# Detectable dimension-6 proton decay in SUSY SO(10) GUT at Hyper-Kamiokande

## TL;DR

This paper shows that a specific SUSY SO(10) GUT model predicts an enhanced dimension-6 proton decay rate, making it detectable at Hyper-Kamiokande, unlike minimal SUSY SU(5) models.

## Contribution

It identifies a SUSY SO(10) GUT framework with specific Higgs fields that leads to a larger, observable proton decay rate due to Planck-suppressed SU(5)-breaking VEVs.

## Key findings

- Proton decay width is within Hyper-Kamiokande's detection range.
- SU(5)-breaking VEVs are enhanced by Planck-suppressed terms.
- The gauge boson masses are smaller, increasing decay rate.

## Abstract

In the minimal SUSY SU(5) GUT with $O(1)$ TeV SUSY particles and $O(1)$ or below self-coupling for the GUT-breaking Higgs field, the width of the dimension-6 proton decay is suppressed below the reach of Hyper-Kamiokande. In this paper, we point out that a SUSY SO(10) GUT which adopts only ${\bf 45}_{\rm H}+{\bf 16}_{\rm H}+{\bf \overline{16}}_{\rm H}$ GUT-breaking Higgs fields leads to an enhanced dimension-6 proton decay width detectable at Hyper-Kamiokande. The enhancement is because the SU(5)-breaking VEV of ${\bf 45}_{\rm H}$ arises due to Planck-suppressed terms, $W\propto ({\bf 45}_{\rm H}^2)^2/M_*+{\bf 45}_{\rm H}^4/M_*$, and is therefore substantially larger than the other VEVs that conserve SU(5). As a result, the $({\bf 3},{\bf 2},1/6)$ GUT gauge boson mass is about $1/5$ smaller than the $({\bf 3},{\bf 2},-5/6)$ GUT gauge boson mass and can induce a fast dimension-6 proton decay. Through a numerical analysis on threshold corrections of the GUT gauge bosons and the physical components of the GUT-breaking Higgs fields, we confirm that the dimension-6 proton decay can be within the reach of Hyper-Kamiokande.