From Neutrino Masses to Proton Decay

Current theoretical and experimental issues are reviewed in the light of the recent SuperKamiokande discovery. By using quark-lepton symmetries, derived from Grand Unification and/or string theories, we show how to determine the necessary neutrino parameters. In addition, the seesaw neutrino masses set the scale for the proton decay operators by ``measuring'' the standard model cut-off. The SuperKamiokande values suggest that proton decay is likely to be observed early in the XXIst Century.Comment: Invited Talk at the Workshop on the Next generation Nucleon decay and Neutrino detector (NNN99), September 23-25, 1999. Latex, 9 page

Mass Hierarchies from Anomalies: a Peek Behind the Planck Curtain

The masses of quarks and leptons suggest a strong hierarchical structure. We argue that their patterns can be reproduced through the introduction of a new Abelian symmetry. The data suggest that this symmetry is anomalous. We suggest that the cancellation of its anomalies occur through the Green-Schwarz mechanism. An important check of this idea is that it links the Weinberg angle to a mass ratio of the elementary fermions. The Green-Schwarz mechanism occurs naturally in many superstring compactifications, and produces a small parameter, which we use to determine the quark mass hierarchy. We show that hierarchy and mixings among the chiral fermions is a consequence of the Green-Schwarz mechanism. We present several models where this idea is realized.Comment: Based on a talk delivered in the honor of Professor K. Kikkawa's 60th birthday, December 1995, Osaka, Japan. Latex, 15 pages, macros include

Neutrinos: Windows to Planck Physics

After recalling some elegant contributions of the late Freydoon Mansouri, we turn to neutrino physics and use a {\it modicum} of grand unification to relate quark and lepton mixing matrices. We advocate an expansion for the MNS matrix, {\it \`a la} Wolfenstein, and argue that in a wide class of models, $\theta_{13}$ is a Cabibbo mixing effect. Also the large neutrino mixing angles reflect the mass patterns of the right-handed neutrinos near the Planck scale, and provide evidence for family structure at that scale.Comment: COntribution to Quantum Theory and Symmetries COnference, Univ of Cincinatti, October 2003; Latex, 11 page

The Sirens of Eleven Dimensions

While most theorists are tied to the mast of four dimensions, some have found it irresistible to speculate about eleven dimensions, the domain of M-theory. We outline a program which starts from the light-cone description of supergravity, and tracks its divergences to suggest the existence of an infinite component theory which in the light-cone relies on the coset $F_4/SO(9)$, long known to be linked to the Exceptional Jordan Algebra.Comment: Contribution to "From Fields to Strings: Circumnavigating Theoretical Physics", Edited by M. Shifman, A. Vainshtein, and J. Wheater, in memory of Ian Koga