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

TL;DR

This paper systematically connects electroweak scale WIMP models to hadronic-scale effective theories, computing QCD effects and hadronic matrix elements crucial for accurate WIMP-nucleus scattering predictions.

Contribution

It provides a comprehensive QCD analysis, including anomalous dimensions, threshold matching, and operator basis, for WIMP direct detection phenomenology.

Findings

Computed anomalous dimensions and threshold matching for effective operators.

Reviewed and clarified hadronic matrix elements and uncertainties.

Derived operator basis and Lorentz constraints up to order v^2/c^2.

Abstract

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 $SU(2)_W\times U(1)_Y$ 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 $n_f=3$ flavor QCD operators. The complete basis of operators and Lorentz invariance constraints through order $v^2/c^2$ in the nonrelativistic nucleon effective theory are derived.