The link between neutrino masses and proton decay in supersymmetric unification

Following recent joint works with K. Babu and F. Wilczek, I stress here that supersymmetric unification, based on symmetries like SO(10) or a string-derived G(224)=SU(2) _L ×SU(2) _R ×SU(4) ^C possesses some crucial features that are intimately linked to each other. They are (a) gauge-coupling unification; (b) the masses and mixings of all fermions, including especially the neutrinos; and last but not least (c) proton decay. In this context, it is noted that the value of $m_{v_L^tau } sim 1/20{text{ }}eV$ , suggested by the Super-Kamiokande result, goes extremely well with the unification-hypothesis, based on the ideas of (i) SU(4)-color, (ii) left-right symmetry, and (iii) supersymmetry. A concrete proposal is presented within an economical SO(10)-framework that makes five successful predictions for the masses and mixings of the quarks and the charged leptons. The same framework explains why the ν_π?ν_τ oscillation angle is so large $(sin ^2 2theta _{nu _mu nu _tau }^{osc} approx 0.82 - 0.96)$ and yet V _bc is so small (≈0.04), both in accord with observation. The influence of the masses of the neutrinos and of the charged fermions on proton decay is discussed concretely, within this framework. The $bar nu K^ + $ mode is expected to be dominant for SUSY SO(10) as well as SU(5). A distinctive feature of the SO(10) model, however, is the likely prominence of the μ⁺ K ⁰ mode, which, for SU(5), is highly suppressed. Our study shows that while current limits on the rate of proton decaying into $bar nu K^ + $ are compatible with theoretical expectations, improvements in these limits by a factor of 5–10 should either turn up events, or else the SO(10)-framework described here, which is otherwise so successful, will be in jeopardy. Prominence of theμ⁺ K ⁰ mode, if observed, will be most significant in that it will reveal the intriguing link that exists between neutrino masses and proton decay in the context of supersymmetric unification.