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

David Delepine, A. Yebra

TL;DR

This work generalizes the Dirac-Majorana confusion framework by introducing a CP-violating New Physics vector boson $Z'$ that couples to neutrinos. The Majorana case then couples only to the CP-violating imaginary part of the vector current, making the cross-section difference between Dirac and Majorana neutrinos governed by the CP phase $\phi$ rather than the neutrino mass $m_\nu$. In CE$\nu$NS on spin-zero targets, the vector current can be effectively filtered, enabling a potentially observable distinction in the presence of CP violation, while COHERENT data constrain Dirac-vector NP and leave room for CP-violating Majorana effects. The findings motivate precision CE$\nu$NS and nu-e scattering measurements at COHERENT and DUNE to probe the CP structure and determine the neutrino’s fundamental nature.

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.

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

TL;DR

This work generalizes the Dirac-Majorana confusion framework by introducing a CP-violating New Physics vector boson that couples to neutrinos. The Majorana case then couples only to the CP-violating imaginary part of the vector current, making the cross-section difference between Dirac and Majorana neutrinos governed by the CP phase rather than the neutrino mass . In CENS on spin-zero targets, the vector current can be effectively filtered, enabling a potentially observable distinction in the presence of CP violation, while COHERENT data constrain Dirac-vector NP and leave room for CP-violating Majorana effects. The findings motivate precision CENS and nu-e scattering measurements at COHERENT and DUNE to probe the CP structure and determine the neutrino’s fundamental nature.

Abstract

The ``Practical Dirac-Majorana Confusion Theorem'' said that phenomenological differences between Dirac and Majorana neutrinos are suppressed by 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 () 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 . We apply this framework to Coherent Elastic Neutrino-Nucleus Scattering (CENS), showing that for spin-zero targets, the distinguishability of the neutrino nature is determined by the CP structure of the interaction.
Paper Structure (18 sections, 13 equations, 1 figure)

This paper contains 18 sections, 13 equations, 1 figure.

Table of Contents

  1. Introduction
  2. Formalism: Effective Majorana Couplings with CP Violation
  3. Majorana Constraints
  4. Effective Couplings
  5. Scattering Cross-Sections and Phenomenological Consequences
  6. Elastic Neutrino-Electron Scattering ($\nu e^- \to \nu e^-$)
  7. Dirac Case
  8. Majorana Case
  9. Coherent Elastic Neutrino-Nucleus Scattering (CE$\nu$NS)
  10. The Exclusive Neutral Current Nature of CE$\nu$NS
  11. Nuclear Selection Rules and Spin-Zero Targets
  12. The Generalized Confusion Theorem at Work
  13. Discussion and Conclusions
  14. Experimental Implications
  15. Compatibility with COHERENT Data
  16. ...and 3 more sections

Figures (1)

  • Figure 1: Comparison of CE$\nu$NS event rates for Dirac and Majorana neutrinos in an Argon detector. The Majorana rate is suppressed by the absence of the SM vector current contribution, surviving only through the CP-violating imaginary coupling of the $Z'$ ($\epsilon=0.02$).