Probing grand unification with fermion masses, neutrino oscillations and proton decay

Abstract

It is noted that one is now in possession of a set of facts, which may be viewed as the matching pieces of a puzzle; in that all of them can be resolved by just one idea-that is grand unification. These include (i) the observed family-structure, (ii) quantization of electric charge, (iii) the meeting of the three gauge couplings, (iv) neutrino oscillations [in particular the value ∆m 2 (ν µ − ν τ ), suggested by SuperK], (v) the intricate pattern of the masses and mixings of the fermions, including the smallness of V cb and the largeness of θ osc νµντ , and (vi) the need for B-L as a generator to implement baryogenesis (via leptogenesis). All these pieces fit beautifully together within a single puzzle board framed by supersymmetric unification, based on either SO(10) or a string-unified G(224)-symmetry. The two notable pieces of the puzzle still missing, however, are proton decay and supersymmetry.A concrete proposal is presented within a predictive SO(10)/G(224)-framework that successfully describes the masses and mixings of all fermions, including the neutrinos-with eight predictions, all in agreement with observation. Within this framework, a systematic study of proton decay is carried out, which (a) pays special attention to its dependence on the fermion masses, and (b) limits the threshold corrections so as to preserve natural coupling unification. The study updates prior work by Babu, Pati and Wilczek, in the context of both MSSM and its (interesting) variant, the so-called ESSM, by allowing for improved values of the matrix elements and of the short-and long-distance renormalization effects. It shows that a conservative upper limit on the proton lifetime is about (1/3 -2)×10 34 years, with νK + being the dominant decay mode, and quite possibly µ + K 0 and e + π 0 being prominent. This in turn strongly suggests that an improvement in the current sensitivity by a factor of five to ten (compared to SuperK) ought to reveal proton decay. Otherwise some promising and remarkably successful ideas on unification would suffer a major setback. For comparison, some alternatives to the conventional approach to unification pursued here are mentioned at the end.