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

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.