On the capture rates of big bang neutrinos by nuclei within the Dirac and Majorana hypotheses

Abstract

The capture rates of non-relativistic neutrinos on beta decaying nuclei depends on whether their mass is Dirac or Majorana. It is known that for relic neutrinos from the big-bang, and within minimal assumptions, the rate is a factor two larger in the Majorana case. We show that this difference also depends on the value of the lightest neutrino mass and on the type of mass hierarchy. If the lightest neutrino has a mass below the meV, so that it is still relativistic today, its capture rate for the case of Dirac masses becomes equal to that for Majorana masses. As a consequence, for the case of normal neutrino mass hierarchy, for which the total capture rate is dominated by the contribution from the lightest neutrino, if this one is below the meV the distinction between the Dirac and Majorana scenarios can only rely on the detection of the two heavier neutrinos, which is something very challenging.