Relic Right-handed Dirac Neutrinos and Implications for Detection of Cosmic Neutrino Background

It remains to be determined experimentally if massive neutrinos are Majorana or Dirac particles. In this connection, it has been recently suggested that the detection of cosmic neutrino background of left-handed neutrinos $\nu^{}_{\rm L}$ and right-handed antineutrinos $\overline{\nu}^{}_{\rm R}$ in future experiments of neutrino capture on beta-decaying nuclei (e.g., $\nu^{}_e + {^3{\rm H}} \to {^3}{\rm He} + e^-$ for the PTOLEMY experiment) is likely to distinguish between Majorana and Dirac neutrinos, since the capture rate is twice larger in the former case. In this paper, we investigate the possible impact of right-handed neutrinos on the capture rate, assuming that massive neutrinos are Dirac particles and both right-handed neutrinos $\nu^{}_{\rm R}$ and left-handed antineutrinos $\overline{\nu}^{}_{\rm L}$ can be efficiently produced in the early Universe. It turns out that the capture rate can be enhanced at most by $28\%$ due to the presence of relic $\nu^{}_{\rm R}$ and $\overline{\nu}^{}_{\rm L}$ with a total number density of $95~{\rm cm}^{-3}$, which should be compared to the number density $336~{\rm cm}^{-3}$ of cosmic neutrino background. The enhancement has actually been limited by the latest cosmological and astrophysical bounds on the effective number of neutrino generations $N^{}_{\rm eff} = 3.14^{+0.44}_{-0.43}$ at the $95\%$ confidence level. For illustration, two possible scenarios have been proposed for thermal production of right-handed neutrinos in the early Universe.