Abstract
Nonzero neutrino masses imply the existence of degrees of freedom and interactions beyond those in the Standard Model. A powerful indicator of what these might be is the nature of the massive neutrinos: Dirac fermions versus Majorana fermions. While addressing the nature of neutrinos is often associated with searches for lepton-number violation, there are several other features that distinguish Majorana from Dirac fermions. Here, we compute in great detail the kinematics of the daughters of the decays into charged-leptons and neutrinos of hypothetical heavy neutral leptons at rest. We allow for the decay to be mediated by the most general four-fermion interaction Lagrangian. We demonstrate, for example, that when the daughter charged-leptons have the same flavor or the detector is insensitive to their charges, polarized Majorana-fermion decays have zero forward-backward asymmetry in the direction of the outgoing neutrino (relative to the parent spin), whereas Dirac-fermion decays can have large asymmetries. Going beyond studying forward-backward asymmetries, we also explore the fully differential width of the three-body decays. It contains a wealth of information not only about the nature of the new fermions but also the nature of the interactions behind their decays.
Highlights
Massive fermions with no conserved quantum numbers can be either Majorana fermions or Dirac fermions
II, we present arguments based upon the CPT properties of the final states to show that if the heavy neutral lepton (HNL) is a Majorana fermion in certain classes of decays, there is no forward-backward asymmetry of the charged-lepton-pair system relative to the spin of the HNL
The fact that neutrinos have mass implies the existence of new particles or interactions beyond those that make up the Standard Model of particle physics
Summary
Massive fermions with no conserved quantum numbers can be either Majorana fermions or Dirac fermions. Nonzero neutrino masses imply the existence of new degrees of freedom Their nature and properties are very poorly constrained. The deepest probes for the violation of lepton number are searches for the neutrinoless double-beta decay of various nuclei These are the subject of intense experimental research (see [8] for a recent review).
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