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Abstract We discuss Dirac neutrinos whose right-handed component ν R has new interac­tions that may lead to a measurable contribution to the effective number of relativistic neutrino species N eff . We aim at a model-independent and comprehensive study on a variety of possibilities. Processes for ν R -genesis from decay or scattering of thermal species, with spin-0, spin-1/2, or spin-1 initial or final states are all covered. We calculate numerically and analytically the contribution of ν R to N eff primarily in the freeze-in regime, since the freeze-out regime has been studied before. While our approximate analytical results apply only to freeze-in, our numerical calculations work for freeze-out as well, including the transition between the two regimes. Using current and future constraints on N eff , we obtain limits and sensitivities of CMB experiments on masses and couplings of the new interactions. As a by-product, we obtain the contribution of Higgs-neutrino interactions, Δ N eff SM ≃ 7.5 × 10 -12 , assuming the neutrino mass is 0.1 eV and generated by the standard Higgs mechanism.