We perform a renormalisation group (RG) analysis of neutrino masses and mixing angles in the see-saw mechanism in the minimal supersymmetric standard model with three right-handed neutrinos, including the effects of the heavy neutrino thresholds.We focus on the case that one of the right-handed neutrinos provides the dominant contribution to the 23 block of the light Majorana matrix, causing its determinant to approximately vanish and giving an automatic neutrino mass hierarchy, so called single right-handed neutrino dominance which may arise from a U(1) family symmetry.In these models radiative corrections can increase atomospheric and solar neutrino mixing by up to about 10% and 5%, respectively, and may help to achieve bi-maximal mixing. Significantly we find that the radiative corrections over the heavy neutrino threshold region are at least as important as those usually considered from the lightest right-handed neutrino down to low energies.

We study models of neutrino masses which naturally give rise to an inverted mass hierarchy and bi-maximal mixing. The models are based on the see-saw mechanism with three right-handed neutrinos, which generates a single mass term of the form ν e (ν µ +ν τ ) corresponding to two degenerate neutrinos ν e and ν µ +ν τ , and one massless neutrino ν µ −ν τ . Atmospheric neutrino oscillations are accounted for if the degenerate mass term is about 5 × 10 −2 eV. Solar neutrino oscillations of the Large Mixing Angle MSW type arise when small perturbations are included leading to a mass splitting between the degenerate pair of about (1.7 − 2.0) × 10 −4 eV for the successful cases. We study the conditions that such models must satisfy in the framework of a U(1) family symmetry broken by vector singlets, and catalogue the simplest examples. We then perform a renormalisation group analysis of the neutrino masses and mixing angles, assuming the supersymmetric standard model, and find modest radiative corrections of a few per cent, showing that the model is stable. At low energies we find sin 2 2θ 23 ≈ 0.93 − 0.96 and sin 2 2θ 12 ≈ 0.9 − 1.0.

A model-independent ansatz to describe lepton and quark mixing in a unified way is suggested based upon the Cabibbo angle. In our framework neutrinos mix in a "Bi-Large" fashion, while the charged leptons mix as the "down-type" quarks do. In addition to the standard Wolfenstein parameters (λ, A) two other free parameters (ψ, δ) are needed to specify the physical lepton mixing matrix. Through this simple assumption one makes specific predictions for the atmospheric angle as well as leptonic CP violation in good agreement with current observations.

Using radiative corrections and the seesaw mechanism, we derive analytic formulas for neutrino masses at low energies in SUSY unified theories exhibiting, for the first time, a tan ␤ dependence of mass ratios. The enhancements of the hierarchial ratios are found to be quite significant for smaller values of tan ␤. Renormalization coefficients and mass predictions are evaluated, with uncertainties, in SUSY SO͑10͒ models having a grand desert and intermediate breaking. ͓S0556-2821͑98͒06223-7͔ PACS number͑s͒: 12.10.Dm, 12.60.Jv

In this paper we propose a kind of natural selection which can discriminate the three possible neutrino mass models, namely the degenerate, inverted hierarchical and normal hierachical models, using the framework of Type II seesaw formula. We arrive at a conclusion that the inverted hierarchical model appears to be most favourable whereas the normal hierarchical model follows next to it. The degenerate model is found to be most unfavourable. The neutrino mass matrices which are obtained using the usual canonical seesaw formula (Type I), and which also give almost good predictions of neutrino masses and mixings consistent with the latest neutrino oscillation data, are re-examined in the light of non-canonical seesaw formula (Type II). We then estimate a parameter γ which represents the minimum degree of suppression of the extra term arising from the left-handed Higgs triplet, so as to restore the good predictions on neutrino masses and mixings already had in Type I seesaw model.

Radiative generation of the solar scale ∆ ⊙ is discussed in the presence of leptonic CP violation. We assume that both the solar scale and U e3 are zero at a high scale and the weak radiative corrections generate them. It is shown that all leptonic mass matrices satisfying these requirements lead to a unique prediction ∆ ⊙ cos 2θ ⊙ ≈ 4δ τ sin 2 θ A |m ee | 2 for the solar scale in terms of the radiative correction parameter δ τ , the physical solar (atmospheric) mixing angles θ ⊙ (θ A ) and the Majorana neutrino mass m ee probed in neutrinoless double beta decay. This relation is independent of the mixing matrix and CP-violating phases at the high scale. The presence of CP-violating phases leads to dilution in the solar mixing angle defined at the high scale. Because of this, bi-maximal mixing pattern at the high energy leads to large but non-maximal solar mixing in the low-energy theory. An illustrative model with this feature is discussed.

No abstract

In this Letter we highlight the inherent problems associated with the inverted hierarchical model of neutrinos with only three generations and then suggest possible solutions within the MSSM. We discuss the new parametrization of the solar mixing angle which can identify the light side and dark side of the data. We then argue whether the inverted hierarchical neutrino mass matrix can explain the large mixing angle (LMA) MSW solution of the solar neutrino anomaly in the presence of an appropriate texture of charged lepton mass matrix. In a model independent way we explore such specific form of the charged lepton mass matrix having a special structure in 1-2 block. The contribution to the solar mass splitting arising out of radiative corrections in MSSM, is calculated, thus making the model stable under radiative corrections.