Quantum guts of the minimal potentially realistic $\mathrm{SO}(10)$ Higgs model

Abstract

We study several aspects of the quantum structure of the minimal potentially realistic renormalizable SO( 10) Higgs model in which the 45 ⊕ 126 scalars spontaneously break the symmetry down to the Standard Model group SU(3) c × SU(2) L × U(1) Y . With a complete information about the one-loop corrections to the masses of all scalars in the theory and the one-loop beta functions governing the running of all dimensionless scalar self-couplings, the domains of the parameter space where the model can be treated perturbatively are established, along with improved bounds from the requirements of the SM vacuum stability and gauge coupling unification. We demonstrate that the model is fully consistent and potentially realistic only in very narrow regions of the parameter space corresponding to the breaking chains with well pronounced SU(4) C × SU(2) L × U(1) R and SU(3) c × SU(2) L × SU(2) R × U(1) B−L intermediate symmetries, with a clear preference for the former case. Barring accidental fine-tunings in the scalar sector, this makes it possible to provide a very sharp prediction for the position of the unification scale and the value of the associated gauge coupling, with clear implications for the phenomenology of grand unified models based on this structure.

Searches for baryon number violation in neutrino experiments: a white paper

“…In [168], a minimal renormalizable model with a symmetry breaking sector consisting of Higgs fields in the 10 54 126 + + is analyzed and shown to have an upper limit on the lifetime τ p (p → e + π 0 )  5 × 10 35 years. A variant of this framework with the adjoint 45 scalar instead of 54 has been studied thoroughly in [169,170] due to its very special quantum structure [171][172][173] and particular robustness with respect to the leading Planck-scale effects.…”

“…As for the first class, the most prominent of these effects are the uncertainties related to the generally unknown shape of the GUT-scale spectrum of the models at stakes, to the proximity of the GUT and the Planck scales enhancing the uncontrolled corrections from higher-dimensional operators (for instance those due to gravity effects) [244][245][246] and to the limited precision attainable in the perturbative accounts (see e.g. [173]), all inflicting uncertainties in the GUT-scale matching conditions. The second class corresponds to the (c here represents the coefficient of a Planck suppressed dimension-5 operator, for details, see [110].)…”