Proton Decay in Supersymmetric $SU(4)_c \times SU(2)_L \times SU(2)_R$

TL;DR

This paper explores proton decay predictions within a supersymmetric $SU(4)_c imes SU(2)_L imes SU(2)_R$ model, highlighting observable decay modes and the role of a $U(1)\, R$ symmetry in suppressing unwanted operators.

Contribution

It introduces a supersymmetric hybrid inflation model with specific gauge symmetry and analyzes proton decay mediated by color triplets, providing decay mode predictions and lifetime estimates.

Findings

Proton decay lifetimes estimated between 10^{34} and 10^{36} years.

Decay modes include $p ightarrow e^{+} ext{ or } ar{ u} + ext{pions}$ and kaons.

Decay predictions are testable at Hyper-Kamiokande and future experiments.

Abstract

We discuss proton decay in a recently proposed model of supersymmetric hybrid inflation based on the gauge symmetry $SU(4)_c \times SU(2)_L \times SU(2)_R$. A $U(1)\, R$ symmetry plays an essential role in realizing inflation as well as in eliminating some undesirable baryon number violating operators. Proton decay is primarily mediated by a variety of color triplets from chiral superfields, and it lies in the observable range for a range of intermediate scale masses for the triplets. The decay modes include $p \rightarrow e^{+}(\mu^+) + \pi^0$, $p \rightarrow \bar{\nu} + \pi^{+}$, $p \rightarrow K^0 + e^+(\mu^{+})$, and $p \rightarrow K^+ + \bar{\nu}$, with a lifetime estimate of order $10^{34}-10^{36}$ yrs and accessible at Hyper-Kamiokande and future upgrades. The unification at the Grand Unified Theory (GUT) scale $M_{\rm GUT}$ ($\sim 10^{16}$ GeV) of the Minimal Supersymmetric Standard Model (MSSM) gauge couplings is briefly discussed.