Proton Lifetime in Minimal Supersymmetric SU(5) with Gauge Mediation

In this paper, we discuss the predicted proton lifetimes in minimal supersymmetric (SUSY) $SU(5)$ grand unified theory (GUT) with gauge mediated supersymmetry breaking (GMSB). We focus on the case of $\mathbf{5} + \mathbf{\bar{5}}$ messengers and determine the low-scale mass spectrum of the scalar particles and gauginos using the renormalization group equations. With the obtained mass spectrum, we calculate the dominant proton decay mode for SUSY $SU(5)$ GUT, $p \to K^+ \bar{\nu}$. In our setup, we assume the messenger scale to be $\mathcal{O}(10^3)$ TeV in order to obtain a proper Higgs mass in GMSB scenario. For this messenger scale, we find the proton lifetime is consistent with current experimental limits and can be tested by future proton decay experiments.