Teeny, tiny Dirac neutrino masses: an unorthodox point of view

There are now strong hints suggesting that neutrinos do have a mass after all. If they do have a mass, it would have to be tiny. Why is it so? Is it Dirac or Majorana? Can one build a model in which a teeny, tiny Dirac neutrino mass arises in a natural way? Can one learn something else other than just neutrino masses? What are the extra phenomenological consequences of such a model? These are the questions that I will try to focus on in this talk.Comment: 11 pages, 2 figures, LateX, aipproc style. Talk presented at the Second Tropical Workshop on Particle Physics and Cosmology, Neutrino and Flavor Physics, 1-6 May 2000, San Juan, Puerto Ric

Groups whose prime graphs have no triangles

Let G be a finite group and let cd(G) be the set of all complex irreducible character degrees of G Let \rho(G) be the set of all primes which divide some character degree of G. The prime graph \Delta(G) attached to G is a graph whose vertex set is \rho(G) and there is an edge between two distinct primes u and v if and only if the product uv divides some character degree of G. In this paper, we show that if G is a finite group whose prime graph \Delta(G) has no triangles, then \Delta(G) has at most 5 vertices. We also obtain a classification of all finite graphs with 5 vertices and having no triangles which can occur as prime graphs of some finite groups. Finally, we show that the prime graph of a finite group can never be a cycle nor a tree with at least 5 vertices.Comment: 13 page

On neutrino and charged lepton masses and mixings: A view from the electroweak-scale right-handed neutrino model

We present a model of neutrino masses within the framework of the EW-$\nu_R$ model in which the experimentally desired form of the PMNS matrix is obtained by applying an $A_4$ symmetry to the \emph{Higgs singlet sector} responsible for the neutrino Dirac mass matrix. This mechanism naturally avoids potential conflict with the LHC data which severely constrains the Higgs sector, in particular the Higgs doublets. Moreover, by making a simple $ans\ddot{a}tz$ we extract $\mathcal{M}_l {\mathcal{M}_l}^\dagger$ for the charged lepton sector. A similar $ans\ddot{a}tz$ is proposed for the quark sector. The sources of masses for the neutrinos are entirely different from those for the charged leptons and for the quarks and this might explain why $U_{PMNS}$ is {\em very different} from $V_{CKM}$.Comment: 19 pages. Two figure