CP Violation, Neutrino Mixing and the Baryon Asymmetry

We study neutrino masses and mixings based on the simplest SO(10) mass relations and the seesaw mechanism. We find that the requirement of large neutrino mixings determines the relative magnitude of the heavy Majorana neutrino masses in terms of the known quark mass hierarchy. This leads to specific predictions for the structure of the neutrino mixing matrix, the light neutrino masses, CP violation in neutrino oscillations, neutrinoless double β-decay and the baryon asymmetry. Recent results from the Sudbury Neutrino Observatory [1] and from the SuperKamiokande experiment [2] provide further evidence for the neutrino oscillation hypothesis as the solution of the solar neutrino problem. Neutrino oscillations can also account for the atmospheric neutrino anomaly [3, 4], and a consistent picture is obtained with just three neutrinos, νe, νμ and ντ , undergoing ‘nearest neighbour’ oscillations, νe ↔ νμ and νμ ↔ ντ . The experimental results on the νe deficit in the solar neutrino flux favour the LMA or LOW solutions [5] of of the MSW conversion with large mixing angle. A large mixing also fits the atmospheric neutrino oscillations. As a result, the leptonic mixing matrix Uαi seems to be very different from the familiar CKM quark mixing matrix Vαi. One finds |Uαi| = O(1) for all elements, except for |Ue3| < 0.16 [6]. Furthermore, a possible hierarchy among the neutrino masses mi has to be much weaker than the known hierarchy of quarks and charged leptons. The seesaw mechanism naturally explains the smallness of light Majorana neutrino masses m by the largeness of right-handed neutrino masses M [7], mν ≃ −mD 1 M mD , (1) where mD is the Dirac neutrino mass matrix. In unified theories one expects mD to be related to the quark and charged lepton mass matrices. Since they have a large hierarchy, the almost non-hierarchical structure of the leptonic mixing matrix is quite surprising. The simplest grand unified theory (GUT) which unifies one generation of quarks and leptons including the right-handed neutrino in a single irreducible representation is based on the gauge group SO(10) [8]. In the following we shall demonstrate that, given the known properties of the up-quark mass matrix, the puzzle of large neutrino mixings can be resolved in SO(10) theories provided the heavy neutrino masses also obey a specific hierarchy. We then explore the consequences for several observables in neutrino physics including the cosmological baryon asymmetry. The role of the heavy neutrino mass hierarchy for the light neutrino mixings has already been discussed in different contexts [9, 10, 11, 12]. In SO(10) theories quark and lepton masses are obtained by coupling the fermion multiplet 16 = (qL, u c R, e c R, d c R, lL, νR) to the Higgs multiplets H1(10), H2(10) and Φ(126), L = huij16i16jH1(10) + hdij16i16jH2(10) + hNij16i16jΦ(126) . (2) Here we have assumed that the two Higgs doublets of the standard model are contained