Seesaw mirroring between light and heavy Majorana neutrinos with the help of the $S_3^{}$ reflection symmetry

Abstract

In the canonical seesaw mechanism we require the relevant neutrino mass terms to be invariant under the $S_3^{}$ charge-conjugation transformations of left- and right-handed neutrino fields. Then both the Dirac mass matrix $M_{\mathrm{D}}^{}$ and the right-handed neutrino mass matrix $M_{\mathrm{R}}^{}$ are well constrained, so is the effective light Majorana neutrino mass matrix $M_{\nu }^{}$ via the seesaw formula. We find that these mass matrices can be classified into 22 categories, among which some textures respect the well-known $\mu$-$\tau$ permutation or reflection symmetry and flavor democracy. It is also found that there exist remarkable structural equalities or similarities between $M_{\nu }^{}$ and $M_{\mathrm{R}}^{}$, 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 $M_{\mathrm{D}}^{}$ and $M_{\mathrm{R}}^{}$ in the $S_3^{}$ reflection symmetry limit.

Comments: 33 pages, 1 table. v2: matches the version accepted for publication in JHEP