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Re-Evaluation of the Elastic Scattering of Supersymmetric Dark Matter

John Ellis, Andrew Ferstl, Keith A. Olive

TL;DR

This work re-evaluates the elastic scattering of relic neutralinos on nucleons within the constrained MSSM by updating hadronic matrix elements and enforcing cosmological and LEP constraints. By scanning the $(m_{1/2}, m_0)$ plane and requiring a relic density in $0.1 \le \Omega_\chi h^2 \le 0.3$, the authors find that the spin-dependent and spin-independent cross sections occupy narrow bands and are generally smaller than many prior estimates, with the LSP expected to be bino-like under these assumptions. The study highlights the role of coannihilation in expanding viable parameter space and clarifies hadronic uncertainties that propagate into cross-section predictions. The results have practical implications for direct-detection experiments, setting realistic target sensitivities and suggesting a clear mass–cross-section correlation to aid interpretation of potential signals.

Abstract

We examine the cross sections for the elastic scattering of neutralinos $χ$ on nucleons $p,n$, as functions of $m_χ$ in the constrained minimal supersymmetric standard model. We find narrow bands of possible values of the cross section, that are considerably lower than some previous estimates. The constrained model is based on the minimal supergravity-inspired framework for the MSSM, with universal scalar and gaugino masses $m_0, m_{1/2}$, and $μ$ and the MSSM Higgs masses treated as dependent parameters. We explore systematically the region of the $(m_{1/2}, m_0)$ plane where LEP and other accelerator constraints are respected, and the relic neutralino density lies in the range $0.1 \le Ω_χ h^2 \le 0.3$ preferred by cosmology. We update previous discussions of both the spin-independent and -dependent scattering matrix elements on protons and neutrons, using recent analyses of low-energy hadron experiments.

Re-Evaluation of the Elastic Scattering of Supersymmetric Dark Matter

TL;DR

This work re-evaluates the elastic scattering of relic neutralinos on nucleons within the constrained MSSM by updating hadronic matrix elements and enforcing cosmological and LEP constraints. By scanning the plane and requiring a relic density in , the authors find that the spin-dependent and spin-independent cross sections occupy narrow bands and are generally smaller than many prior estimates, with the LSP expected to be bino-like under these assumptions. The study highlights the role of coannihilation in expanding viable parameter space and clarifies hadronic uncertainties that propagate into cross-section predictions. The results have practical implications for direct-detection experiments, setting realistic target sensitivities and suggesting a clear mass–cross-section correlation to aid interpretation of potential signals.

Abstract

We examine the cross sections for the elastic scattering of neutralinos on nucleons , as functions of in the constrained minimal supersymmetric standard model. We find narrow bands of possible values of the cross section, that are considerably lower than some previous estimates. The constrained model is based on the minimal supergravity-inspired framework for the MSSM, with universal scalar and gaugino masses , and and the MSSM Higgs masses treated as dependent parameters. We explore systematically the region of the plane where LEP and other accelerator constraints are respected, and the relic neutralino density lies in the range preferred by cosmology. We update previous discussions of both the spin-independent and -dependent scattering matrix elements on protons and neutrons, using recent analyses of low-energy hadron experiments.

Paper Structure

This paper contains 6 sections, 24 equations, 4 figures.

Table of Contents

  1. Introduction
  2. Theoretical Framework
  3. Hadronic Matrix Elements
  4. Cosmological and Experimental Constraints
  5. Results
  6. Discussion

Figures (4)

  • Figure 1: The spin-dependent cross section for the elastic scattering of neutralinos on protons as a function of the LSP mass. The central curves are based on the inputs (\ref{['spincontent']}), and their thicknesses are related to the spreads in the allowed values of $m_0$. The shaded regions correspond to the uncertainties in the hadronic inputs (\ref{['spincontent']}).
  • Figure 2: The spin-independent scalar cross section for the elastic scattering of neutralinos on protons as a function of the LSP mass. The central curves are based on the inputs (\ref{['pinput']}), their thicknesses are again related to the spread in the allowed values of $m_0$, and the shaded regions now correspond to the uncertainties in the hadronic inputs (\ref{['pinput']}).
  • Figure 3: As in Figures 1 and 2, but now illustrating a) the effect of enlarging the uncertainty in $y$ to $\pm 0.2$, b) the spin-dependent cross section for the elastic scattering of neutralinos on neutrons, c) and d) the effects of setting $A_0 = 0$ for $\mu < 0$ and two choices of $\tan \beta$.
  • Figure 4: Summary plot compiling our predictions in the constrained MSSM for (a) the spin-dependent and (b) the spin-independent elastic LSP scattering cross sections on protons, compared in each case with current and projected limits on the scattering cross sections, as obtained from uppersigma.