacings.

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arXiv1994

Four-Quark Binding Energies from SU(2) Lattice Monte Carlo

Energies of four-quark systems have been extracted in a static quenched SU(2) lattice Monte Carlo calculation for six different geometries, both planar and non-planar, with $β=2.4$ and lattice size $16^3\times 32$. In all cases, it is found that the binding energy is greatly enhanced when the four quarks can be partitioned in two ways with comparable energies. Also it is shown that the energies of the four-quark states cannot be understood simply in terms of two-quark potentials.

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arXiv1994

Instanton size distribution in O(3)

We present calculations of the size distribution of instantons in the 2d O(3) non-linear sigma-model, and briefly discuss the effects cooling has upon the configurations and the topological objects. (This preprint is also available via anonymous ftp to suna.amtp.liv.ac.uk in /pub/pss/ as instdist.uue.)

hep-lat↗
arXiv1994

The Nature of the Hadronic String

We study a closed hadronic string using pure glue lattice simulation. We measure the energy of the flux state encircling the periodic boundary condition (the torelon). From these data we deduce the string fluctuation component and compare with models for the hadronic string. [The TEX source file is also available by anonymous ftp from suna.amtp.liv.ac.uk in directory pub/cmi ]

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arXiv1994

Topography of the cooled $\cal{O}(3)$ vacuum

We investigate the {\it topography\/} of the \o3 vacuum after various degrees of under-relaxed cooling, using the na\"ıve action density and geometric and field theoretical definitions of the topological charge density. The results are presented graphically. (This is a cutdown version of the full paper which is available via anonymous ftp to suna.amtp.liv.ac.uk in /pub/pss/. The figures missing from this version are available from the same site.)

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arXiv1993

Fitting Correlated Data

We discuss fitting correlated data - with the example of hadron mass spectroscopy in mind. The main conclusion is that the method of minimising correlated $χ^2$ is unreliable if the data sample is too small.

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arXiv1993

Multi-Quark Energies in SU(2) Lattice Gauge Theory

Energies of four-quark systems have been extracted in a quenched SU(2) lattice Monte Carlo calculation for two different geometries, rectangular and colinear, with $β=2.4$ and lattice size $16^3\times 32$. Also, by going to a lattice $24^3\times 32$ and to $β=2.5$, the effect of the finite lattice size and scaling are checked. An attempt is made to understand these results in terms of a model based on interquark two-body potentials but modified very significantly by a phenomenological gluon-field overlap factor.

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arXiv1992

Multi-quark energies in QCD

Four-quark potentials for $SU(2)$ are evaluated in the static limit with the quenched approximation -- using a lattice of $16^3\times 32$ and $β=2.4$. The four quarks are restricted to the corners of rectangles with sides upto seven lattice spacings long. The results are analysed in terms of a strategy based on interquark two-body potentials -- as advocated earlier by the authors. This shows that a standard two-body approach overestimates the four-quark binding energy by upto a factor of about three for the largest rectangles.

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arXiv1992

The Running Coupling from SU(3) Lattice Gauge Theory

{}From an accurate determination of the inter-quark potential, one can study the running coupling constant for a range of $R$-values and hence estimate the scale $Λ_{\msbar} $. Detailed results are presented for $SU(3)$ pure gauge theory.

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arXiv1992

SU(2) Potentials from Large Lattices

We measure accurate values of the inter-quark potentials on a $48^{3}56$ lattice with SU(2) pure gauge theory at $ β=2.85$. The scale is set by extracting the string tension - we obtain ${\sqrt K}a=0.063(3)$ at $β=2.85.$ From a careful study of the small-$R$ potentials in the region 2 GeV $< R^{-1} < 5$ GeV, we extract a running coupling constant and estimate the scale $Λ_{\msbar} = 272(24)$ MeV.

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arXiv1992

The Hyperfine Splitting in Charmonium: Lattice Computations Using the Wilson and Clover Fermion Actions

We compute the hyperfine splitting $m_{J/ψ}-m_{η_c}$ on the lattice, using both the Wilson and $O(a)$-improved (clover) actions for quenched quarks. The computations are performed on a $24^3\times48$ lattice at $β= 6.2$, using the same set of 18 gluon configurations for both fermion actions. We find that the splitting is 1.83\err{13}{15} times larger with the clover action than with the Wilson action, demonstrating the sensitivity of the spin-splitting to the magnetic moment term which is present in the clover action. However, even with the clover action the result is less than half of the physical mass-splitting. We also compute the decay constants $f_{η_c}$ and $f^{-1}_{J/ψ}$, both of which are considerably larger when computed using the clover action than with the Wilson action. For example for the ratio $f^{-1}_{J/ψ}/f^{-1}_ρ$ we find 0.32\err{1}{2} with the Wilson action and $0.48\pm 3$ with the clover action (the physical value is 0.44(2)).

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