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 $\overrightarrow{p}{K}^{+}{\overline{\nu }}_{\tau }$ over that from the $\mathrm{LLLL}$ operator, and the decay rate of this mode can be comparable with that of $\overrightarrow{p}{K}^{+}{\overline{\nu }}_{\mu }$ which is dominated by the $\mathrm{LLLL}$ contribution. It is found that we cannot reduce both the decay rate of $\overrightarrow{p}{K}^{+}{\overline{\nu }}_{\tau }$ and that of $\overrightarrow{p}{K}^{+}{\overline{\nu }}_{\mu }$ simultaneously by adjusting relative phases between Yukawa couplings at colored Higgs interactions. Constraints on the colored Higgs boson mass $M_C$ and a typical squark and slepton mass $m_{\tilde{f}}$ from the super-Kamiokande limit become considerably stronger due to the Higgsino dressing diagram of the $\mathrm{RRRR}$ operator: $M_C>6.5\mathrm{}\times {10}^{16}\hspace{0.5em}\mathrm{GeV}$ for $m_{\tilde{f}}<1\mathrm{}\hspace{0.5em}\mathrm{TeV}$ and $m_{\tilde{f}}>2.5\mathrm{}\hspace{0.5em}\mathrm{TeV}$ for $M_C<2.5\mathrm{}\times {10}^{16}\hspace{0.5em}\mathrm{GeV}$.