The Importance of Being Majorana: Neutrinos versus Charged Fermions in Flavor Models

Abstract

We argue that neutrino flavor parameters may exhibit features that are very different from those of quarks and charged leptons. Specifically, within the Froggatt-Nielsen (FN) framework, charged fermion parameters depend on the ratio between two scales, while for neutrinos a third scale-that of lepton number breaking-is involved. Consequently, the selection rules for neutrinos may be different. In particular, if the scale of lepton number breaking is similar to the scale of horizontal symmetry breaking, neutrinos may become flavor-blind even if they carry different horizontal charges. This provides an attractive mechanism for neutrino flavor anarchy.Introduction. The measured neutrino flavor parameters are neither manifestly small (apart from the overall mass scale) nor manifestly hierarchical. The two measured mixing angles are O(1) and the measured mass ratio is O(0.2) or larger. With the upper bound on the third mixing angle of O(0.2), and with no information on the remaining mass ratio and CP violating phases, it could well be that all neutrino flavor parameters are nonhierarchical, that is, anarchical [1] (see however [2]). This is in sharp contrast to the charged fermion flavor parameters. Of these, only two parameters-the top Yukawa and the KM phase-are O(1), while all other eleven parameters-eight masses and three mixing angles-are small and hierarchical.It is of course possible that yet-unmeasured neutrino parameters (θ 13 and/or m 1 /m 2 ) are small, and there is hierarchy in all sectors. We assume here that this is not the case. Then, it is interesting to understand the reason for the difference between the flavor structure of neutral and charged fermions. This difference could be accidental. For example, one could imagine that the flavor structure is a result of an approximate symmetry, and it just so happens that all lepton doublets carry the same charge under this symmetry (see, for example, [3]). In other words, each of the sectors-up, down, charged lepton and neutrino-could equally well be hierarchical or accidentally anarchical. However, a far more intriguing possibility is that the difference is due to the fact that, of all the standard model fermions, only neutrinos are Majorana fermions. Then the measured parameters reflect the interplay between flavor physics and lepton number violation. It is this interplay that we wish to explore.In order to relate the flavor structure and the Majorana/Dirac nature of fermions, one must work within a framework that explains the flavor hierarchy of quarks and charged leptons. One of the most attractive such frameworks is the Froggatt-Nielsen (FN) mechanism [4]. One assumes an Abelian horizontal symmetry that is broken by a small parameter near some high "flavor scale", M F . This implies various selection rules for the flavor

How a non-hierarchical neutrino mass matrix can arise

“…Integrating out these other states can induce contributions to M ν that do not involve the N c at all, and thus do not depend on the form of the Dirac neutrino mass matrix M N . Finally, it should be mentioned that a recent paper of Nir and Shadmi [8] has interesting points of contact with the present work. For a discussion of the similarities and differences of their approach and the ideas on which the present work is based, see the discussion at the end of [7].…”

Combined flavor symmetry violation and lepton number violation in neutrino physics

“…Our model achieves approximately this form (absent the extra µ-τ symmetry that guarantees the exact bimaximal form) but implements perturbations, consistent with Eq. (1), that are needed to be in agreement with the solar and atmospheric neutrino data.…”

“…The fundamental new feature we add to the models examined in Ref. [1,2] is to give the lepton number violating scalar field a horizontal charge. We refer to this as "combining" the lepton number violation with the flavor symmetry violation.…”

“…In Ref. [1] examples were provided that involved two light neutrino generations and that exhibited the variety of behavior that can arise in that case. In this section we introduce a full three-generation model.…”

“…Nir and Shadmi [1,2] made an interesting observation regarding the unique characteristics of the neutrino sector where the right-handed neutrino is a Standard Model gauge singlet. In their framework new possibilities exist for generating mass terms because there is a new scale associated with the fact that the heavy neutrinos can have a Majorana mass that violates lepton number.…”