On neutrino-mediated potentials in a neutrino background

The exchange of a pair neutrinos with Standard Model weak interactions generates long-range force between fermions. associated potential is extremely feeble, $\propto G_F^2/r^5$ for massless neutrinos, whichrenders it far from observable even in the most sensitive experiments testing fifth forces. presence neutrino background has been argued to induce correction propagator that enhances by orders magnitude. In this brief note, we point out such modified propagators are invalid if wavepackets have finite width. By reevaluating 2--$\nu$ including width effects, find background-induced enhancement reduced several Unfortunately, pushes resulting away present and near-future sensitivity tests new