Abstract: Simple SO(10) Higgs models with the adjoint representation triggering the grand unified symmetry breaking, discarded long ago due to inherent tree-level tachyonic instabilities in the physically interesting scenarios, have been recently brought back to life by quantum effects. In this work we focus on the variant with 45(H) circle plus 126(H) in the Higgs sector and show that there are several regions in the parameter space of this model that can support stable unifying configurations with the B – L-breaking scale as high as 10(14) GeV, well above the previous generic estimates based on the minimal survival hypothesis. This admits for a renormalizable implementation of the canonical seesaw and makes the simplest potentially realistic scenario of this kind a good candidate for a minimal SO(10) grand unification. Last, but not least, this setting is likely to be extensively testable at future large-volume facilities such as Hyper-Kamiokande.

Abstract: In calculations of the elementary scalar spectra of spontaneously broken gauge theories there are a number of subtleties which, though it is often unnecessary to deal with them in the order-of-magnitude type of calculations, have to be taken into account if fully consistent results are sought for. Within the “canonical” effective-potential approach these are, for instance: the need to handle infinite series of nested commutators of derivatives of field-dependent mass matrices, the need to cope with spurious IR divergences emerging in the consistent leading-order approximation and, in particular, the need to account for the fine interplay between the renormalization effects in the one-and two-point Green functions which, indeed, is essential for the proper stable vacuum identification and, thus, for the correct interpretation of the results. In this note we illustrate some of these issues in the realm of the minimal Abelian Higgs model and two of its simplest extensions including extra heavy scalars in the spectrum in attempt to exemplify the key aspects of the usual “hierarchy problem” lore in a very specific and simple setting. We emphasize that, regardless of the omnipresent polynomial cut-off dependence in the one-loop corrections to the scalar two-point function, the physical Higgs boson mass is always governed by the associated symmetry-breaking VEV and, as such, it is generally as UV-robust as all other VEV-driven masses in the theory.

Abstract: We investigate the conditions on the Higgs sector that allow supersymmetric SO(10) grand unified theories to break spontaneously to the standard electroweak model at the renormalizable level. If one considers Higgs representations of dimension up to the adjoint, a supersymmetric standard model vacuum requires, in most cases, the presence of nonrenormalizable operators. The active role of Planck-induced nonrenormalizable operators in the breaking of the gauge symmetry introduces a hierarchy in the mass spectrum at the grand unified theory scale that may be an issue for gauge unification and proton decay. We show that the minimal Higgs scenario that allows for a renormalizable breaking to the standard model is obtained by considering flipped SO(10) circle times U(1) with one adjoint (45(H)) and two pairs of 16(H) circle plus (16) over bar (H) Higgs representations. We consider a nonanomalous matter content and discuss the embedding of the model in an E-6 grand unified scenario just above the flipped SO(10) scale.