Triangle Inequalities for Majorana-Neutrino Magnetic Moments

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, $|{\mu }_{{\nu }_{\tau }}{|}^2\le |{\mu }_{{\nu }_{\mu }}{|}^2+|{\mu }_{{\nu }_e}{|}^2$ 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.

10 pages, 1 figure. Extended discussion of sterile neutrinos; accepted by PRD

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• A facility to Search for Hidden Particles (SHiP) at the CERN SPS
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• High Energy Physics and Cosmology at the Unification Frontier: Opportunities and Challenges in the coming years
• Status and perspectives of neutrino magnetic moments
• Letter of Intent: The Forward Physics Facility