The Standard Model partial unification scale as a guide to new physics model building

TL;DR

The paper investigates how the Standard Model’s non-Abelian partial unification scale $μ^{\rm SM}_{32}$ informs the construction of beyond-Standard-Model theories that achieve full or partial gauge coupling unification. It introduces a simple three-parameter framework with $\epsilon_i$ to parametrize corrections from new physics, distinguishing mirage-SUSY-like scenarios (where $ε_2\approx ε_3$) that place the unification scale $M_X$ near $μ^{\rm SM}_{32}$ from cases with $ε_2\neq ε_3$ that shift $M_X$ away. The analysis covers non-desert models (MSSM, 2HDM, split-SUSY) where new states below $M_X$ adjust beta functions, and desert/string-inspired scenarios where UV corrections (Kac-Moody level relations) can yield unification at $M_X$ as low as roughly $10^2$ TeV or higher, depending on the relative non-Abelian corrections. A key takeaway is the exponential sensitivity of $M_X$ to the difference $ε_3-ε_2$ and the practical utility of the framework for guiding model-building and phenomenology, including proton decay expectations and potential access to new physics scales.

Abstract

In the Standard Model, partial unification of the non-Abelian running gauge couplings is achieved at the scale $μ^{\rm SM}_{32} \approx 2.8 \times 10^{16}$ GeV. Elaborating on this fact, we discuss a simple general parametrization for the new physics corrections leading to full unification at some scale $M_X$. We show that for any new physics model such that the corrections to the non-Abelian couplings are equal (or nearly so), $M_X$ is equal (or close to) the partial unification scale $μ^{\rm SM}_{32}$; the latter scales could be disentangled only if the corrections to the non-Abelian couplings are significantly different. We explore how the parametrization works for some relevant models with new physics below $M_X$, as low energy supersymmetry, split supersymmetry, etc. As for models with a desert up to $M_X$, we explore in particular how the parametrization works for string inspired corrections; we find a phenomenologically remarkable possibility for unification at about $100$ TeV, suggesting a low string scale, in addition to the more conservative possibility for unification at $μ^{\rm SM}_{32}$.

Figures (8)

• Figure 1: Running gauge couplings in the SM at NNLO (dashed) and in the MSSM at LO (solid). The SUSY running starts at $10\, {\rm TeV}$.
• Figure 2: Running gauge couplings at LO (solid) in the MSSM, 2HDM and split-SUSY, in the upper left, upper right and lower panel, respectively, with respect to the SM ones (dashed). The new physics running starts at the mass threshold $\mu_S=10\, {\rm TeV}$.
• Figure 3: The case of equal corrections to the non-Abelian gauge couplings. The dependence of $\epsilon_1$ (left) and $\alpha_G$ (right) with respect to $\epsilon_{32}$. Fits are provided in Eq. (\ref{['eq-fit-e32']}).
• Figure 4: Examples of models with unification at $M_X=\mu^{\rm SM}_{32}$. Left panel: a model mimicking SUSY with $\epsilon_{32}=0.68$ and $\epsilon_1=0.35$, so that $\alpha_G = \alpha^{(S1)}_{32} \approx 0.0364$. Right panel: a model of the mirage SUSY type, obtained taking $\epsilon_{32}=0.1$ and $\epsilon_1=-0.116$; in this case $\alpha_G =0.0238$.
• Figure 5: The case of unequal corrections to the non-Abelian gauge couplings. Top panels: Case $\epsilon_2=0$: the dependence of $\epsilon_{3,1}$ and $\alpha_G$ on $M_X$. Bottom panels: Case $\epsilon_3=0$: the dependence of $\epsilon_{2,1}$ and $\alpha_G$ on $M_X$.