Effect of an RRRR dimension 5 operator on the 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 dimension 5 operator with right-handed matter fields ($RRRR$ operator). It is shown that this diagram gives a dominant contribution for $p\to K^+\bar{\nu}_\tau$ over that from $LLLL$ operator, and decay rate of this mode can be comparable with that of $p\to K^+\bar{\nu}_\mu$ which is dominated by the $LLLL$ contribution. It is found that we cannot reduce both the decay rate of $p\to K^+\bar{\nu}_\tau$ and that of $p\to K^+\bar{\nu}_\mu$ simultaneously by adjusting relative phases between Yukawa couplings at colored Higgs interactions. Constraints on the colored Higgs mass $M_C$ and a typical squark and slepton mass $m_{\tilde{f}}$ from Super-Kamiokande limit become considerably stronger due to the Higgsino dressing diagram of the $RRRR$ operator: $M_C > 6.5 \times 10^{16}\gev$ for $m_{\tilde{f}} < 1 \tev$, and $m_{\tilde{f}} > 2.5 \tev$ for $M_C < 2.5 \times 10^{16} \gev$.