Generalizing the Dirac-Majorana Confusion Theorem: The Role of CP-Violating Phases in New Physics Vector Interactions

Abstract: The ``Practical Dirac-Majorana Confusion Theorem'' said that phenomenological differences between Dirac and Majorana neutrinos are suppressed by $(m_ν/E)^2$ in lepton-number-conserving processes, making them experimentally indistinguishable at high energies. In this work, we propose a generalization of this theorem by introducing a New Physics vector boson ($Z'$) with CP-violating couplings. We demonstrate that the Majorana condition imposes that only CP-violating imaginary part contributes to the vector neutral interaction. Consequently, the difference between Dirac and Majorana neutrinos in cross-section becomes directly dependent on the CP-violating phase $φ$. We apply this framework to Coherent Elastic Neutrino-Nucleus Scattering (CE$ν$NS), showing that for spin-zero targets, the distinguishability of the neutrino nature is determined by the CP structure of the interaction.