Unification without low-energy supersymmetry

Abstract

Abstract. Without supersymmetry, the gauge couplings in the standard model with five Higgs doublets unify around 10 14 GeV. In this case, the trinified model, SU(3) C × SU(3) L × SU(3) R × 3 , with the minimal Higgs sector required for symmetry breaking, is the ideal grand-unified candidate. Small neutrino masses are generated via a radiative seesaw mechanism, without the need for intermediate scales, additional Higgs fields, or higher-dimensional operators. The proton lifetime is above the experimental limits, with the decay modes p →νK + and p → µ + K 0 potentially observable. The split-SUSY version of the model, with one light Higgs doublet, is equally attractive.Grand unification of the strong, weak, and electromagnetic interactions into a simple gauge group is a very appealing idea that has been vigorously pursued for many years. The fact that the three gauge couplings of the minimal supersymmetric standard model meet almost exactly at M U = 2 × 10 16 GeV, has made supersymmetric GUTs a beautiful framework for theories beyond the standard model (SM). However, if we go beyond SU(5), as suggested by neutrino experiments, we do not need single-step unification. Furthermore, unification is possible without supersymmetry if we extend the Higgs sector of the SM to five or six Higgs doublets [1].In this talk, we present a viable candidate for a unified theory without (low-energy) supersymmetry [2]. Since the unification of the gauge couplings occurs at a lower scale, M U ≃ 10 14 GeV, we do not choose a simple GUT group, which would yield too rapid proton decay. Instead, we consider a product group, supplemented with a discrete symmetry to enforce the equality of the gauge couplings. The simplest theory of this type that has the same condition on the gauge couplings at the unification scale as SU (5) . As we shall see, the minimal trinified model can have as many as five light Higgs doublets. Minimal TrinificationWe begin by briefly reviewing the minimal trinified model [2,3]. The gauge bosons are assigned to the adjoint representation, the fermions to ψ