Accurate evaluation of hadronic uncertainties in spin-independent WIMP-nucleon scattering: Disentangling two- and three-flavor effects

We show how to avoid unnecessary and uncontrolled assumptions usually made in the literature about soft $SU(3)$ flavor symmetry breaking in determining the two-flavor nucleon matrix elements relevant for direct detection of weakly interacting massive particles (WIMPs). Based on $SU(2)$ chiral perturbation theory, we provide expressions for the proton and neutron scalar couplings fᵤp,n and fdp,n with the pion-nucleon σ term as the only free parameter, which should be used in the analysis of direct detection experiments. This approach for the first time allows for an accurate assessment of hadronic uncertainties in spin-independent WIMP-nucleon scattering and for a reliable calculation of isospin-violating effects. We find that the traditional determinations of Vfᵤᵖ-fᵤⁿ and fdᵖ-fdⁿ are off by a factor of 2.