Diphoton Excess in Consistent Supersymmetric SU(5) Models with Vector-like Particles

We consider the diphoton resonance at the 13 TeV LHC in the context of SU(5) grand unification. A leading candidate to explain this resonance is a standard model singlet scalar decaying to a pair of photon by means of vector-like fermionic loops. We demonstrate the effect of the vector-like multiplets (5, 5 bar) and (10, 10 bar) on the evolution of the gauge couplings and perturbatively evaluate the weak scale values of the new couplings and masses run down from the unification scale. We use these masses and couplings to explain the diphoton resonance after considering the new dijet constraints. We show how to accommodate the larger decay width of the resonance particle, which seems to be preferred by the experimental data. In addition, we consider new couplings relating various components of (5, 5 bar) and (10, 10 bar) in the context of the orbifold GUTs, where the resonance scalar can be a part of the new vector-like lepton doublets. We also calculate the Higgs mass and proton decay rate to positron and neutral pion in the context of SU(5) grand unification, including effects of the new vector-like multiplets.