Power Corrections to the Universal Heavy WIMP-Nucleon Cross Section

TL;DR

This paper calculates power corrections to WIMP-nucleon scattering in Heavy WIMP Effective Theory, revealing model-dependent effects on direct detection rates and providing robust predictions for electroweak triplet Majorana fermion dark matter.

Contribution

It performs detailed two-loop matching calculations for WIMP interactions, incorporating $1/M$ corrections and analyzing their impact on direct detection predictions for different WIMP models.

Findings

Small $1/M$ correction for electroweak triplet Majorana fermions, close to universal limit.

Larger, uncertain corrections for composite scalar WIMPs, further suppressing cross section.

Results set targets for future direct detection experiments near the neutrino floor.

Abstract

WIMP-nucleon scattering is analyzed at order $1/M$ in Heavy WIMP Effective Theory. The $1/M$ power corrections, where $M\gg m_W$ is the WIMP mass, distinguish between different underlying UV models with the same universal limit and their impact on direct detection rates can be enhanced relative to naive expectations due to generic amplitude-level cancellations at leading order. The necessary one- and two-loop matching calculations onto the low-energy effective theory for WIMP interactions with Standard Model quarks and gluons are performed for the case of an electroweak SU(2) triplet WIMP, considering both the cases of elementary fermions and composite scalars. The low-velocity WIMP-nucleon scattering cross section is evaluated and compared with current experimental limits and projected future sensitivities. Our results provide the most robust prediction for electroweak triplet Majorana fermion dark matter direct detection rates; for this case, a cancellation between two sources of power corrections yields a small total $1/M$ correction, and a total cross section close to the universal limit for $M \gtrsim {\rm few} \times 100\,{\rm GeV}$. For the SU(2) composite scalar, the $1/M$ corrections introduce dependence on underlying strong dynamics. Using a leading chiral logarithm evaluation, the total $1/M$ correction has a larger magnitude and uncertainty than in the fermionic case, with a sign that further suppresses the total cross section. These examples provide definite targets for future direct detection experiments and motivate large scale detectors capable of probing to the neutrino floor in the TeV mass regime.