Supersymmetric dark matter and the energy of a linear electron-positron collider

We suggest that supersymmetric dark matter be used to set the energy scale of a linear e+e− collider. Assuming that the lightest supersymmetric particle (LSP) is a stable neutralino χ, as in many incarnations of the MSSM with conserved R parity, previous calculations that include coannihilation effects have delineated the region of the (m1/2,m0) plane where the LSP cosmological relic density lies in the preferred range 0.1≲Ωχh2≲0.3. We evaluate here the total cross section for e+e−→ visible pairs of supersymmetric particles, for different values of m1/2 and m0, and investigate how much of the dark matter region can be explored by e+e− colliders with different centre-of-mass energies ECM. We find that a collider with ECM=500 GeV or 1 TeV can only explore part of the cosmological region, and that a collider with ECM=1.5 TeV with sufficient luminosity can explore all of the supersymmetric dark matter region.