Proton Decay and Gauge Coupling Unification in an Extended SU(5) GUT with 45-Dimensional Higgs

TL;DR

The paper investigates an extended SU(5) GUT incorporating a $45$-dimensional Higgs to address fermion mass hierarchies and proton stability. By enforcing a hierarchical mass spectrum among the $45_H$ components, it demonstrates gauge coupling unification can be achieved with light $S_8$, $S_3$, and $S_1$, signaling a broader viable parameter space. Proton decay is analyzed with a focus on $S_1$-mediated channels; the strongest constraint comes from the $p \to \nu \pi$ mode, which imposes $M_{S_1} \gtrsim 3\times10^{11}$ GeV, with correlations to other modes revealing the role of Yukawa and mixing structures. Yukawa couplings at the GUT scale are obtained via RG evolution and matching conditions, ensuring realistic low-energy fermion masses while satisfying unification and proton decay limits.

Abstract

We present a comprehensive study of an extended SU(5) grand unified theory (GUT) that incorporates a 45-dimensional 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 45-Higgs, we demonstrate that successful gauge coupling unification (GCU) can be achieved. The color octet scalar, color triplet scalar, and color anti-triplet scalar play crucial roles in realizing GCU when their masses are significantly lighter than other components of the 45-Higgs. We focuses on the proton decay channels mediated by the exchange of the color anti-triplet scalar. Assuming that the 45-Higgs couples to all three generations of fermions, we determine the 45-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 $p \to νπ$ mode imposes the most stringent constraint on the mass of the color anti-triplet scalar $M_{S_1}$. We also study the correlations between the lower bounds on $M_{S_1}$ derived from different proton decay modes.

Figures (2)

• Figure 1: The probability distributions for the lower bound on the mass scale $M_{S_1}$ derived from the experimental constraints on various proton decay modes.
• Figure 2: The correlations between the lower bounds on $M_{S_1}$ derived from various proton decay modes.