Realizing unification in two different SO(10) models with one intermediate breaking scale

TL;DR

This paper calculates threshold corrections in two SO(10) grand unified models with intermediate symmetry breaking scales, showing that large corrections are needed for unification, which challenges their viability given experimental proton decay limits.

Contribution

It provides detailed threshold correction calculations for two specific SO(10) models with intermediate scales, assessing their compatibility with gauge unification and experimental constraints.

Findings

Both models require large threshold corrections for unification.

Unification is disfavored due to the need for large corrections.

Predicted proton lifetime is below current experimental bounds.

Abstract

We derive the threshold corrections in $\mathrm{SO}(10)$ grand unified models with the intermediate symmetry being flipped $\mathrm{SU}(5)\times\mathrm{U}(1)$ or $\mathrm{SU}(3)\times\mathrm{SU}(2)\times\mathrm{U}(1)\times\mathrm{U}(1)$, with the masses of the scalar fields set by the survival hypothesis. These models do not achieve gauge coupling unification if the matching conditions do not take threshold corrections into account. We present results showing the required size of threshold corrections for any value of the intermediate and unification scales. In particular, our results demonstrate that both of these models are disfavored since they require large threshold corrections to allow for unification with a predicted proton lifetime above current experimental bounds.