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| u¯ u, d¯ d, s¯ s| N⟩ , we also discuss the importances of heavy quark scalar densities ⟨ N| c¯ c, b¯ b, 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| u¯ u+ d¯ d| N⟩ that is larger than has been assumed in some phenomenological analyses, and a range of ⟨ N| s¯ s| N⟩ that is smaller but compatible with earlier estimates. We also analyze the importance of the O(αs3) 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.
Bibliographical noteFunding Information:
We would like to thank M. Hoferichter, F. Kahlhoefer, U. Meißner and M. Voloshin for useful discussions. The work of JE was supported partly by the United Kingdom STFC Grant ST/P000258/1 and partly by the Estonian Research Council via a Mobilitas Pluss grant. The work of N.N. was supported by the Grant-in-Aid for Scientific Research (No.17K14270). The work of K.A.O. was supported in part by DOE grant DE-SC0011842 at the University of Minnesota.
© 2018, The Author(s).