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

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