From quarks to nucleons in dark matter direct detection

TL;DR

This paper derives detailed nonperturbative matching formulas connecting quark and gluon level operators to nonrelativistic dark matter interactions with nucleons, highlighting the importance of multiple operators and pion pole effects in direct detection.

Contribution

It provides the first comprehensive expressions for matching dark matter-quark/gluon operators to nonrelativistic nucleon interactions, including subleading chiral order effects.

Findings

Single partonic operators match onto multiple nonrelativistic operators.

Momentum suppressed terms can be numerically significant due to pion poles.

Properly accounting for these effects alters the interpretation of direct detection experiments.

Abstract

We provide expressions for the nonperturbative matching of the effective field theory describing dark matter interactions with quarks and gluons to the effective theory of nonrelativistic dark matter interacting with nonrelativistic nucleons. We give the leading and subleading order expressions in chiral counting. In general, a single partonic operator already matches onto several nonrelativistic operators at leading order in chiral counting. Thus, keeping only one operator at the time in the nonrelativistic effective theory does not properly describe the scattering in direct detection. Moreover, the matching of the axial--axial partonic level operator, as well as the matching of the operators coupling DM to the QCD anomaly term, naively include momentum suppressed terms. However, these are still of leading chiral order due to pion poles and can be numerically important. We illustrate the impact of these effects with several examples.