Dirac-Majorana neutrinos distinction in four-body decays

A novel method to differentiate the effects of Dirac and Majorana (D-M) neutrinos in four-body decays has been discussed in arXiv:2106.11785. There, it is concluded that the back-to-back kinematic scenario seems to avoid the constraint imposed by the "practical Dirac-Majorana confusion theorem", as one does not need to fully integrate over neutrino and antineutrino momenta. In this paper, we propose to analyse radiative leptonic lepton-decays ($\ell\to\ell'\nu\bar{\nu}\gamma$), as an independent alternative process to study the possible Majorana nature of neutrinos. Our approach demonstrates that, in the back-to-back kinematic configuration (for the $\ell'- \gamma$ and $\nu-\bar{\nu}$ systems, respectively), the distinction between Dirac and Majorana cases disappears when the inaccessible neutrino angle is integrated out, which might appear unexpected considering the claims in arXiv:2106.11785. Our results apply in absence of non-standard interactions, which can enhance generally the sensitivity to the neutrino nature.