Proton Decay in the Supersymmetric Grand Unified Models

TL;DR

This paper analyzes proton decay within supersymmetric grand unified theories, focusing on two mechanisms: dimension-six X-boson exchange and dimension-five colored-Higgs exchange. It shows that in minimal SUSY SU(5) the dimension-five channel leads to rapid proton decay and is experimentally excluded, while X-boson–driven decays depend on the high-scale mass $M_X$ and unification constraints, offering a more model-stable probe. The discussion highlights how extra matter content and Peccei–Quinn symmetry can alter the predicted rates by affecting the renormalization factor $A_R$ and the effective colored-Higgs mass $M_{H_C}$, thereby preserving or constraining SUSY GUTs. The work emphasizes the crucial role of current and future proton-decay experiments, lattice inputs for hadronic matrix elements like $\alpha_H$, and precise gauge-unification bounds in validating or ruling out SUSY GUT scenarios, with key relations such as $\tau \propto M_X^4$ for X exchange and $\tau \propto M_{H_C}^2$ for colored-Higgs exchange guiding the interpretation of results.

Abstract

In this article we review proton decay in the supersymmetric grand unified models.

Figures (3)

• Figure 1: Higgsino and gaugino dressing to the baryon-number violating dimension-five operators.
• Figure 2: Lifetime of proton as a function of $M_X$. The shaded region has been excluded by Super-Kamiokande experiment ($3.3 \times 10^{33}$ years). The dash-doted line is the expected reach of ten years run of the Super-Kamiokande experiment ($1.4 \times 10^{34}$ years) shiozawa-nnn.
• Figure 3: Lifetime of proton as a function of contribution to the beta functions of the gauge coupling constants from the extra matters. Here, we take $M_X=1.0\times 10^{16}$ GeV. The masses for the extra matters $M$ are taken to be $10^2$, $10^4$, and $10^6$ GeV.