A parametrization for the neutrino mixing matrix

Abstract

We propose a flexible and model independent parametrization of the neutrino mixing matrix, which takes advantage of the fact that there are up to three small quantities in neutrino mixing phenomenology: (i) the deviation from maximal mixing of solar neutrinos, (ii) the mixing matrix element U e3 and (iii) the deviation from maximal mixing of atmospheric neutrinos. It is possible to quantify those three observations with a parameter λ ∼ 0.2, which appears at least linearly in all elements of the mixing matrix. The limit λ → 0 corresponds to exact bimaximal mixing. Present and future experiments can be used to pin down the power of λ required to usefully describe the observed phenomenology. Observing that the ratio of the two measured mass squared differences is roughly λ 2 allows to further study the structure of the Majorana mass matrix. We comment on the implications of this parametrization for neutrinoless double beta decay and on the oscillation probabilities in long-baseline experiments.

Lepton flavor violation as a probe of quark-lepton unification

“…parameterized in terms of a small parameter λ ∼ sin θ C have been proposed as parametrization of U PMNS [8,9,10,11]:…”

Quark-lepton complementarity relation and neutrino mass hierarchy

“…This substantial improvement has confirmed that the leptonic mixing matrix, heretoafter called MNSP matrix [8], is nearly bimaximal [9,10] and the deviation from bimaximality observed has revealed a surprising relation between the Cabibbo angle, θ C and the solar mixing angle [11], θ C + θ 12 = 45.1 • ± 2.4 • (1σ), * Electronic address: ferrandis @ mac.com; URL: http://homepage.mac.com/ferrandis † Electronic address: pakvasa @ phys.hawaii.edu sometimes called the quark-lepton complementarity relation, hereafter referred to as QLC relation. There is a similar relation satisfied by the leptonic angle θ 23 and the corresponding angle in the quark sector, although the errors are somewhat larger.…”

“…Therefore, in the inverted hierarchy case with same CPparities, the correction to M atm ν coming from the matrix M sol ν is at most of order γ/2 ≈ λ 3 in the entry (11) and ≈ λ 3 /2 the rest. The entries in the QLC correction, M QLC ν , are at most a correction of order λ 3 /2 in the entry (11) and ≈ λ 4 the rest.…”

“…The entries in the QLC correction, M QLC ν , are at most a correction of order λ 3 /2 in the entry (11) and ≈ λ 4 the rest. Therefore for the inverted hierarchy case with same CP-parities to reproduce the neutrino data we need the following hierarchy between the different corrections,…”

“…There is a similar relation satisfied by the leptonic angle θ 23 and the corresponding angle in the quark sector, although the errors are somewhat larger. Based on the experimental data it is convenient to define the following parametrization [12] of the mixing angles,…”