The 10(-3) eV frontier in neutrinoless double beta decay

The observation of neutrinoless double beta decay would allow to establish lepton number violation and the Majorana nature of neutrinos. The rate of this process in the case of 3-neutrino mixing is controlled by the neutrinoless double beta decay effective Majorana mass vertical bar < m >vertical bar. For a neutrino mass spectrum with normal ordering, which is favoured over the spectrum with inverted ordering by recent global fits,vertical bar < m >vertical bar can be significantly suppressed. Taking into account updated data on the neutrino oscillation parameters, we investigate the conditions under which vertical bar < m >vertical bar in the case of spectrum with normal ordering exceeds 10(-3)(5 x 10(-3)) eV: vertical bar < m >vertical bar(NO) > 10(-3)(5 x 10(-3)) eV. We analyse first the generic case with unconstrained leptonic CP violation Majorana phases. We show, in particular, that if the sum of neutrino masses is found to satisfy Sigma > 0.10 eV, then vertical bar < m >vertical bar(NO) > 5 x 10(-3) eV for any values of the Majorana phases. We consider also cases where the values for these phases are either CP conserving or are in line with predictive schemes combining flavour and generalised CP symmetries. (C) 2018 The Authors. Published by Elsevier B.V