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.Comment: Talk at Lattice '94: 3 pages, latex using espcrc2 and epsf with 4 tar'd and feathered PS figures appended in self-extracting shell archive. PostScript file available on the WorldWide Web as http://python.swan.ac.uk/~pypeters/p2pbiel.p

Properties of the non-Gaussian fixed point in 4D compact U(1) lattice gauge theory

We examine selected properties of the gauge-ball spectrum and fermionic variables in the vicinity of the recently discussed non-Gaussian fixed point of 4D compact U(1) lattice gauge theory within the quenched approximation. Approaching the critical point from within the confinement phase, our data support scaling of $T1^{+-}$ gauge-ball states in units of the string tension square root. The analysis of the chiral condensate within the framework of a scaling form for the equation of state suggests non mean-field values for the magnetic exponents $\delta$ and $\beta_{exp}$.Comment: 73K postscript fil

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.Comment: LATTICE98(confine

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 $-\sum_P(\beta \cos\Theta_P + \gamma \cos2\Theta_P)$ is used with $\gamma= -0.2$ 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 $\nu_{ng}\approx 0.36$. The $A_1^{++}$ gauge-ball mass scales with the Gaussian value $\nu_{g} \approx 0.5$ in the investigated range of correlation lengths. The static potential is examined with Sommer's method. The long range part scales consistently with $\nu_{ng}$ but the short range part tends to yield smaller values of $\nu$. The $\beta$-function, having a UV stable zero, is obtained from the running coupling. These results hold for both $\gamma$ values, supporting universality. Consequences for the continuum limit of the theory are discussed.Comment: Contribution to the Lattice 97 proceedings, LaTeX, 3 pages, 3 figure

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.Comment: LaTeX2e, 20 pages, 15 figures with epsfig; uses amstex, amssymb, a4wide; minor change to presentation (notation for operators) onl

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 $S = -\sum_P [\beta \cos(\Theta_P) + \gamma \cos(2\Theta_P)]$ we address the question of universality of the phase transition line in the ($\beta,\gamma$) plane between the confinement and the Coulomb phases. Our present results at $\gamma= -0.5$ for the gauge-ball spectrum are fully consistent with the previous results obtained at $\gamma= -0.2$. Again, two different correlation length exponents, $\nu_{ng} = 0.35(3)$ and $\nu_{g} = 0.49(7)$, 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 $\gamma\leq -0.2$.Comment: 16 page

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.Comment: 22 pages plus three PostScript figures (appended), Liverpool preprint LTH 288, University of Michigan preprint UM-TH-92-2

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.Comment: 18 pages, 8 figures, LaTeX 2e with epsfig and amstex; discussion following eq. 24 modified; figure 8 replotted; various references added; substance unchange

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 $\nu=0.89\pm 0.07$. The specific heat exponent, $\alpha=0.2\pm 0.15$, 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.Comment: 9 pages latex plus 5 postscript figures, OUTP 92/40