Reduction in the number of coupling parameters

Abstract

A method is developed for reducing the formulation of massless models with several independent couplings to a description in terms of a single coupling parameter. The original as well as the reduced system are supposed to be renormalizable and invariant under the renormalization group. For most models there are, if any, only a finite number of reductions possible including those which correspond to symmetries of the system. The reduction method leads to a consistent formulation of the reduced model in any order of perturbation theory even in cases where it is difficult to establish a symmetry in higher orders. An example where no symmetry seems to be involved is the interaction of a spinor field with a pseudoscalar field. For this model the reduction method determines the quartic coupling constant uniquely as a function of the Yukawa coupling constant. The Wess-Zumino model is an exceptional case for which the reduction method admits an infinite number of solutions besides the supersymmetric one.

Constraints on finite soft supersymmetry-breaking terms

“…In most studies the freedom resulted as a consequence of the degeneracy in the one-and two-loop solutions has been used to make specific ansätze that could lead to phenomenologically acceptable predictions. Note that the existence of such freedom is incompatible with the power series solutions [7,17].…”

“…Thus, the idea of gauge-Yukawa unification (GYU) [4]- [6] relies not only on a symmetry principle, but also on the principle of reduction of couplings [7,8] (see also [9]). This principle is based on the existence of RGI relations among couplings, which do not necessarily result from a symmetry, but nevertheless preserve perturbative renormalizability or even finiteness.…”

Constraints on Finite Soft Supersymmetry Breaking Terms

“…(6). Note further that the O(g 3 ) term is absent in (7). As for b ij there is no constraint; b ij is finite if eqs.…”

Superconformal transformation properties of the supercurrent

“…which fixes the couplingξ uniquely as a function of the coupling g and thus amounts to a reduction of couplings [13].…”

“…The spinorial components 13) such that a theory involving A + , A − describes the coupling of a Dirac particle to the electromagnetic field. The appropriate gauge superfield Φ is dimensionless and real.…”