Abstract
We further study the previously proposed Ansatz, Tr(M)=0, for a prediagonal light Majorana type neutrino mass matrix. If CP violation is neglected this enables one to use the existing data on squared mass differences to estimate (up to a discrete ambiguity)the neutrino masses themselves. If it is assumed that only the conventional CP phase is present, the ansatz enables us to estimate this phase in addition to all three masses. If it is assumed that only the two Majorana CP phases are present, the Ansatz enables us to obtain a one parameter family of solutions for the masses and phases. This enables us to obtain a simple "global" view of lepton number violation effects. Furthermore, using an SO(10) motivation for the Ansatz suggests an amusing toy (clone) model in which the heavy neutrinos have the same mixing pattern and mass ratios as the light ones. In this case only their overall mass scale is not known (although it is constrained by the initial motivation). Using this toy model we make a rough estimate of the baryon to photon ratio induced by the leptogenesis mechanism. Solutions close to the CP conserving cases seem to be favored.
Highlights
The recent KamLAND [1], SNO [2] and K2K [3] experiments have added so much to the results obtained from earlier solar neutrino, atmospheric neutrino and accelerator experiments [4] that our knowledge about the neutrino masses and presumed lepton mixing matrix is almost as great as our knowledge of the corresponding quantities in the quark sector
There is a simple complementary Ansatz for the 3 x 3 neutrino mass matrix, Mν which, with some assumptions, enables one to obtain the neutrino masses themselves from Eq (1); it requires: T r(Mν) = 0
We investigated an Ansatz which correlates information about the four quantities in the light neutrino sector which are not yet known from experiment; namely, the absolute mass of any particular neutrino, the “conventional” CP violation phase and the two Majorana phases
Summary
We will obtain an approximate equation which will be useful for relating the complementary ansatz to experimental information on neutrino squared mass differences and mixing angles in the general case where CP violation is allowed. We will use what seems to be the most common convention for the part of the leptonic mixing matrix, Kexp, which is measured in the usual neutrino oscillation experiments. This part can be constructed as a product of elementary transformations in the (12), (23) and (13) subspaces. Which has three mixing angles and three independent CP violating phases We shall use this form in what follows. M3 is relatively small compared to the others
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