Uncertainties in WIMP Dark Matter Scattering Revisited

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 $\langle N |{{{\bar{u}}}} u, {{{\bar{d}}}} d, {{{\bar{s}}}} s| N \rangle $ , we also discuss the importances of heavy quark scalar densities $\langle N |{{{\bar{c}}}} c, {{{\bar{b}}}} b, {{{\bar{t}}}} t| N \rangle $ , 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 $\langle N |{{{\bar{u}}}} u + {{{\bar{d}}}} d | N \rangle $ that is larger than has been assumed in some phenomenological analyses, and a range of $\langle N |{{{\bar{s}}}} s| N \rangle $ that is smaller but compatible with earlier estimates. We also analyze the importance of the ${{{\mathcal {O}}}}(\alpha _s^3)$ 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.