Seesaw mirroring between light and heavy Majorana neutrinos with the help of the S3 reflection symmetry

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.