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

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 M_D and the right-handed neutrino mass matrix M_R are well constrained, so is the effective light Majorana neutrino mass matrix M_ν 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 M_ν and M_R, 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 M_D and M_R in the S₃ reflection symmetry limit.