Standard Model anatomy of WIMP dark matter direct detection I: weak-scale matching

Abstract

We present formalism necessary to determine weak-scale matching coefficients in the computation of scattering cross sections for putative dark matter candidates interacting with the Standard Model. Particular attention is paid to the heavy-particle limit. A consistent renormalization scheme in the presence of nontrivial residual masses is implemented. Two-loop diagrams appearing in the matching to gluon operators are evaluated. Details are given for the computation of matching coefficients in the universal limit of WIMP-nucleon scattering for pure states of arbitrary quantum numbers, and for singlet-doublet and doublet-triplet mixed states.