Abstract
In the canonical seesaw mechanism we require the relevant neutrino mass terms to be invariant under the S3 charge-conjugation transformations of left- and right-handed neutrino fields. Then both the Dirac mass matrix MD and the right-handed neutrino mass matrix MR are well constrained, so is the effective light Majorana neutrino mass matrix Mν via the seesaw formula. We find that these mass matrices can be classified into 22 categories, among which some textures respect the well-known μ-τ permutation or reflection symmetry and flavor democracy. It is also found that there exist remarkable structural equalities or similarities between Mν and MR, reflecting a seesaw mirroring relationship between light and heavy Majorana neutrinos. We calculate the corresponding light neutrino masses and flavor mixing parameters as well as the CP-violating asymmetries in decays of the lightest heavy Majorana neutrino, and show that only the flavored leptogenesis mechanism is possible to work for three categories of MD and MR in the S3 reflection symmetry limit.
Highlights
Where MD ≡ Yν H with H ≃ 174 GeV being the vacuum expectation value of the Higgs field
We calculate the corresponding light neutrino masses and flavor mixing parameters as well as the CP-violating asymmetries in decays of the lightest heavy Majorana neutrino, and show that only the flavored leptogenesis mechanism is possible to work for three categories of MD and MR in the S3 reflection symmetry limit
Flavor symmetry is most likely to manifest itself at a high energy scale far above the electroweak scale, the phenomenological approach under discussion fits the spirit of the bottom-up approach of model building in particle physics
Summary
To characterize the relationship between light and heavy Majorana neutrinos in the seesaw framework under consideration, we refer to the structural equality or similarity between Mν and MR as a seesaw mirroring relationship Another thing that deserves attention is that the mass matrices constrained by any one of S(123), S(231) and S(312) must be real. Only categories A1, A2 and A3 allow us to obtain the complex textures of Mν via the seesaw formula This observation means that in the S3 reflection symmetry limit there are only four possibilities to accommodate CP violation in the lepton-number-violating decays of heavy Majorana neutrinos, and only three possibilities to accommodate CP violation in the effective light neutrino mass matrix Mν. Since S3 is so simple and instructive in reflecting the possible interchange among three flavor families, it should be qualified as a good bottom-up example in probing what is behind tiny neutrino masses and significant flavor mixing effects
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