Representing seesaw neutrino models and their motion in lepton flavour space

Abstract

We discuss how seesaw neutrino models can be graphically represented in lepton flavour space. We examine various popular models and show how this representation helps understanding their properties and connection with experimental data showing in particular how certain texture zero models are ruled out. We also introduce a new matrix, the bridging matrix, that brings from the light to the heavy neutrino mass flavour basis, showing how this is related to the orthogonal matrix and how different quantities are easily expressed through it. We then show how one can randomly generate orthogonal and leptonic mixing matrices uniformly covering all flavour space in an unbiased way (Haar-distributed matrices). Using the isomorphism between the group of complex rotations and the Lorentz group, we also introduce the concept of Lorentz boost in flavour space for a seesaw model and how this has an insightful physical interpretation. Finally, as a significant application, we consider N2-leptogenesis. Using current experimental values of low energy neutrino parameters, we show that the probability that at least one flavoured decay parameter of the lightest right-handed neutrino is smaller than unity is about 49% (to be compared with the tiny probability that the total decay parameter is smaller than unity, P (KI< 1) ∼ 0.1%, confirming the crucial role played by flavour effects). On the other hand when m1 ≳ 0.1 eV this probability reduces to less than 5%, showing how also N2-leptogenesis disfavours degenerate light neutrinos.

More information

Identifiers

Catalogue record

Export record

Altmetrics