NLO electroweak potentials for minimal dark matter and beyond

TL;DR

This paper computes the one-loop electroweak corrections to the static potential for heavy standard model multiplets, revealing a Casimir-like scaling and providing practical tools for phenomenological applications.

Contribution

It introduces a general calculation of NLO electroweak potentials for arbitrary heavy multiplets, highlighting their scaling behavior and offering fitting functions for use in phenomenology.

Findings

NLO corrections follow Casimir-like scaling.

The potential exhibits known asymptotic limits.

Fitting functions are provided for practical use.

Abstract

We calculate the one-loop correction to the static potential induced by $\gamma$, $W$ and $Z$-exchange at tree-level for arbitrary heavy standard model multiplets. We find that the result obeys a "Casimir-like" scaling, making the NLO correction to the potential a "low-energy" property of the electroweak gauge bosons. Furthermore, we discuss the phenomenology of the NLO potentials, the analytically known asymptotic limits and provide fitting functions in position space for easy use of the results.