Proton Lifetime in Minimal SUSY SU(5) in Light of LHC Results

We examine proton decay mediated by color-triplet Higgsinos in minimal supersymmetric $SU(5)$ grand unified theory in light of the discovery of the Higgs boson and the absence of SUSY signals at the LHC. We pay special attention to various threshold effects arising from Planck-suppressed operators that affect the color-triplet Higgsino mass and also correct the wrong mass relations for the light fermions. Our analysis allows for a non-universal SUSY spectrum with the third family scalars having a separate mass compared to the first two families. We identify the allowed parameter space of the model and show that the SUSY scalar masses are constrained by current limits from proton lifetime to be above 5 TeV, while the glunio, Wino and the Higgsinos may be within reach of the LHC. When the SUSY scalar masses are required to be $\leq 20$ TeV, so that they are within reach of next generation collider experiments, we find that proton lifetime for the decay $p\to \bar{\nu }{K}^{+}$ is bounded by $\tau (p\to \bar{\nu }{K}^{+})\le 1.1\times {10}^{35}$ yrs.