Minimal SU(5) theory on the edge: the importance of being effective

TL;DR

This paper demonstrates that adding higher-dimensional operators to minimal SU(5) GUTs can fix their known issues, but it introduces a low unification scale that risks proton decay, prompting reconsideration of the model's viability.

Contribution

It shows that higher-dimensional effective operators can resolve the problems of minimal SU(5) and explores minimal extensions for neutrino mass generation.

Findings

Unification scale can be as low as 10^14 GeV with added operators.

Proton lifetime constraints challenge the model's viability.

Extensions can provide a dynamical origin for neutrino masses.

Abstract

It is well known that the minimal renormalizable $SU(5)$ grand unified theory is ruled out: it predicts same masses of down quarks and charged leptons, the gauge couplings do not unify and neutrinos are massless. We show here that all this can be cured simultaneously by the addition of higher-dimensional effective operators. However, the theory lives on the edge since the unification scale turns out as low as roughly $10^{14}\,$GeV, threatening proton longevity. If the lower bound on the proton lifetime was to be increased by an order of magnitude, the usual desert in energies between the weak and unification scales would be populated. We also revisit two minimal extensions of this theory that offer a dynamical seesaw origin of neutrino mass, and discuss the resulting consequences.