Triangle Inequalities for Majorana-Neutrino Magnetic Moments

TL;DR

This paper derives triangle inequalities for Majorana neutrino magnetic moments, proposing that their violation could indicate Dirac neutrinos or additional sterile neutrino modes, thus providing a test for neutrino nature.

Contribution

It introduces specific triangle inequalities for Majorana neutrino magnetic moments and discusses their implications for neutrino nature and potential experimental tests.

Findings

Majorana neutrino magnetic moments must satisfy triangle inequalities.

Violation of these inequalities suggests Dirac neutrinos or extra sterile modes.

Measuring tau neutrino magnetic moment could test these inequalities.

Abstract

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.