On the Nature of Massive Neutrinos

During the last thirty years, the compelling experimental evidences for oscillations of solar, reactor, atmospheric and accelerator neutrinos imply the existence of 3-neutrino mixing.Since in the Standard Model neutrinos are massless, the mechanism of generation of these small masses is unknown and different according to their nature: Dirac or Majorana? Neutrino oscillations experiments cannot give the answer. In the same way as the mixing of quarks is parametrized by the Cabibbo Kobayashi Maskawa quark mixing matrix - which is a unitary matrix that contains information on the strength of the flavour-changing weak interaction - , neutrino mixing can be parameterized by a 3x3 leptonic mixing matrix,called the Pontecorvo Maki Nakagawa Sakata matrix (PMNS matrix). Neutrino oscillation experiments have improved and stabilised the precision on the measurements of three mixing angles and one CP violating phase, constraining strongly unitarity violation of PMNS matrix. If neutrinos are of Majorana type there are 2 additionnal phases that cannot be accessed by oscillation experiments. In this work, we will use the most recent Nu-Fit of the PMNS parameters at 3σ in normal and inverted neutrino masses hierarchies.We will first discuss the constraints on the sum of neutrino masses and mass hierarchies taking also into account cosmological bounds and KATRIN and DESI experiments. Neutrinoless double beta decay (hereafter denoted 0νββ decay) constrains the effective Majorana mass |mee|.Within its experimental limits we will study the sensitivity to the 2 additionnal Majorana phases α and β. We will show that only one phase - α - can be extracted from data. We finally discuss the possibility that neutrino antineutrino oscillations involving muons could be complementary to 0νββ decay to help in finding the nature of neutrinos.