Quark-lepton unification and eight-fold ambiguity in the left-right symmetric seesaw mechanism

In many extensions of the Standard Model, including a broad class of left-right symmetric and grand unified theories, the light neutrino mass matrix is given by the left-right symmetric seesaw formula Mν=fvL−v2vRYνf−1Yν, in which the right-handed neutrino mass matrix and the SU(2)L triplet couplings are proportional to the same matrix f. We propose a systematic procedure for reconstructing the 2n solutions (in the n-family case) for the matrix f as a function of the Dirac neutrino couplings (Yν)ij and of the light neutrino mass parameters, which can be used in both analytical and numerical studies. We apply this procedure to a particular class of supersymmetric SO(10) models with two 10-dimensional and a pair of 126⊕126¯ representations in the Higgs sector, and study the properties of the corresponding 8 right-handed neutrino spectra. Then, using the reconstructed right-handed neutrino and triplet parameters, we study leptogenesis and lepton flavour violation in these models, and comment on flavour effects in leptogenesis in the type I limit. We find that the mixed solutions where both the type I and the type II seesaw mechanisms give a significant contribution to neutrino masses provide new opportunities for successful leptogenesis in SO(10) GUTs.