The “practical Dirac-Majorana confusion theorem” (PDMCT) asserts that phenomenological differences between Dirac and Majorana neutrinos are kinematically suppressed by $(m_{\nu }/E{)}^2$ in lepton-number-conserving processes. The PDMCT relies on standard left-handed neutrino interactions, as in the Standard Model, in which case Dirac and Majorana neutrinos are experimentally indistinguishable in lepton-number-conserving processes. Our scenario explicitly goes beyond these assumptions by introducing a neutral vector boson $Z^{\prime }$ with $CP$-violating, flavor-changing neutral current (FCNC) couplings, which generate observable Dirac-Majorana differences while remaining fully consistent with the PDMCT. In strict accordance with the PDMCT, Fermi-Dirac statistics dictate that the flavor-diagonal vector current identically vanishes for Majorana neutrinos. For nondiagonal transitions, the Majorana condition strictly forbids the real ($CP$-conserving) component of the vector interaction, leaving only an imaginary coupling. As a consequence, the observable difference in inclusive scattering cross sections between Dirac and Majorana neutrinos is driven entirely by the FCNC $CP$-violating couplings. We apply these results to coherent elastic neutrino-nucleus scattering, showing that for spin-zero targets, the distinguishability of the neutrino’s nature is determined by the $CP$ structure of the new interaction.

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• Majorana neutrinos
• Neutrinos