Advantages of Unity With SU(4)-Color: Reflections Through Neutrino Oscillations, Baryogenesis and Proton Decay

Abstract

As a tribute to Abdus Salam, I recall the initiation in 1972-73 of the idea of grand unification based on the view that lepton number is the fourth color. Motivated by aesthetic demands, these attempts led to the suggestion that the existing $SU(2)\times U(1)$ symmetry be extended minimally to the quark-lepton and left-right symmetric non-Abelian gauge structure $G(2,2,4) = SU(2)_L\times SU(2)_R\times SU(4)$-color. This unified members of a family within a single L-R self-conjugate multiplet. It also explained: the quantization of electric charge, the co-existence of quarks and leptons, and that of their three forces, while providing the appealing possibility that nature is fundamentally left-right symmetric. The minimal extension of $G(2,2,4)$ to a simple group is given by the symmetry $SO(10)$ that came a year later. The advantages of the core symmetry $G(2,2,4)$, including those listed above (which are of course retained by $SO(10)$), are noted. These include the introductions of: (i){ \it the right-handed neutrino as a compelling member of each family}, (ii) (B-L) as a local symmetry, and (iii) the relation $ m(\nu^\tau)_{Dirac} = m_{top}$. These three features, as well as the gauge coupling unification scale, are crucially needed to understand the tiny mass-scales of the neutrino oscillations within the seesaw mechanism, and to implement successfully the mechanism of baryogenesis via leptogenesis. Implications of a well-motivated class of models based on supersymmetric $SO(10)$ or a string-unified $G(2,2,4)$ symmetry in 4D for (a) gauge coupling unification, (b) fermion masses and mixings, (c) neutrino osillations, (d) baryogenesis via leptogenesis, and last but not least (e) proton decay are presented. Recent works on the latter providing upper limits on proton lifetimes suggest that the potential for discovery of proton decay in the next-generation detectors would be high.