Hadronic uncertainties in the elastic scattering of supersymmetric dark matter

TLDR

The paper reviews uncertainties in supersymmetric dark matter elastic scattering cross sections and calls for experimental determination of the π‑nucleon σ term. The authors propagate uncertainties in quark masses and hadronic matrix elements linked to the π‑nucleon σ term and nucleon spin content. The largest uncertainty in spin‑independent scattering stems from poorly known π‑nucleon σ‑term matrix elements, which alter proton‑to‑neutron cross‑section ratios and absolute values, already biasing cold‑dark‑matter search interpretations, while proton spin‑content uncertainties also affect indirect‑search rate calculations.

Abstract

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 $\ensuremath{\pi}$-nucleon $\ensuremath{\sigma}$ 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 $\ensuremath{\pi}$-nucleon $\ensuremath{\sigma}$ 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 $\ensuremath{\pi}$-nucleon $\ensuremath{\sigma}$ term. Uncertainties in the spin content of the proton affect significantly, but less strongly, the calculation of rates used in indirect searches.