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A<sc>bstract</sc> The neutrino force results from the exchange of a pair of neutrinos. A neutrino background can significantly influence this force. In this work, we present a comprehensive calculation of the neutrino force in various neutrino backgrounds with spin dependence taken into account. In particular, we calculate the spin-independent and spin-dependent parity-conserving neutrino forces, in addition to the spin-dependent parity-violating neutrino forces with and without the presence of a neutrino background for both isotropic and anisotropic backgrounds. Compared with the vacuum case, the neutrino background can effectively violate Lorentz invariance and lead to additional parity-violating terms that are not suppressed by the velocity of external particles. We estimate the magnitude of the effect of atomic parity-violation experiments, and it turns out to be well below the current experimental sensitivity. 

Abstract A singlet majoron can arise from the seesaw framework as a pseudo-Goldstone boson when the heavy Majorana neutrinos acquire masses via the spontaneous breaking of global U(1)_Lsymmetry. The resulting cosmological impacts are usually derived from the effective majoron-neutrino interaction, and the majoron abundance is accumulated through the freeze-in neutrino coalescence. However, a primordial majoron abundance can be predicted in a minimal setup and lead to distinctive cosmological effects. In this work, we consider such a primordial majoron abundance from relativistic freeze-out and calculate the modification to the effective neutrino numberN_eff. We demonstrate that the measurements ofN_effwill constrain the parameter space from a primordial majoron abundance in an opposite direction to that from neutrino coalescence. When the contributions from both the primordial abundance and the freeze-in production coexist, the U(1)_L-breaking scale (seesaw scale)fwill be pushed into a “sandwiched window”. Remarkably, for majoron masses below 1 MeV and above the eV scale, the future CMB-S4 experiment will completely close such a low-scale seesaw window forf∈ [1,10⁵] GeV. We highlight that any new light particle with a primordial abundance that couples to Standard Model particles may lead to a similar sandwiched window, and such a general phenomenon deserves careful investigation. 

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.