We provide a model independent criterion which would guarantee a large flavor mixing of two quasidegenerate Majorana neutrinos at the low scale, irrespective of the mixing at the high scale. We also show that such a situation is realizable for a phenomenologically interesting range of parameters of the weak scale theory. We further claim that for a similar condition to be implementable for the three generation case, the CP parity of one of the neutrinos needs to be opposite to that of the others.PACS numbers: 14.60. Pq, 11.30.Hv, 12.15.Lk I. Introduction.-The observed atmospheric and solar neutrino anomalies from the terrestrial experiments [1,2] seem to provide strong evidence in favor of neutrino flavor conversions, implying that neutrinos are massive and they mix among themselves. While the details are fuzzy at this stage, it is clear that the atmospheric neutrino data require a large mixing of n m $ n t or n m $ n s , although the latter possibility is beginning to look less and less likely [3]. Regarding the solar neutrino anomaly, the mixing angle (between n e and n m,t or n s ) could be small, as in the small angle MSW scenario, or large, as in the large angle MSW or vacuum oscillation scenarios [2].Since large mixing angles are involved in the possible solutions of both the anomalies, a great deal of theoretical work has gone in the understanding of the maximal mixing. There are two complementary approaches: (i) searching for scenarios and symmetries beyond the standard model, and (ii) establishing general model independent criteria which guarantee the stability at the weak scale of the masses and mixing pattern that emerge at the high scale. The second approach has the advantage that it may not only narrow down the search for new physics scenarios to a manageable level, but it may also throw light on the parameters of the theory at the high scale, and on the value of the high scale itself. In this paper, we present some model independent criteria for such theories, first focusing on the two flavor case and subsequently on the three flavor models.If neutrinos contribute even a small fraction of the dark matter [4] of the universe, the oscillation observations imply a situation where at least two neutrinos (and possibly even three) are quasidegenerate in mass. If the neutrino mass hierarchy is inverted (m 3 , m 1 , m 2 where jDm

We examine the neutrino mass matrix in the version of Zee model where both Higgs doublets couple to the leptons. We show that in this case one can accommodate the large mixing angle (LMA) MSW solution of the solar neutrino problem, while avoiding maximal solar mixing and conflicts with constraints on lepton family number-violating interactions. In the simplified scenario we consider, we have the neutrino mass spectrum characterized by m 1 ≃ m 2 ≃ ∆m 2 atm / sin 2θ and m 3 /m 1 ≃ cos 2θ, where θ is the solar mixing angle. *

The renormalization group evolution equation for two neutrino mixing is known to exhibit nontrivial fixed point structure corresponding to maximal mixing at the weak scale. The presence of the fixed point provides a natural explanation of the observed maximal mixing of ν µ − ν τ if the ν µ and ν τ are * balaji@imsc.ernet.in † rmohapat@physics.umd.edu ‡ mparida@dte.vsnl.net.in § paschos@hal1.physik.uni-dortmund.de 1 assumed to be quasi-degenerate at the seesaw scale without constraining on the mixing angles at that scale. In particular, it allows them to be similar to the quark mixings as in generic grand unified theories. We discuss implementation of this program in the case of MSSM and find that the predicted mixing remains stable and close to its maximal value, for all energies below the O(TeV) SUSY scale. We also discuss how a particular realization of this idea can be tested in neutrinoless double beta decay experiments.

The polarization of the cosmic microwave background radiation (CMBR) can serve as a probe for nonstandard parity violating interactions. Many such interactions are predicted in particle physics models arising from theories with extra dimensions such as superstring theory. These interactions produce an optical activity that depends on the space-time nature of the parity violating field. In particular, it is possible to obtain a frequency-dependent differential rotation of the polarization axis. The form of the frequency dependence is sensitive to the time evolution of the parity odd background field. Thus, one may be able to study a broad class of parity violating operators through polarization measurements of the CMBR.