Testing the bimodal/schizophrenic neutrino hypothesis in neutrinoless double beta decay and neutrino telescopes

The standard assumption is that all three neutrino mass states are either Dirac or Majorana. However, it was recently suggested by Allaverdi, Dutta, and one of the authors (R.N.M.) that mixed, or bimodal, flavor neutrino scenarios are conceivable and are consistent with all known observations (these were called schizophrenic in the ADM paper). In that case each individual mass eigenstate can be either Dirac or Majorana, so that the flavor eigenstates are large admixtures of both. An example of this bimodal situation is to consider one mass state as a Dirac particle (with a sterile partner), while the other two are of Majorana type. Since only Majorana particles contribute to neutrinoless double beta decay, the usual dependence of this observable on the neutrino mass is modified within this scenario. We study this in detail and, in particular, generalize the idea for all possible bimodal combinations. Inevitably, radiative corrections will induce a pseudo-Dirac nature to the Dirac states at the one-loop level, and the effects of the pseudo-Dirac mass splitting will show up in the flavor ratios of neutrinos from distant cosmological sources. Comparison of the effective mass in neutrinoless double beta decay as well as flavor ratios at neutrino telescopes, for different pseudo-Dirac cases and with their usual phenomenology, can distinguish the different bimodal possibilities.