arXiv subjects

P. W. Stephenson

Publications and source records attributed to P. W. Stephenson.

At least 19 recordsLinked to original sources

arXiv1999

Centre vortices and their friends

We report two probes of centre vortices in pure SU(2). First, we attempt to generate plaquette-size Z(2) vortices in a quasi-random way to compare the structure with those of projected centre vortices from the full theory; our prescription is, however, not completely random. Second, we test the effect of centre vortices on Wilson loops as a function of position. This shows clearly that the major effect is the piercing of the Wilson loop regardless of the position of the vortex inside.

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arXiv1999

Breaking of the adjoint string in 2+1 dimensions

The roughly linear rise of the potential found between adjoint sources in SU(N) in lattice simulations is expected to saturate into a state of two `gluelumps' due to gluonic screening. We examine this in SU(2) in 2+1 dimensions. Crossover between string-like and broken states is clearly seen by the mixing-matrix technique, using different operators to probe the two states; the breaking behaviour is rather abrupt. Furthermore, we are able to show that both types of operator have a finite overlap with both states; in the case of the Wilson loops the overlap with the broken string is, as predicted, very small.

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arXiv1998

Wilson loop distributions, higher representations and centre dominance in SU(2)

To help understand the centre dominance picture of confinement, we look at Wilson loop distributions in pure SU(2) lattice gauge theory. A strong coupling approximation for the distribution is developed to use for comparisons. We perform a Fourier expansion of the distribution: centre dominance here corresponds to suppression of odd terms beyond the first. The Fourier terms correspond to SU(2) representations; hence Casimir scaling behaviour leads to centre dominance. We examine the positive plaquette model, where only thick vortices are present. We show that a simple picture of random, non-interacting centre vortices gives a string tension about 3/4 of the measured value. Finally, we attempt to limit confusion about the adjoint representation.

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arXiv1998

Putting centre dominance under the microscope

We make various short points on the phenomenon of centre dominance in SU(2). The Z(2) dominance seen in Wilson loops is related to the loop distribution and to half-odd-integer representations of the group. The distributions also make it clear that, in this picture, the requirement of vortices for confinement is essentially trivial. We confirm that the same effect appears in the positive plaquette model. The simple random vortex picture is shown to give a substantial fraction of the string tension.

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arXiv1998

Universality of the gauge-ball spectrum of the four-dimensional pure U(1) gauge theory

We continue numerical studies of the spectrum of the pure U(1) lattice gauge theory in the confinement phase, initiated in our previous work. Using the extended Wilson action $ S = -\sum_P [β\cos(Θ_P) + γ\cos(2Θ_P)] $ we address the question of universality of the phase transition line in the ($β,γ$) plane between the confinement and the Coulomb phases. Our present results at $γ= -0.5$ for the gauge-ball spectrum are fully consistent with the previous results obtained at $γ= -0.2$. Again, two different correlation length exponents, $ν_{ng} = 0.35(3)$ and $ν_{g} = 0.49(7)$, are obtained in different channels. We also confirm the stability of the values of these exponents with respect to the variation of the distance from the critical point at which they are determined. These results further demonstrate universal critical behaviour of the model at least up to correlation lengths of 4 lattice spacings when the phase transition is approached in some interval at $γ\leq -0.2$.

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arXiv1998

Topological properties of full QCD at the phase transition

We investigate the topological properties of the QCD vacuum with 4 flavours of dynamical staggered fermions at finite temperature. To calculate the topological susceptibility we use the field-theoretical method. As in the quenched case, a sharp drop is observed for the topological susceptibility across the phase transition.

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arXiv1997

Scaling of gauge balls and static potential in the confinement phase of the pure U(1) lattice gauge theory

We investigate the scaling behaviour of gauge-ball masses and static potential in the pure U(1) lattice gauge theory on toroidal lattices. An extended gauge field action $-\sum_P(β\cosΘ_P + γ\cos2Θ_P)$ is used with $γ= -0.2$ and -0.5. Gauge-ball correlation functions with all possible lattice quantum numbers are calculated. Most gauge-ball masses scale with the non-Gaussian exponent $ν_{ng}\approx 0.36$. The $A_1^{++}$ gauge-ball mass scales with the Gaussian value $ν_{g} \approx 0.5$ in the investigated range of correlation lengths. The static potential is examined with Sommer's method. The long range part scales consistently with $ν_{ng}$ but the short range part tends to yield smaller values of $ν$. The $β$-function, having a UV stable zero, is obtained from the running coupling. These results hold for both $γ$ values, supporting universality. Consequences for the continuum limit of the theory are discussed.

