Unraveling the Dirac Neutrino with Cosmological and Terrestrial Detectors

We point out a correlation between the effective number of relativistic degrees of species $\Delta N_\text{eff}$, the cosmologically measured $m_{\nu,\text{sterile}}^{\text{eff}}$, and the terrestrially measured neutrino mass sum and effective electron neutrino mass, $\Sigma m_\nu$ and $m_{\nu_e}$, which arises in the Dirac neutrino hypothesis. If the neutrinos are Dirac particles, and if the active neutrinos' sterile partners were once thermalized in the early universe, then this new cosmological relic would simultaneously contribute to the effective number of relativistic species, $\Delta N_\text{eff}$, and also lead to a correlation between the cosmologically-measured effective sterile neutrino mass $m_{\nu,\text{sterile}}^\text{eff}$ and the terrestrially-measured active neutrino mass sum $\Sigma m_\nu$. We emphasize that specifically correlated deviations in $\Delta N_\text{eff}\gtrsim 3$, $m_{\nu,\text{sterile}}^\text{eff}$ and $\Sigma m_\nu$ above their standard predictions could be the harbinger revealing the Dirac nature of neutrinos. We provide several benchmark examples, including Dirac leptogenesis, that predict a thermal relic population of the sterile partners, and we discuss the relevant observational prospects with current and near-future experiments. If the correlation highlighted in this work is observed in future surveys, it could be interpreted as supporting evidence of Dirac neutrino masses.