Visualizing gauge unification with high-scale thresholds

TL;DR

This paper introduces $\Delta\lambda$ plots as a new IR analysis tool to evaluate high-scale threshold corrections in gauge unification, aiding the assessment of supersymmetric and non-supersymmetric theories.

Contribution

It proposes $\Delta\lambda$ plots for efficient high-scale threshold analysis, clarifies prospects for non-supersymmetric unification, and compares threshold requirements in $SO(10)$ and $SU(5)$ models.

Findings

$\Delta\lambda$ plots provide qualitative and quantitative insights into threshold corrections.

Non-supersymmetric $SO(10)$ unification shows feasible threshold corrections.

Supersymmetric $SU(5)$ requires low summed threshold corrections, indicating potential tuning.

Abstract

Tests of gauge coupling unification require knowledge of thresholds between the weak scale and the high scale of unification. If these scales are far separated, as is the case in most unification scenarios considered in the literature, the task can be factorized into IR and UV analyses. We advocate "$\Delta\lambda$ plots" as an efficient IR analysis projected to the high scale. The data from these plots gives an immediate qualitative guide to the size of threshold corrections needed at the high scale (e.g., the indices of high-scale representations) and provides precise quantitative data needed to test the viability of hypothesized high-scale unification theories. Such an approach shows more clearly the reasonable prospects of non-supersymmetric grand unification in large rank groups, and also shows the low summed values of high-scale threshold corrections required for supersymmetric unification. The latter may imply tuned cancellations of high-scale thresholds in theories based on weak-scale supersymmetry. For that reason we view non-supersymmetric unification to be just as viable as supersymmetric unification when confining ourselves only to the question of reasonable high-scale threshold corrections needed for exact unification. We illustrate these features for a non-supersymmetric $SO(10)$ graund unified theory and a supersymmetric $SU(5)$ theory.