Effect of anRRRRdimension 5 operator on proton decay in the minimal SU(5) SUGRA GUT model

We reanalyze the proton decay in the minimal SU(5) SUGRA GUT model. Unlike previous analyses, we take into account a Higgsino dressing diagram of a dimension 5 operator with right-handed matter fields $(RRRR$ operator). It is shown that this diagram gives a dominant contribution for →pK⁺ν_τ over that from the LLLL operator, and the decay rate of this mode can be comparable with that of →pK⁺ν_μ which is dominated by the LLLL contribution. It is found that we cannot reduce both the decay rate of →pK⁺ν_τ and that of →pK⁺ν_μ simultaneously by adjusting relative phases between Yukawa couplings at colored Higgs interactions. Constraints on the colored Higgs boson mass MC and a typical squark and slepton mass m_ ̃ \~f from the super-Kamiokande limit become considerably stronger due to the Higgsino dressing diagram of the RRRR operator: MC>6.5×10¹⁶ GeV for m_ ̃ \~f<1 TeV and m_ ̃ \~f>2.5 TeV for MC<2.5×10¹⁶ GeV.