Anarchy and Hierarchy

Abstract

We advocate a new approach to study models of fermion masses and mixings, namely anarchy proposed in hep-ph/9911341. In this approach, we scan the O(1) coefficients randomly. We argue that this is the correct approach when the fundamental theory is sufficiently complicated. Assuming there is no physical distinction among three generations of neutrinos, the probability distributions in MNS mixing angles can be predicted independent of the choice of the measure. This is because the mixing angles are distributed according to the Haar measure of the Lie groups whose elements diagonalize the mass matrices. The near-maximal mixings, as observed in the atmospheric neutrino data and as required in the LMA solution to the solar neutrino problem, are highly probable. A small hierarchy between the Delta m^2 for the atmospheric and the solar neutrinos is obtained very easily; the complex seesaw case gives a hierarchy of a factor of 20 as the most probable one, even though this conclusion is more measure-dependent. U_{e3} has to be just below the current limit from the CHOOZ experiment. The CP-violating parameter sin delta is preferred to be maximal. We present a simple SU(5)-like extension of anarchy to the charged-lepton and quark sectors which works well phenomenologically.