Triangle Inequalities for Majorana-Neutrino Magnetic Moments

Electromagnetic properties of neutrinos, if ever observed, could help to decide the Dirac versus Majorana nature of neutrinos. We show that the magnetic moments of Majorana neutrinos have to fulfill triangle inequalities, $|\mu_{\nu_\tau}|^2 \leq |\mu_{\nu_\mu}|^2 +|\mu_{\nu_e}|^2$ and cyclic permutations, which do not hold for Dirac neutrinos. Observing a violation of these inequalities, e.g. by measuring the magnetic moment of $\nu_\tau$ at SHiP, would thus strongly hint either at the Dirac nature of neutrinos or at the presence of at least one extra light sterile mode.