Unification and Extra Space-Time Dimensions

TL;DR

This work analyzes gauge coupling unification in supersymmetric models with additional space-time dimensions below the four-dimensional unification scale, using a two-loop renormalization group framework with Kaluza-Klein towers and a decompactification scale $\mu_0$. The authors derive the running above $\mu_0$ via an effective theory with UV cutoff $\Lambda$, incorporating the integral ${\cal J}(\Lambda/\mu_0,\delta)$ and KK contributions, and then evolve the couplings down to $M_Z$ with MSSM-like two-loop RGEs. They find that $\alpha_3(M_Z)$ is systematically increased compared to the MSSM prediction, while the unification scale $\Lambda$ decreases; the dominant effect is a power-law running from KK states, highly sensitive to $\Lambda/\mu_0$, $\delta$, and threshold details. Reconciliation with experimental $\alpha_3(M_Z)$ at low $\mu_0$ requires fine-tuning KK thresholds across gauge sectors, whereas larger $\mu_0$ dilutes this sensitivity and tends toward the MSSM prediction, underscoring the crucial role of KK spectrum details in such unification scenarios.

Abstract

We analyse the phenomenological implications of a particular class of supersymmetric models with additional space-time dimensions below the unification scale. Assuming the unification of the gauge couplings and using a two-loop calculation below the scale of the additional space-time dimensions, we show that the value of $α_3(M_z)$ is further increased from the two-loop Minimal Supersymmetric Standard Model prediction. We consider whether decompactification threshold effects could bring $α_3(M_z)$ into agreement with experiment and discuss the associated level of fine tuning needed.