Hadronic Uncertainties in the Elastic Scattering of Supersymmetric Dark Matter

TL;DR

This work analyzes the hadronic uncertainties in spin-independent and spin-dependent neutralino–nucleon scattering within the CMSSM, quantifying how quark masses, scalar densities, and spin content propagate into cross sections. The authors find that the π-nucleon σ term Σ_{ π N} (and σ_0) dominantly control SI cross sections, while the strange-quark spin content Δ_s^{(p)} governs SD cross sections, with top-quark mass effects mainly shifting MSSM parameters but not relative cross-section ratios. Using CMSSM benchmark scenarios and Monte Carlo sampling, they show SI predictions can vary by orders of magnitude for plausible Σ_{ π N} ranges, and SD/SD ratios can vary by factors of 2–3, significantly complicating interpretation of current and future experiments. They advocate a dedicated experimental program to determine Σ_{ π N} given its critical impact on interpreting dark matter searches and potential connections to collider data and relic density calculations.

Abstract

We review the uncertainties in the spin-independent and -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 $π$-nucleon $σ$ 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 $<N | {\bar q} q | N>$ matrix elements linked to the $π$-nucleon $σ$ 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. {\it We plead for an experimental campaign to determine better the $π$-nucleon $σ$ term.} Uncertainties in the spin content of the proton affect significantly, but less strongly, the calculation of rates used in indirect searches.

Figures (10)

• Figure 1: The neutralino-nucleon scattering cross sections along the WMAP-allowed coannihilation strip for $\tan{\beta} = 10$ (left panels) and coannihilation/funnel strip for $\tan{\beta} = 50$ (right panels) using the parameters in Table \ref{['tab:params']}. CMSSM predictions for the spin-independent (SI) cross sections are shown in the upper panels ($\sigma_{\chi\rm p,SI}$ in solid/blue, $\sigma_{\chi\rm n,SI}$ in solid/red), along with experimental contraints from CDMS (dotted/black) and XENON10 (dashed/black), where the constraints apply to either SI cross section under the reasonable MSSM assumption $\sigma_{\chi\rm p,SI} \approx \sigma_{\chi\rm n,SI}$. Note that $\sigma_{\chi\rm p,SI}$ and $\sigma_{\chi\rm n,SI}$ are nearly indistinguishable at the scale used for these plots. The lower panels show CMSSM predictions for the spin-dependent (SD) cross-sections ($\sigma_{\chi\rm p,SD}$ in solid/green, $\sigma_{\chi\rm n,SD}$ in solid/magenta). Experimental constraints for $\sigma_{\chi\rm p,SD}$ are shown for KIMS (dotted/green) and Super-Kamiokande (dashed/green), while constraints for $\sigma_{\chi\rm n,SD}$ are given by CDMS (dotted/magenta) and XENON10 (dashed/magenta). Limits are based upon a local neutralino density of 0.3 GeV/cm$^3$.
• Figure 2: The spin-independent neutralino-nucleon scattering cross section as a function of $\Sigma_{\pi\!{ N}}$ for benchmark models C, L, and M. Note that $\sigma_{\chi\rm p,SI}$ and $\sigma_{\chi\rm n,SI}$ are nearly indistinguishable at the scale used in this plot.
• Figure 3: The spin-independent neutralino-nucleon scattering cross section ratio along the WMAP-allowed strips for $\tan{\beta} = 10$ (left panel) and $\tan{\beta} = 50$ (right panel) for several values of $\Sigma_{\pi\!{ N}}$. Experimental constraints from CDMS and XENON10 are also shown.
• Figure 4: The ratios of the spin-dependent and spin-independent neutralino-nucleon scattering cross sections as functions of $\Sigma_{\pi\!{ N}}$ for the benchmark models C, L, and M.
• Figure 5: The ratios of the spin-dependent and spin-independent neutralino-nucleon scattering cross sections along the WMAP-allowed strips for $\tan{\beta} = 10$ (left panel) and $\tan{\beta} = 50$ (right panel) for several values of $\Sigma_{\pi\!{ N}}$.