Abstract
The Standard Model predicts a long-range force between fermions due to the
exchange of a pair of neutrinos. However, this quantum force, proportional to
$G_F^2/r^5$ in the massless neutrino limit, is feeble and has not yet been
observed in experiments. In this paper, we compute this force, including the
background effect caused by cosmic, reactor, and solar neutrinos. We find that
the neutrino force can be significantly stronger in the presence of neutrino
backgrounds. Remarkably, reactor neutrino background can strengthen the
neutrino force by more than 20 orders of magnitude compared with the one in
vacuum. 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. The results are encouraging
and a detailed experimental study is called for to check if the effect can be
probed.
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