Effective Field Theory for Dark Matter Direct Detection up to Dimension Seven

TL;DR

This paper develops a comprehensive set of effective operators up to dimension seven for dark matter direct detection, considering various dark matter types and their electroweak representations, with detailed matching conditions.

Contribution

It provides the complete basis of effective operators up to dimension seven for dark matter, including a systematic procedure for deriving minimal operator sets and matching conditions.

Findings

Full basis of operators up to dimension seven for various dark matter types.

Algorithmic method for obtaining minimal operator sets.

Tree-level matching conditions onto low-energy effective theory.

Abstract

We present the full basis of effective operators relevant for dark matter direct detection, up to and including operators of mass dimension seven. We treat the cases where dark matter is either a Dirac fermion, a Majorana fermion, a complex scalar, or a real scalar, allowing for dark matter to furnish a general representation of the electroweak gauge group. We describe the algorithmic procedure used to obtain the minimal set of effective operators and provide the tree-level matching conditions onto the effective theory valid below the electroweak scale.