The double mass hierarchy pattern: simultaneously understanding quark and lepton mixing

Abstract

The charged fermion masses of the three generations exhibit the two strong hierarchies m_3 >> m_2 >> m_1. We assume that also neutrino masses satisfy m_{nu 3} > m_{nu 2} > m_{nu 1} and derive the consequences of the hierarchical spectra on the fermionic mixing patterns. The quark and lepton mixing matrices are built in a general framework with their matrix elements expressed in terms of the four fermion mass ratios m_u/m_c, m_c/m_t, m_d/m_s, and m_s/m_b and m_e/m_mu, m_mu/m_tau, m_{nu 1}/m_{nu 2}, and m_{nu 2}/m_{nu 3}, for the quark and lepton sector, respectively. In this framework, we show that the resulting mixing matrices are consistent with data for both quarks and leptons, despite the large leptonic mixing angles. The minimal assumption we take is the one of hierarchical masses and minimal flavour symmetry breaking that strongly follows from phenomenology. No special structure of the mass matrices has to be assumed that cannot be motivated by this minimal assumption. This analysis allows us to predict the neutrino mass spectrum and set the mass of the lightest neutrino well below 0.01 eV. The method also gives the 1 sigma allowed ranges for the leptonic mixing matrix elements. Contrary to the common expectation, leptonic mixing angles are found to be determined solely by the four leptonic mass ratios without any relation to symmetry considerations as commonly used in flavor model building. Still, our formulae can be used to build up a flavor model that predicts the observed hierarchies in the masses---the mixing follows then from the procedure which is developed in this work.