Gauge coupling unification and proton decay via 45 Higgs boson in SU(5) GUT

We study the gauge coupling unification (GCU) and proton decay in a non-supersymmetric SU(5) grand unified theory (GUT) incorporating a 45 representation Higgs field. Our analysis is based on the assumption that Georgi-Jarlskog-type mass matrices for fermions are responsible for explaining the mass ratio of the strange quark and the muon. We examine the conditions of GCU, taking into account the possibility that certain components of the 45 Higgs field have masses much smaller than the GUT scale. We have found that to satisfy the GCU conditions, at least two components of the 45 Higgs field should have such small masses. We search the parameter space to identify regions where the GCU conditions are satisfied, in the scenarios where two or three components of the 45 Higgs boson are hierarchically light. If the colored Higgs component of the 45 Higgs boson has a mass much smaller than the GUT scale, proton decay via colored Higgs boson exchange can occur with an observably large rate. We estimate the mass bounds for the colored Higgs component from the proton decay search at Super-Kamiokande and thereby further restrict the parameter space.