Anomalous dimensions of operators in polarized deep inelastic scattering at O(1/N_f)

Critical exponents are computed for a variety of twist-2 composite operators, which occur in polarized and unpolarized deep inelastic scattering, at leading order in the 1/N_f expansion. The resulting d-dimensional expressions, which depend on the moment of the operator, are in agreement with recent explicit two and three loop perturbative calculations. An interesting aspect of the critical point approach which is used, is that the anomalous dimensions of the flavour singlet eigenoperators, which diagonalize the perturbative mixing matrix, are computed directly. We also elucidate the treatment of gamma^5 at the fixed point which is important in simplifying the calculation for polarized operators. Finally, the anomalous dimension of the singlet axial current is determined at O(1/N_f) by considering the renormalization of the anomaly in operator form.Comment: 22 latex pages plus 7 figure

Destabilising Divergences in the NMSSM

The problem of destabilising divergences is discussed for singlet extensions of the MSSM. It is shown that models which possess either gauged-$R$ symmetry or target space duality at the Planck scale are able to circumvent this problem whilst avoiding cosmological domain walls.Comment: 19 pages, 5 figures requiring axodraw.sty, plain LaTeX, to appear in Nucl.Phys.

Naturally Light Higgs Doublets in the Supersymmetric Grand Unified Theories with Dynamical Symmetry Breaking

We construct a supersymmetric grand unified model in which a dynamical symmetry breaking of SU(5)$_{GUT}$ generates large masses for color-triplet Higgs multiplets while keeping SU(2)$_L$-doublet Higgs multiplets naturally light. The vanishing masses for the Higgs doublets are guaranteed by the Peccei-Quinn symmetry. We also show that the Peccei-Quinn symmetry suppresses the dangerous dimension 5 operators for the nucleon decay

Resolving the Constrained Minimal and Next-to-Minimal Supersymmetric Standard Models

We perform a detailed analysis of the next-to-minimal supersymmetric standard model (NMSSM), imposing the constraints of two-loop gauge coupling unification, universal soft supersymmetry breaking and the correct pattern of electroweak symmetry breaking. We compare our results with those for the minimal supersymmetric standard model (MSSM) using closely related techniques and, as far as possible, a common set of input and output variables. In general, in the constrained NMSSM, there are much stronger correlations between parameters than in the constrained MSSM, and we map out the allowed parameter space. We also give a detailed discussion of how to resolve the two models experimentally, concentrating primarily on the prospects at LEPII.Comment: 76 pages, latex, no macros, uuencoded figures included separately. This version (to appear in Phys. Rev. D) contains various minor change