Proton decay and gauge coupling unification in an extended SU(5) GUT with 45-dimensional higgs

Abstract We present a comprehensive study of an extended SU (5) grand unified theory (GUT) that incorporates a 45D Higgs representation to address the shortcomings of the minimal SU (5) GUT, such as the inability to generate realistic fermion mass hierarchies and insufficient proton stability. By considering a hierarchical mass spectrum for the scalar components of the 45D Higgs, we demonstrate that successful gauge coupling unification (GCU) can be achieved. The color octet scalar, color triplet scalar, and color antitriplet scalar play crucial roles in realizing GCU when their masses are significantly lighter than other components of the 45D Higgs. We focus on the proton decay channels mediated by the exchange of the color antitriplet scalar. Assuming that the 45D Higgs couples to all three generations of fermions, we determine the 45D Higgs Yukawa couplings with which the observed fermion mass matrices at low energies are realized. We calculate proton decay rates using the Yukawa couplings obtained from renormalization group evolutions and matching conditions at the GUT scale, thereby exploring the dependence of proton decay rates on model parameters. We find that the p mode imposes the most stringent constraint on the mass of the color antitriplet scalar Mₒ䃑. We also study the correlations between the lower bounds on Mₒ䃑 derived from different proton decay modes.