The Essential Role of String-Derived Symmetries in Ensuring Proton-Stability and Light Neutrino Masses

The paper addresses the problem of suppressing naturally the unsafe d=4 as well as the color-triplet mediated and/or gravity-linked d=5 proton-decay operators, which generically arise in SUSY-unification. It also attempts to give light masses to the neutrinos, of the type suggested by current experiments. It is noted that neither the symmetries in $SO(10)$, nor those in $E_6$, suffice for the purpose -- especially in the matter of suppressing naturally the d=5 proton-decay operators. By contrast, it is shown that a certain {\it string-derived symmetry}, which cannot arise within conventional grand unification, but which does arise within a class of three-generation string-solutions, suffices, in conjuction with $B-L$, to safeguard proton-stability from all potential dangers, including those which may arise through higher dimensional operators and the color-triplets in the infinite tower of states. At the same time, the symmetry in question permits neutrinos to acquire appropriate masses. This shows that {\it string theory plays an essential role in ensuring natural consistency of SUSY-unification with two low-energy observations -- proton-stability and light masses for the neutrinos}. The correlation between the masses of the extra $Z'$-boson (or bosons), which arise in these models, and proton-decay rate is noted.Comment: 20 pages, plain LaTeX. Footnote 26 expanded to include implication of neutrino-higgsino mixing, and two new footnotes adde

The Role of Gravity in Determining Physics at High as Well as Low Energies

It is noted that in the context of a supersymmetric preonic approach to unification, gravity, though weak, can play an essential role in determining some crucial aspects of low-energy physics. These include: (i) SUSY-breaking, (ii) electroweak symmetry-breaking, and (iii) generation of masses of quarks and leptons, all of which would vanish if we turn off gravity. Such a role of gravity has its roots in the Witten index theorem which would forbid SUSY-breaking, within the class of theories under consideration, in the absence of gravity.Comment: 14 pages, 2 figures, Plain Te

Discovery of Proton Decay: A Must for Theory, a Challenge for Experiment

It is noted that, but for one missing piece -- proton decay -- the evidence in support of grand unification is now strong. It includes: (i) the observed family-structure, (ii) the meeting of the gauge couplings, (iii) neutrino-oscillations, (iv) the intricate pattern of the masses and mixings of all fermions, including the neutrinos, and (v) the need for $B-L$ as a generator, to implement baryogenesis. Taken together, these not only favor grand unification but in fact select out a particular route to such unification, based on the ideas of supersymmetry, SU(4)-color and left-right symmetry. Thus they point to the relevance of an effective string-unified G(224) or SO(10)-symmetry. 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 pays special attention to its dependence on the fermion masses, including the superheavy Majorana masses of the right-handed neutrinos. The study shows that a conservative upper limit on the proton lifetime is about (1/2 - 1)$\times10^{34}$ yrs, with $\overline{\nu}K^{+}$ being the dominant decay mode, and as a distinctive feature, $\mu^{+}K^{0}$ 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.Comment: LaTex file 29 pages, no figures. Minor correction

With Grand Unification Signals in, Can Proton Decay be Far Behind?

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) meeting of the three gauge couplings, (iv) neutrino oscillations; in particular the mass of $\nu_{\tau}$ 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 $B$-$L$ to implement baryogenesis (via leptogenesis). All these pieces fit beautifully together within a single puzzle board framed by supersymmetric unification, based on SO(10) or a string-unified G(224)-symmetry. The one and the most notable piece of the puzzle still missing, however, is proton decay. 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. An updated study of proton decay is carried out within this framework, which shows that a conservative upper limit on its lifetime is about (1/2-1)\times 10^34 yrs