On neutrino-mediated potentials in a neutrino background

TL;DR

This paper reevaluates neutrino-mediated potentials in a neutrino background, showing that finite width effects significantly reduce the potential's enhancement, making it undetectable with current or near-future experiments.

Contribution

It demonstrates that background neutrino wavepacket widths diminish the previously claimed enhancement of neutrino-mediated potentials, correcting earlier assumptions.

Findings

Background-induced enhancement is reduced by several orders of magnitude.

The potential remains far below the sensitivity of current experiments.

Finite width effects are crucial in accurate potential calculations.

Abstract

The exchange of a pair of neutrinos with Standard Model weak interactions generates a long-range force between fermions. The 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. The presence of a neutrino background has been argued to induce a correction to the neutrino propagator that enhances the potential by orders of magnitude. In this brief note, we point out that such modified propagators are invalid if the background neutrino wavepackets have a finite width. By reevaluating the 2--$\nu$ exchange potential in the presence of a neutrino background including finite width effects, we find that the background-induced enhancement is reduced by several orders of magnitude. Unfortunately, this pushes the resulting 2--$\nu$ exchange potential away from present and near-future sensitivity of tests of new long-range forces.