Knotted strings and leptonic flavor structure

Abstract

We propose a third idea for the explanation of the leptonic flavor structure in addition to the prominent approaches based on flavor symmetry and anarchy. Typical flavor patterns can be modeled by using mass spectra obtained from the discrete lengths spectrum of tight knots and links. We assume that a string theory model exists in which this idea can be incorporated via the Majorana mass structure of a type I seesaw model. It is shown by a scan over the parameter space that such a model is able to provide an excellent fit to current neutrino data and that it predicts a normal neutrino mass hierarchy as well as a small mixing angle \theta_{13}. Startlingly, such scenarios could be related to the dimensionality of space time via an anthropic argument.