Uncertainties in WIMP Dark Matter Scattering Revisited

TL;DR

This paper critically revisits the uncertainties in calculating WIMP dark matter scattering cross sections, emphasizing nucleonic matrix elements, heavy quark contributions, and recent lattice and phenomenological estimates.

Contribution

It provides a comprehensive analysis of uncertainties in nucleonic and heavy-quark matrix elements affecting WIMP scattering predictions, incorporating recent lattice and higher-order QCD calculations.

Findings

Uncertainty in < N |{ar u} u + {ar d} d | N > is larger than previously assumed.

Range of < N |{ar s} s| N > is smaller but compatible with earlier estimates.

Heavy-quark matrix elements calculated at { m O}( ext{α}_s^3) refine scattering cross section estimates.

Abstract

We revisit the uncertainties in the calculation of spin-independent scattering matrix elements for the scattering of WIMP dark matter particles on nuclear matter. In addition to discussing the uncertainties due to limitations in our knowledge of the nucleonic matrix elements of the light quark scalar densities < N |{\bar u} u, {\bar d} d, {\bar s} s| N>, we also discuss the importances of heavy quark scalar densities < N |{\bar c} c, {\bar b} b, {\bar t} t| N >, and comment on uncertainties in quark mass ratios. We analyze estimates of the light-quark densities made over the past decade using lattice calculations and/or phenomenological inputs. We find an uncertainty in the combination < N |{\bar u} u + {\bar d} d | N > that is larger than has been assumed in some phenomenological analyses, and a range of < N |{\bar s} s| N > that is smaller but compatible with earlier estimates. We also analyze the importance of the {\cal O}(\alpha_s^3) calculations of the heavy-quark matrix elements that are now available, which provide an important refinement of the calculation of the spin-independent scattering cross section. We use for illustration a benchmark CMSSM point in the focus-point region that is compatible with the limits from LHC and other searches.