On the short-range behavior of neutrino forces beyond the Standard Model: from $1/r^5$ to $1/r^4$, $1/r^2$, and $1/r$

Understand

The exchange of a pair of neutrinos between two objects, seperated by a distance $r$, leads to a long-range effective potential proportional to $1/r_{}^5$, assuming massless neutrinos and four-fermion contact interactions.

• In this paper, we investigate how this known form of neutrino-mediated potentials might be altered if the distance $r$ is sufficiently short, corresponding to a sufficiently large momentum transfer which could invalidate the contact interactions.
• We consider two possible scenarios to open up the contact interactions by introducing a $t$-channel or an $s$-channel mediator.
• We derive a general formula that is valid to describe the potential in all regimes as long as the external particles remain non-relativistic.