Standard Model anatomy of WIMP dark matter direct detection. II. QCD analysis and hadronic matrix elements

Models of weakly interacting massive particles (WIMPs) specified at the electroweak scale are systematically matched to effective theories at hadronic scales where WIMP-nucleus scattering observables are evaluated. Anomalous dimensions and heavy-quark threshold matching conditions are computed for the complete basis of lowest-dimension effective operators involving quarks and gluons. The resulting QCD renormalization group evolution equations are solved. The status of relevant hadronic matrix elements is reviewed and phenomenological illustrations are given, including details for the computation of the universal limit of nucleon scattering with heavy SU(2)W×U(1)Y charged WIMPs. Several cases of previously underestimated hadronic uncertainties are isolated. The results connect arbitrary models specified at the electroweak scale to a basis of nf=3-flavor QCD operators. The complete basis of operators and Lorentz invariance constraints through order v2/c2 in the nonrelativistic nucleon effective theory are derived.