Quark-Lepton Unification and Eight-Fold Ambiguity in the Left-Right Symmetric Seesaw Mechanism

Abstract

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 $M_{\nu }=f{v}_L-\frac{v^2}{v_R}{Y}_{\nu }{f}^{-1}{Y}_{\nu }$, 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 $2^n$ solutions (in the n-family case) for the matrix f as a function of the Dirac neutrino couplings $(Y_{\nu }{)}_{ij}$ 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 $126+\overline{126}$ 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.

arXiv comment31 pages, 32 figures. Appendix augmented with useful analytic formulae, a few typos corrected, 2 references added

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