Neutrino forces in neutrino backgrounds

Abstract

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.

On neutrino-mediated potentials in a neutrino background

“…In particular, if f ( k ) is a thermal distribution we recover the results obtained for the CνB [27][28][29][30]. Notice however, that as discussed above, the Pauli exclusion principle makes this limit unphysical for the non-thermal neutrino backgrounds from the Sun, nuclear reactors, or SN.…”

“…Furthermore, this is the scenario for which the largest background-induced enhancement is obtained in ref. [30]. For this case, and neglecting the neutrino mass, we find for…”

“…The key technical ingredient to evaluate neutrino background effects in refs. [27][28][29][30] is the use of the background-modified propagator obtained in finite temperature field theory (TQFT) (for reviews of TQFT, see for example refs. [31,32]),…”

“…Interestingly, one can still use QFT techniques to show that eq. (2.1) may be used for the neutrino propagator in the presence of a class of backgrounds, see [30]. This derivation, however, implicitly assumes that the neutrino background is well-described by an incoherent superposition of plane waves.…”

“…Most recently, the effect of neutrino backgrounds has been restudied and extended in ref. [30]. This work claims that the intense neutrino fluxes from the Sun, supernovae (SN), or nuclear reactors, may substantially enhance the potential (by up to 20 orders of magnitude), in particular in the direction of the incoming background neutrino flux.…”