Two-photon exchange in leptophilic dark matter scenarios

TL;DR

This paper provides new analytical calculations for two-photon exchange processes in leptophilic dark matter models, revealing significant deviations from previous approximations and emphasizing the importance of momentum transfer dependence.

Contribution

It introduces exact analytical expressions for two-loop form factors in leptophilic dark matter interactions, improving accuracy over prior approximate methods.

Findings

Previous approximations can underestimate cross sections by orders of magnitude.

Form factors decrease with increasing momentum transfer, contrary to common assumptions.

Exact calculations show significant differences from earlier estimates.

Abstract

In leptophilic scenarios, dark matter interactions with nuclei, relevant for direct detection experiments and for the capture by celestial objects, could only occur via loop-induced processes. If the mediator is a scalar or pseudo-scalar particle, which only couples to leptons, the dominant contribution to dark matter-nucleus scattering would take place via two-photon exchange with a lepton triangle loop. The corresponding diagrams have been estimated in the literature under different approximations. Here, we present new analytical calculations for one-body two-loop and two-body one-loop interactions. The two-loop form factors are presented in closed analytical form in terms of generalized polylogarithms up to weight four. In both cases, we consider the exact dependence on all the involved scales, and study the dependence on the momentum transfer. We show that some previous approximations fail to correctly predict the scattering cross section by several orders of magnitude. Moreover, we show that form factors, in the range of momentum transfer relevant for local galactic dark matter, are smaller than their value at zero momentum transfer, which is usually considered.