Generation of Large Flavor Mixing from Radiative Corrections

Abstract

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

Large neutrino mixing from renormalization group evolution

“…Taking M S = M Z , this is recognised exactly as the condition that was derived in [4,5] for magnifying small mixing at high scale to large mixing at low-energies through radiative corrections. But, as noted here, In the SM, 2δ τ (t Z ) and 2δ µ (t Z ) in (4.1) are replaced by −δ τ (t Z ) and −δ µ (t Z ), respectively, and (4.1) predicts m 0 2 > m 0 3 .…”

“…With a view to simplifying model building, we recently suggested criteria for radiative magnification of neutrino mixing [4,5] which allow a small mixing at high scale to be amplified to large mixing at the weak scale after renormalization group evolution. The only condition that needs to be fulfilled is that the ν µ and ν τ be quasi-degenerate in mass, as for example would be independently required if LSND results are confirmed.…”

Renormalization group evolution of neutrino masses and mixing in the Type-III seesaw mechanism

“…These effects can have interesting consequences such as the generation of large mixing angles [33,34,35,36,37,38], small mass splittings for degenerate neutrinos [39,40,41,42,43,44,45,46,47], or radiative generation of θ 13 starting from a zero value at the high scale [48,49,50,51]. RG induced deviations from various high scale symmetries like tri-bimaximal mixing scenario [52,53,54] or quark-lepton complimentarity [54,55,56,57] and correlations with low scale observables have been explored.…”

Neutrino mass and New physics

“…For m 0 = 0.3 eV and (Z τ − 1) ∼ 10 −3 it can give the solar mass split [57]. Furthermore, the mixing angles depend on mass differences whereas corrections are proportional to the absolute values of the elements so that the relative corrections to the mixing get enhanced [56] by ∆θ ∝ m/∆m ∝ m 2 0 /∆m 2 . Essentially, the enhancement of mixing occurs when neutrinos become even more degenerate at low energies.…”

“…This means that the large 1-2 mixing at low energies may have the radiative origin being small at, e.g., the GUT scale [55,56]. Another interesting possibility is that at M GU T equality of the quark and leptonic 1-2 mixings, θ 12 = θ C , is realized.…”