Effective field theories for dark matter direct detection

I will discuss 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. 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. I will illustrate the impact of these effects with several examples. Finally, I will comment about the importance of renormalization group running in direct dark matter detection.