On Invariants of Quark and Lepton Mass Matrices in the Standard Model

In this article I present the motivation for introducing the invariant functions of mass matrices, based on my own work, and give some examples. Since their introduction in 1985, in the framework of the standard electroweak model, they have been used by many authors. Some authors have gone further along this path and have studied the extensions of this concept to frameworks beyond the standard model. I hope, in the near future, to give a more detailed account of this subject, including recent developments

Supersymmetry - Roots That Didn't Grow

This article is about early roots of supersymmetry, as found in the literature from 1940s and early 1950s. There were models where the power of "partners" in alleviating divergences in quantum field theory was recognized. However, other currently known remarkable features of supersymmetry, such as its role in the extension of the Poincar\'{e} group, were not known. There were, of course, no supersymmetric non-abelian quantum field theories in those days

Lord Rutherford of Nelson, His 1908 Nobel Prize in Chemistry and Why He Didn't Get a Second Prize

"I have dealt with many different transformations with various periods of time, but the quickest that I have met was my own transformation in one moment from a physicist to a chemist." Ernest Rutherford (Nobel Banquet, 1908) This article is about how Ernest Rutherford (1871-1937) got the 1908 Nobel Prize in Chemistry and why he did not get a second Prize for his subsequent outstanding discoveries in physics, specially the discovery of the atomic nucleus and the proton. Who were those who nominated him and who did he nominate for the Nobel Prizes. In order to put the Prize issue into its proper context, I will briefly describe Rutherford's whereabouts. Rutherford, an exceptionally gifted scientist who revolutionized chemistry and physics, was moulded in the finest classical tradition. What were his opinions on some scientific issues such as Einstein's photon, uncertainty relations and the future prospects for atomic energy? What would he have said about the "Theory of Everything"?Comment: Extended version of an invited talk presented at the neutrino conference "Neutrino 2008", Christchurch, New Zealand, 25-31 May 200

Non-decoupling of heavy neutrinos and lepton flavor violation

We consider a class of models predicting new heavy neutral fermionic states, whose mixing with the light neutrinos can be naturally significant and produce observable effects below the threshold for their production. We update the indirect limits on the flavour non-diagonal mixing parameters that can be derived from unitarity, and show that significant rates are in general expected for one-loop-induced rare processes due to the exchange of virtual heavy neutrinos, involving the violation of the muon and electron lepton numbers. In particular, the amplitudes for μ--e conversion in nuclei and for μ→ee+e− show a non-decoupling quadratic dependence on the heavy neutrino mass M, while μ→eγ is almost independent of the heavy scale above the electroweak scale. These three processes are then used to set stringent constraints on the flavour-violating mixing angles. In all the cases considered, we point out explicitly that the non-decoupling behaviour is strictly related to the spontaneous breaking of the SU(2) symmetry

Zee Mass Matrix and Bi-Maximal Neutrino Mixing

We investigate neutrino masses and mixings within the framework of the Zee mass matrix, with three lepton flavors. It is shown that the bi-maximal solution is the only possibility to reconcile atmospheric and solar neutrino data, within this ansatz. We obtain two almost degenerate neutrinos, which are mixtures of all three neutrino flavors, with heavy masses $\simeq \sqrt{\Delta m_{atm}^2}$. The predicted mass of the lightest neutrino, which should consist mostly of $\nu_{\mu}$ and $\nu_{\tau}$, is $\simeq \Delta m_{\odot}^2/(2\sqrt{\Delta m_{atm}^2})$.Comment: 15 pages, 1 figure. Minor typos corrected. Reference adde