Proton decay and realistic models of quark and lepton masses

It is shown that in realistic SUSY GUT models of quark and lepton masses both the proton decay rate and branching ratios differ in general from those predicted in the minimal SU(5) supersymmetric model. The observation of proton decay, and in particular the branching ratio B[(p → π+ν)(p → K+ν)], would thus allow decisive tests of these fermion mass schemes. It is shown that the charged lepton decay mode p → K0μ+ arising through gluino dressing diagrams is significant and comparable to the neutrino modes in large tanβ models. Moreover, it is found that in certain classes of models the higgsino-mediated proton decay amplitudes are proportional to a model-dependent group-theoretical factor which in some cases can be quite small. There is thus a natural suppression mechanism which can explain without adjustment of parameters why in the context of SUSY GUTs proton decay has not yet been seen. The most interesting such class consists of SO(10) models in which the dominant flavor-symmetric contribution to the up-quark mass matrix comes from an effective operator of the form 16i16j10H45H, where 〈45H〉 points approximately in the I3R-direction. This class includes a recent model of quark and lepton masses proposed by the authors.