Confronting the Conventional Ideas of Grand Unification with Fermion Masses, Neutrino Oscillations and Proton Decay

Abstract

It is noted that a set of facts points to the relevance in four dimensions of conventional supersymmetric unification based on minimally a string-unified G(224)-symmetry, or maximally SO(10). These include: (i) the observed family- structure, (ii) quantization of electric charge, (iii) meeting of the three gauge couplings, (iv) neutrino oscillations [in particular the value of $\Delta m^2(\nu_\mu-\nu_\tau)$, 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 $\theta^{osc}_{\nu_{\mu}\nu_{\tau}}$, and (vi) the need for B-L as a generator to implement baryogenesis (via lepto-genesis). 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, (b) limits the threshold corrections so as to preserve natural coupling unification, and (c) uses recently improved values of the matrix element and renormalization effects. Allowing for both MSSM and its proposed variant, the so-called ESSM, as effective low-energy theories, the study shows that a conservative upper limit on the proton lifetime is about (1/3 - 2)$\times 10^{34}$ years, with $\bar{\nu}K^{+}$ being the dominant decay mode, and quite possibly $\mu^{+}K^{0}$ and $e^+\pi^0$ being prominent. This in turn strongly suggests that an improvement in the current sensitivity by a factor of five to ten ought to reveal proton decay. For comparison, some alternatives to the conven- tional approach to unification pursued here are mentioned at the end.