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 < 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.