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arXiv1997

Gauge-ball spectrum of the four-dimensional pure U(1) gauge theory

We investigate the continuum limit of the gauge-ball spectrum in the four-dimensional pure U(1) lattice gauge theory. In the confinement phase we identify various states scaling with the correlation length exponent $ν\simeq 0.35$. The square root of the string tension also scales with this exponent, which agrees with the non-Gaussian fixed point exponent recently found in the finite size studies of this theory. Possible scenarios for constructing a non-Gaussian continuum theory with the observed gauge-ball spectrum are discussed. The $0^{++}$ state, however, scales with a Gaussian value $ν\simeq 0.5$. This suggests the existence of a second, Gaussian continuum limit in the confinement phase and also the presence of a light or possibly massless scalar in the non-Gaussian continuum theory. In the Coulomb phase we find evidence for a few gauge-balls, being resonances in multi-photon channels; they seem to approach the continuum limit with as yet unknown critical exponents. The maximal value of the renormalized coupling in this phase is determined and its universality confirmed.

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arXiv1996

Physical and unphysical effects in the mixed SU(2)/SO(3) gauge theory

We investigate possible problems with universality in lattice gauge theory where a mixed fundamental SU(2) and SO(3)-invariant gauge group is used: the (second order) finite temperature phase transition becomes involved with first order effects with increased SO(3) coupling, and this first order effect has a noticeable coupling dependence for small lattices. We produce evidence that the first order transition is essentially bulk in nature as generally believed, and that the finite temperature effects start to separate out from the lower end of the bulk effects for a lattice of 8 sites in the finite temperature direction. We strengthen our picture of the first order effects as artefacts by using an improved action: this shifts the end point of the first order line away from the fundamental SU(2) axis.

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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

Point-to-point Hadron Correlation Functions using the Sheikholeslami--Wohlert Action

We calculate correlations between hadronic current operators as a function of their spatial separation, in a quenched lattice QCD simulation at $β=6.2$ on a $24^3\times48$ lattice. The lattice fermion formulation used is that due to Sheikholeslami and Wohlert. The correlation functions are then compared with the corresponding quantities calculated in the infinite volume chiral limit of the non-interacting theory. The ratio of the two quantities contains information on the vacuum structure of QCD. Results obtained are consistent with previous studies, and with known hadron phenomenology, although certain features of the fermion action used make it impossible to probe the $r\to0$ limit directly, thus limiting the accuracy possible.

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arXiv1994

Hadron correlators with improved fermions

We investigate point-to-point correlation functions for various mesonic and baryonic channels using the ${\cal O}(a)$-improved Wilson action due to Sheikholeslami and Wohlert. We consider propagators to both time slices 0 and 1. We find that discretisation effects are more pronounced than those reported with unimproved Wilson fermions, but that the same procedure for removing finite size effects is successful. Extrapolating to the chiral limit, we see the notable features predicted phenomenologically: the ratio of interacting to free correlators in the vector channel is roughly constant to about 1 fm, while in the pseudoscalar channel the ratio increases markedly due to the strong binding.

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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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arXiv1993

The running coupling from lattice gauge theory:

I discuss some calculations of the running coupling in SU($N$) gauge theories from lattice simulations, centering on the work of the UKQCD collaboration. This talk is introductory in nature; full details have been published elsewhere.

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arXiv1993

On the Crumpling Transition in Crystalline Random Surfaces

We investigate the crumpling transition on crystalline random surfaces with extrinsic curvature on lattices up to $64^2$. Our data are consistent with a second order phase transition and we find correlation length critical exponent $ν=0.89\pm 0.07$. The specific heat exponent, $α=0.2\pm 0.15$, is in much better agreement with hyperscaling than hitherto. The long distance behaviour of tangent-tangent correlation functions confirms that the so-called Hausdorff dimension is $d_H=\infty$ throughout the crumpled phase.

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arXiv1992

The effective potential and the renormalisation group

We discuss renormalisation group improvement of the effective potential both in general and in the context of $O(N)$ scalar $\p^4$ and the Standard Model. In the latter case we find that absolute stability of the electroweak vacuum implies that $m_H\geq 1.95m_t-189~GeV$, for $\as (M_Z) = 0.11$. We point out that the lower bound on $m_H$ {\it decreases\/} if $\as (M_Z)$ is increased.

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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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