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A bstract The Standard Model predicts a long-range force, proportional to $$ {G}_F^2/{r}^5 $$ G F 2 / r 5 , between fermions due to the exchange of a pair of neutrinos. This quantum force is feeble and has not been observed yet. In this paper, we compute this force in the presence of neutrino backgrounds, both for isotropic and directional background neutrinos. We find that for the case of directional background the force can have a 1 /r dependence and it can be significantly enhanced compared to the vacuum case. In particular, background effects caused by reactor, solar, and supernova neutrinos enhance the force by many orders of magnitude. The enhancement, however, occurs only in the direction parallel to the direction of the background neutrinos. We discuss the experimental prospects of detecting the neutrino force in neutrino backgrounds and find that the effect is close to the available sensitivity of the current fifth force experiments. Yet, the angular spread of the neutrino flux and that of the test masses reduce the strength of this force. The results are encouraging and a detailed experimental study is called for to check if the effect can be probed.

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.