Maximum And Minimum Dark Matter Detection Cross Sections

The range of neutralino-proton cross sections for R-parity preserving supergravity models with GUT scale unification of the gauge coupling constants is examined. The models considered here are mSUGRA, models with non universal soft breaking and D-brane models. It is found that the current dark matter detectors are sampling significant parts of the SUSY parameter space and future detectors could sample almost the entire space. The special regions of parameter space that may be inaccessible to future detectors are seen to have a squark/gluino spectra beyond 1 TeV, but observable at the LHC. While the existence of dark matter, which is now believed to make up about 30 % of the matter and energy of the universe, has been known for sometime, the nature of dark matter remains unresolved. Supersymmetric models with R parity invariance automatically posses a dark matter candidate, the lightest supersymmetric particle (LSP). We consider here models based on gravity mediated supergravity (SUGRA), where the LSP is generally the lightest neutralino (χ̃ 1 ). Neutralinos in the halo of the Milky Way might be directly detected by their scattering by terrestrial nuclear targets. Such scattering has a spin independent and a spin dependent part. For heavy nuclear targets the former dominates, and it is possible to extract then (to a good approximation) the neutralino -proton cross section, σχ̃0 1 −p. Current experiments (DAMA, CDMS, UKMDC) have sensitivity to halo χ̃ 1 for σχ̃0 1 −p > ∼ 1× 10 pb (1) and future detectors (GENIUS, Cryoarray) plan to achieve a sensitivity of σχ̃0 1 −p > ∼ (10 − 10) pb (2) We consider here two questions: (1) what part of the parameter space is being tested by current detectors, and (2) what is the smallest value of σχ̃0 1 −p the theory is predicting (i.e. how sensitive must detectors be to cover the full SUSY parameter space). The answer to these questions depends in part on the SUGRA model one is considering and also on what range of theoretical and input parameter one assumes. In the following, we examine three