Abstract
Proton decay is one of the most important predictions of the grand unified theory (GUT). In the supersymmetric (SUSY) GUT, proton decays via the dimension-five operators need to be suppressed. In the $SO(10)$ model where ${\bf 10}+\overline{\bf 126}$ Higgs fields couple to fermions, neutrino oscillation parameters including the CP-violating Pontecorvo-Maki-Nakagawa-Sakata (PMNS) phase can be related to the Yukawa couplings to generate the dimension-five operators in the unified framework. We show how the suppressed proton decay depends on the PMNS phase, and stress the importance of the precise measurements of the PMNS phase as well as the neutrino 23-mixing angle. These become especially important if the SUSY particles are found around less than a few TeV at LHC and proton decays are observed at Hyper-Kamiokande and DUNE experiments in the near future.
Highlights
The measurement of the parameters in the neutrino oscillations is one of the recent major progress in particle physics
The SUSY grand unified theory (GUT), suffer from constraints of dimension-five proton decay operators [8], which can be generated by the Yukawa interaction via color triplet Higgs exchange: More than 10 years ago, one of the authors and his collaborators discussed how the proton decay amplitudes can be suppressed by the specific Yukawa structure, which can be connected to the parameters in the neutrino oscillations, and claimed that the neutrino 13-mixing angle θ13 cannot be zero and θ13 ∼ 0.1 under the condition [9]
We argue that the similar Yukawa structure can be applied even if the type I seesaw contribution is incorporated to the neutrino mass matrix in the case where the vacuum expectation value (VEV) of 126, vR, is large
Summary
The measurement of the parameters in the neutrino oscillations is one of the recent major progress in particle physics. The SUSY GUTs, suffer from constraints of dimension-five proton decay operators [8], which can be generated by the Yukawa interaction via color triplet Higgs exchange: More than 10 years ago, one of the authors and his collaborators discussed how the proton decay amplitudes can be suppressed by the specific Yukawa structure, which can be connected to the parameters in the neutrino oscillations, and claimed that the neutrino 13-mixing angle θ13 cannot be zero and θ13 ∼ 0.1 under the condition [9] In these arguments, it was assumed that light neutrino mass matrix is dominated by the type II contribution from the left-handed Majorana neutrino mass. The accurate measurements of the oscillation parameters are important if the dimension-five proton decays are suppressed but it will be observed in the near future
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