Seminarium Fizyki Wielkich Energii

A Balmer-like empirical analysis of quark and neutrino mixing angles and of the charged-lepton mass hierarchy suggests a remarkable interplay between number theory and geometry, involving Fermat primes 5 and 17 (or equivalently the golden ratio in place of the former). The resulting pattern fixes two of the three a priori unknown parameters entering the (presently frequently exploited) Froggatt--Nielsen description of flavour hierarchies. This may provide useful guidance for further phenomenological studies (quark and neutrino masses) and possibly for the search for a more fundamental theory of flavour.