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When solving renormalisation group equations in a quantum field theory, oneoften specifies the boundary conditions at multiple renormalisation scales,such as the weak and grand-unified scales in a theory beyond the standardmodel. A point in the parameter space of such a model is usually specified bythe values of couplings at these boundaries of the renormalisation group flow,but there is no theorem guaranteeing that such a point has a unique solution tothe associated differential equations, and so there may exist multiple,phenomenologically distinct solutions, all corresponding to the same point inparameter space. We show that this is indeed the case in the constrainedminimal supersymmetric standard model (CMSSM), and we exhibit such solutions,which cannot be obtained using out-of-the-box computer programs in the publicdomain. Some of the multiple solutions we exhibit have CP-even lightest Higgsmass predictions between 124 and 126 GeV. Without an exhaustive 11-dimensionalMSSM parameter scan per CMSSM parameter point to capture all of the multiplesolutions, CMSSM phenomenological analyses are incomplete.

The dark side of the $\mu$: on multiple solutions to renormalisation group equations, and why the CMSSM is not necessarily being ruled out