Embedding Zprime models in SO(10) GUTs

TL;DR

This paper explores embedding Zprime models within SO(10) GUTs, analyzing gauge coupling unification, threshold corrections, and experimental constraints to understand the parameter space of Zprime interactions.

Contribution

It provides a detailed analysis of gauge coupling unification constraints and threshold corrections in SO(10) GUTs with Zprime models, including analytic and numerical results.

Findings

Allowed regions for gauge coupling constants identified.

1-loop and 2-loop RGEs compared with experimental data.

Threshold corrections significantly affect unification constraints.

Abstract

We embed a theory with Zprime gauge boson (related to extra U(1) gauge group) into a supersymmetric GUT theory based on SO(10). Two possible sequences of SO(10) breaking via VEVs of appropriate Higgs fields are considered. Gauge coupling unification provides constraints on low energy values of two additional gauge coupling constants related to Zprime interactions with fermions. Our main purpose is to investigate in detail the freedom in these two values due to different scales of subsequent SO(10) breaking and unknown threshold mass corrections in the gauge RGEs. These corrections are mainly generated by Higgs representations and can be large because of the large dimensions of these representations. To account for many free mass parameters, effective threshold mass corrections have been introduced. Analytic results that show the allowed regions of values of two additional gauge coupling constants have been derived at 1-loop level. For a few points in parameter-space that belong to one of these allowed regions 1-loop running of gauge coupling constants has been compared with more precise running, which is 2-loop for gauge coupling constants and 1-loop for Yukawa coupling constants. 1-loop results have been compared with experimental constraints from electroweak precision tests and from the most recent LHC data.