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

Abstract

In the Standard Model, partial unification of the non-Abelian running gauge couplings is achieved at the scale $\hat{I}{¼}_{32}^{SM}\approx 2.8\times 10^{16}$ 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 $\hat{I}{¼}_{32}^{SM}$; 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 $\hat{I}{¼}_{32}^{SM}$; for models with power-low running/threshold corrections, we also outline an interesting connection with the number of fermion families propagating in the bulk.

V1: 20 pages, 8 figures; v2: 25 pages, 12 figures, added new section with figures and references, improved general discussion, matches PRD version