Probing a Finite Unified Theory with Reduced Couplings at Future Colliders

TL;DR

This paper reviews the reduction of couplings in finite $N=1$ supersymmetric GUTs, focusing on the $SU(5)$ model, and assesses the collider prospects for observing its supersymmetric spectrum.

Contribution

It presents a successful all-loop finite $N=1$ supersymmetric $SU(5)$ model with benchmark scenarios for future collider tests.

Findings

Supersymmetric spectrum is beyond 14 TeV HL-LHC reach.

Large parts of the spectrum can be tested at 100 TeV FCC-hh.

Higher mass regions remain inaccessible at current colliders.

Abstract

The search for relations among parameters that are renormalization group invariant to all orders in perturbation theory constitutes the basis of the reduction of couplings idea. Reduction of couplings can be achieved in $N=1$ Grand Unified Theories, few of which can become even all-loop finite. We review the basic idea and a resulting theory in which successful reduction of couplings has been achieved, namely the all-loop finite $N = 1$ supersymmetric $SU(5)$ model. We present three benchmark scenarios and investigate their observability at existing and future hadron colliders. The supersymmetric spectrum is found to be beyond the reach of the 14 TeV HL-LHC. In turn, it is found that large parts of the predicted spectrum can be tested at the 100 TeV FCC-hh, but the higher mass regions remain out of reach.