Hadronic uncertainties in the elastic scattering of supersymmetric dark matter

We review the uncertainties in the spin-independent and spin-dependent elastic scattering cross sections of supersymmetric dark matter particles on protons and neutrons. We propagate the uncertainties in quark masses and hadronic matrix elements that are related to the $\pi$-nucleon $\sigma$ term and the spin content of the nucleon. By far the largest single uncertainty is that in spin-independent scattering induced by our ignorance of the $⟨N|\overline{q}q|N⟩$ matrix elements linked to the $\pi$-nucleon $\sigma$ term, which affects the ratio of cross sections on proton and neutron targets as well as their absolute values. This uncertainty is already impacting the interpretations of experimental searches for cold dark matter. We plead for an experimental campaign to determine better the $\pi$-nucleon $\sigma$ term. Uncertainties in the spin content of the proton affect significantly, but less strongly, the calculation of rates used in indirect searches.