Particle theory

Abstract:

We propose a general scheme for constructing models in which the Standard Model (SM) gauge interactions are the mediators of supersymmetry breaking to the fields in the supersymmetric SM, but where the SM gauge groups couple directly to the sector which breaks supersymmetry dynamically. Despite the direct coupling, the models preserve perturbative unification of the SM gauge coupling constants. Furthermore, the supergravity contributions to the squark and slepton masses can be naturally small, typically being much less than 1% of the gauge-mediated (GM) contributions. Both of these goals can be achieved without need of a fine-tuning or a very small coupling constant. This scheme requires run-away directions at the renormalizable level which are only lifted by non-renormalizable terms in the superpotential. To study the proposed scheme in practice, we develop a modified class of models based on SU(N) x SU(N - 1) which allows us to gauge an SU(N - 2) global symmetry. However, we point out a new problem which can exist in models where the dynamical supersymmetry breaking sector and the ordinary sector are directly coupled - the two-loop renormalization group has contributions which can induce negative (mass)(2) for the squarks and sleptons. We clarify the origin of the problem and argue that it is likely to be surmountable. We give a recipe for a successful model. (C) 1998 Published by Elsevier Science B.V.

Abstract:

The spectrum for the pure gauge sector is calculated for an extended Isgur-Paton model in 2+1 and 3+1 dimensions and compared to recent lattice calculations of the glueball spectrum. The IP model is extended by inclusion of a rigidity (curvature) term and, in D=2+1, mixing through a higer topological contribution. For a choice of parameterizations, near quantitative agreement is found for SU(3) in D=2+1, but in D=3+1 the extensions fail to remedy the qualitative disagreement.

Abstract:

In the maximally Abelian gauge of SU(2), the clusters of monopole current are found to divide into two distinct classes. The largest cluster permeates the lattice, has a density that scales and produces the string tension. The remaining clusters possess an approximate 1/l3 number density distribution (1 is the cluster length), their radii vary as √1 and their total current density does not scale. Their contribution to the string tension is compatible with being exactly zero. Their number density can be thought of as arising from an underlying scale invariant distribution. This suggests that they are not related to instantons. We also observe that when we locally smoothen the SU(2) fields by cooling, the string tension due to monopoles becomes much smaller than the SU(2) string tension. This dramatic loss of Abelian/monopole dominance occurs even after just one cooling step.

Abstract:

We show that the monopole currents which one obtains in the maximally Abelian gauge of SU(2) fall into two quite distinct classes (when the volume is large enough). In each field configuration there is precisely one cluster that permeates the whole lattice volume. It has a current density and a magnetic screening mass that scale and it produces the whole of the string tension. The remaining clusters have a number density that follows an approximate power law [Formula Presented] where [Formula Presented] is the length of the monopole world line in lattice units. These clusters are localized in space-time with radii which vary as [Formula Presented]. In terms of the radius [Formula Presented] these “lumps” have a scale-invariant distribution [Formula Presented]. Moreover they appear not to contribute at all to the string tension. The fact that they are scale invariant at small distances would seem to rule out an instanton origin. © 1998 The American Physical Society.