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 ν3 > m ν2 > m ν1 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 μ , m μ /m τ , m ν1 /m ν2 and m ν2 /m ν3 , 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 flavor 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 1σ 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.

The mass ratios parametrization

“…For last, to fully reparametrise a mass matrix in terms of its singular values the number of independent mass ratios should be larger or equal than the number of mixing parameters. In fact, this only occurs for two and three fermion generations [16]. To see this, assume again n fermion generations.…”

“…where X = q, ℓ, a = u, ν, and b = d, e. There has been many parametrization proposals [6][7][8][9][10][11][12][13][14][15][16]. Among them there is one particular parametrization which has served, in the quark sector, to provide a better connection to the parameters in flavour physics [10,12,14],…”

“…First, we are assuming the viewpoint that if masses ought to explain mixing this should necessarily require having the four independent mass ratios of each fermion sector as mixing parameters without the need to consider other auxiliary parameters, therefore, giving rise to a full mixing parametrization as first suggested in Ref. [16]. Second, the analysis here made is model-independent and follows a bottom-up approach.…”

Neutrino Mixing from SUSY breaking

“…For hierarchical neutrino masses, flavor changing threshold corrections to the mixing matrix as described above are subdominant. However, hierarchical masses may ask for a special treatment which can be combined with the radiative Yukawa couplings discussed in the introduction: a successive breaking of an initial [U(3)] 6 flavor symmetry leads to a description of fermion mixing in terms of mass ratios only, that can be related to the symmetry breaking parameters [32]. We do not give analytic expressions for self-energies in this article since such results can be found in [33] and [34].…”

Texture zeros and hierarchical masses from flavour (mis)alignment

“…This symmetry allows for some arbitrariness in the choice of a weak basis. 1 The largest flavour symmetry is given by the following global symmetries on the fermion fields:…”