A Parameter Space Exploration of the Minimal SU(5) Unification

TL;DR

This paper explores a minimal $SU(5)$ grand unified theory, analyzing its parameter space, predictions for neutrino properties, and implications for proton decay, with potential testability at TeV-scale energies.

Contribution

It provides a detailed phenomenological analysis of the minimal $SU(5)$ model, linking neutrino mass origin to fermion mass differences and predicting new scalar multiplets at accessible energy scales.

Findings

Neutrinos are Majorana particles with one massless state.

Neutrinos have a normal mass hierarchy.

Four scalar multiplets are predicted below 120 TeV.

Abstract

We present phenomenological study of the most minimal realistic $SU(5)$ model that owns its predictivity solely to the gauge symmetry and the representational content. The model is built entirely out of the fields residing in the first five lowest dimensional representations that transform non-trivially under the $SU(5)$ gauge group. It has eighteen real parameters and fourteen phases, all in all, to address experimental observables of the Standard Model fermions and accomplishes that via simultaneous use of three different mass generation mechanisms. Furthermore, it inextricably links the origin of the neutrino mass to the experimentally observed difference between the down-type quark and charged lepton masses. The main predictions of the model are that $(i)$ the neutrinos are Majorana particles, $(ii)$ one neutrino is massless, $(iii)$ the neutrinos have normal mass ordering, and $(iv)$ there are four new scalar multiplets at or below a $120$ TeV mass scale. A one-loop analysis demonstrates that an improvement of the current $p \rightarrow \pi^0 e^+$ partial lifetime limit by a factor of $2$, $15$, and $96$ would require these four scalar multiplets to reside at or below the $100$ TeV, $10$ TeV, and $1$ TeV mass scales, respectively.