A Model for Neutrino Masses

I present a model for neutrino masses based on a hypothesis proposed by Friedberg and Lee. Invited talk presented at the IV International Workshop on Neutrino Oscillations, April 15-18 (2008) Venice, Italy 1 Prelude I am delighted to be giving a talk here in Italy on this very special day, April 15, Leonardo da Vinci’s birthday. Through my talk, I will turn to him for guidance and understanding. 2 Historical Perspective Let me first start with a bit of history. The year 1957 was a wonderful neutrino year due to the discovery of parity violation in weak interactions. See the Nobel lectures by Lee and Yang ([1], [2]), both easily accessible on the internet. The only weak interactions studied at that time were decay processes where one or two neutrino particles were emitted. A remarkable feature of parity violation was that it was compatible with being maximal. A beautiful idea was then put forward that attributed this feature to an intrinsic property of the neutrino, its handedness. Consequently, the neutrino was automatically massless. This proposition came from no less distinguished scientists than Lee and Yang [3], Landau [4] and Salam [5], and perhaps even others. For example, Landau wrote about what he called the longitudinally polarized, or more simply longitudinal neutrino: ”In the sense of the usual scheme this would signify that the neutrino is always polarized in the direction of its motion (or in the opposite direction). The polarization of the antineutrino is correspondingly reversed. According to this model the neutrino is not a truly neutral particle”. He emphasized that ”In the usual theory the neutrino mass is zero, so to say, accidentally”. Lee and Yang referred to it as the two-component neutrino theory. This theory was largely taken for granted for several decades and became a part of the weak-interactionists’ scientific heritage. A lovely, predictive theory that led to simplicity. That explains why the founders of the Standard Electroweak Model chose not to introduce right-handed neutrinos. The same goes for the Grand Unified Georgi-Glashow Model. It would have been a trivial task for the authors in question to extend their models by adding in right-handed neutrinos. One would have had what we could call Slightly Non-minimal Standard Model [6]. Nowadays, due to neutrino oscillations, we generally believe that neutrinos are massive and therefore the two-component neutrino theory is not valid. However, we do not understand why and how the neutrinos are massive. Leonardo would tell us: ”Although nature commences with reason and ends in experience it is necessary for us to do the opposite, that is to commence with experience and from this to proceed to investigate the reason.”