$d=5$ operators in SUSY GUT: fermion masses versus proton decay

Abstract

In the minimal SU(5) SUSY GUT $d =5$ operators lead to $p\to K^+ \nu$ decay with the proton life time of the order of $10^{28}$ years for the natural choice of the parameters of the theory. This value is in strong contradiction with experimental bound $\tau_{p\to K\nu} > 10^{32}$ years. $d=5$ operators are induced by colored Higgsino exchanges and are closely (through SU(5) and super symmetry) related to another wrong prediction of SU(5) SUSY GUT: $m_d /m_s = m_e /m_{\mu}$. We demonstrate how in the model where reasonable pattern of quark and lepton masses and CKM mixing angles are obtained proton decay can be suppressed and proton life time can be close to the present experimental bound.