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

Abstract

The ``Practical Dirac-Majorana Confusion Theorem'' (PDMCT) asserts that phenomenological differences between Dirac and Majorana neutrinos are suppressed by $(m_\nu/E)^2$ in lepton-number-conserving processes, such that at high energy, it is impossible to experimentally distinguish between Dirac o Majorana neutrinos. In this work, we propose a generalization of this theorem by introducing a New Physics vector boson ($Z'$) with CP-violating, flavor-changing neutral current (FCNC) couplings. While Fermi-Dirac statistics dictate that the flavor-diagonal vector current identically vanishes for Majorana neutrinos, we demonstrate that for non-diagonal transitions, the Majorana condition exactly cancels the real (CP-conserving) component of the vector interaction but keeping only the imaginary part induced by CP violation. Consequently, the kinematic mass suppression is lifted, and the difference in inclusive scattering cross-sections between Dirac and Majorana neutrinos becomes directly dependent on the FCNC CP-violating phase $\phi$. We apply this result to Coherent Elastic Neutrino-Nucleus Scattering (CE$\nu$NS), showing that for spin-zero targets, the distinguishability of the neutrino's nature is determined by the CP structure of the new interaction.