UV cut-off of the Standard Model and proton decays
Non-observation of proton decays as well as the smallness of the neutrino masses can naturally be explained by the accidental baryon and lepton number symmetry in the Standard Model, where the approximate symmetries are a consequence of the absence of the baryon or lepton number violating operators at the renormalizable level. The neutrino masses at sub-eV scales can be explained by the presence of the dimension-five term, $\ell\ell HH/Λ$, in the Lagrangian, suggesting that a more fundamental theory takes over beyond the energy scale $Λ$. We consider the possibility that the theory above the scale $Λ$ generates general higher dimensional operators with the flavor structure implied by the Yukawa interactions in the Standard Model. Such a set-up can be realized, for example, in the composite Higgs scenario with partial compositeness of fermions. The fermion masses and the neutrino masses are explained for $Λ\gtrsim 10^{11}$GeV. The lifetime of proton in this scenario is, interestingly, consistent with the observed event of the $p \to π^0 μ^+$ decay at the Super-Kamiokande experiment. The Hyper-Kamiokande experiment should see a large number of events soon after the data taking, if the event observed by the Super-Kamiokande is due to the real proton decay.