Optimizing Yukawa couplings to suppress Dimension-five Proton Decay in $SU(5)$ GUT

TL;DR

This paper employs machine learning optimization to identify Yukawa coupling configurations in a supersymmetric $SU(5)$ GUT that suppress proton decay, addressing a key phenomenological challenge.

Contribution

It introduces a novel application of machine learning techniques to efficiently explore the high-dimensional parameter space of GUT models for proton decay suppression.

Findings

Successfully identified parameter regions with proton lifetime exceeding experimental bounds.

Demonstrated the effectiveness of Adam optimizer in navigating complex GUT parameter spaces.

Showed that Yukawa coupling adjustments can significantly reduce proton decay rates.

Abstract

The minimal supersymmetric $SU(5)$ grand unified theory (GUT) provides a highly compelling framework for physics beyond the Standard Model (SM). However, it suffers from a severe phenomenological challenge: rapid proton decay mediated by colored-Higgsino exchange via dimension-five operators. Resolving this issue often requires adjustments to the Yukawa couplings and the potential sectors, generating a vast and complex parameter space where traditional brute-force numerical scans are rendered computationally intractable due to the curse of dimensionality. In this paper, we overcome this limitation by applying machine learning optimization techniques. We investigate a supersymmetric $SU(5)$ model extended with $\mathbf{45}$ and $\overline{\mathbf{45}}$ Higgs representations, defining a loss function based on the partial decay width of $p \to K^+ \bar{\nu}$. Utilizing the Adam optimizer, we systematically explore the 33-dimensional parameter space to identify regions that suppress proton decay. Furthermore, we vary $\tan \beta$ to thoroughly investigate whether the optimized proton lifetime can consistently exceed the stringent experimental lower bound of $5.9 \times 10^{33}$ years established by the Super-Kamiokande collaboration.