Investigating multiple solutions in the constrained minimal supersymmetric standard model

Recent work has shown that the Constrained Minimal Supersymmetric Standard Model (CMSSM) can possess several distinct solutions for certain values of its parameters. The extra solutions were not previously found by public supersymmetric spectrum generators because fixed point iteration (the algorithm used by the generators) is unstable in the neighbourhood of these solutions. The existence of the additional solutions calls into question the robustness of exclusion limits derived from collider experiments and cosmological observations upon the CMSSM, because limits were only placed on one of the solutions. Here, we map the CMSSM by exploring its multi-dimensional parameter space using the shooting method, which is not subject to the stability issues which can plague fixed point iteration. We are able to find multiple solutions where in all previous literature only one was found. The multiple solutions are of two distinct classes. One class, close to the border of bad electroweak symmetry breaking, is disfavoured by LEP2 searches for neutralinos and charginos. The other class has sparticles that are heavy enough to evade the LEP2 bounds. Chargino masses may differ by up to around 10% between the different solutions, whereas other sparticle masses differ at the sub-percent level. The prediction for the dark matter relic density can vary by a hundred percent or more between the different solutions, so analyses employing the dark matter constraint are incomplete without their inclusion.