We calculate the prominent perturbative contributions shaping the one-loop scalar spectrum of the minimal renormalizable non-supersymmetric SO(10) Higgs model whose unified gauge symmetry is spontaneously broken by an adjoint scalar. Focusing on its potentially realistic 45 ⊕ 126 variant in which the rank is reduced by a VEV of the 5-index antisymmetric self-dual tensor, we provide a thorough analysis of the corresponding Coleman-Weinberg one-loop effective potential, paying particular attention to the masses of the potentially tachyonic pseudo-Goldstone bosons (PGBs) transforming as (1, 3, 0) and (8, 1, 0) under the Standard Model gauge group. The results confirm the assumed existence of extended regions in the parameter space supporting a locally stable SM-like quantum vacuum inaccessible at the tree-level. The effective potential (EP) tedium is compared to that encountered in the previously studied 45 ⊕ 16 SO(10) Higgs model where the polynomial corrections to the relevant pseudo-Goldstone masses turn out to be easily calculable within a very simplified purely diagrammatic approach.

It is a well-known fact that the minimal renormalizable supersymmetric SU(5) model is ruled out assuming superpartner masses of the order of a few TeV. Giving up this constraint and assuming only SU(5) boundary conditions for the soft terms, we find that the model is still alive. The viable region of the parameter space typically features superpartner masses of order 10 2 to 10 4 TeV, with tan β values between 2 and 5, but lighter spectra with single states around 10 TeV are also possible. The main constraints come from proton decay, the Higgs mass, the requirement of the SU(5) spectrum being reasonably below the Planck scale, and the lifetime of the universe. A generic feature of the model is metastability of the electroweak vacuum. In the absence of a suitable dark matter particle in the neutralino sector, a light (order GeV or smaller) gravitino is a natural candidate.

Abstract. We review the main constraints on the parameter space of the minimal renormalizable supersymmetric SU (5) grand unified theory. They consist of the Higgs mass, proton decay, electroweak symmetry breaking and fermion masses. Superpartner masses are constrained both from below and from above, giving hope for confirming or definitely ruling out the theory in the future. This contribution is based on Ref. [1].

We show that simultaneous gauge and supersymmetry breaking can be induced by radiative corrections,à la Coleman-Weinberg. When a certain correlation among the superpotential parameters is present, a local supersymmetry-breaking minimum is induced in the effective potential of a gauge non-singlet field, in a region where the tree-level potential is almost flat. Supersymmetry breaking is then transmitted to the MSSM through gauge and chiral messenger loops, thus avoiding the suppression of gaugino masses characteristic of direct gauge mediation models. The use of a single field ensures that no dangerous tachyonic scalar masses are generated at the one-loop level. We illustrate this mechanism with an explicit example based on an SU(5) model with a single adjoint. An interesting feature of the scenario is that the GUT scale is increased with respect to standard unification, thus allowing for a larger colour Higgs triplet mass, as preferred by the experimental lower bound on the proton lifetime.

We explore the potential of a selected model of radiative neutrino masses to be implemented in a renormalizable SU(5) unification framework. The Zee-type model under consideration uncovers the SU(5) representations in which the new fields are embedded and which may contain also other light states leading to the unification of gauge couplings. We perform an exhaustive search which reveals specific patterns of new states and demonstrate that such patterns are consistent with a general choice of relevant scalar potential. It turns out that all of the specific scenarios which lead to successful unification include the colored scalars testable at the LHC.