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

Abstract

When solving renormalisation group equations in a quantum field theory, one often specifies the boundary conditions at multiple renormalisation scales, such as the weak and grand-unified scales in a theory beyond the standard model. A point in the parameter space of such a model is usually specified by the 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 to the associated differential equations, and so there may exist multiple, phenomenologically distinct solutions, all corresponding to the same point in parameter space. We show that this is indeed the case in the constrained minimal supersymmetric standard model (CMSSM), and we exhibit such solutions, which cannot be obtained using out-of-the-box computer programs in the public domain. Some of the multiple solutions we exhibit have CP-even lightest Higgs mass predictions between 124 and 126 GeV. Without an exhaustive 11-dimensional MSSM parameter scan per CMSSM parameter point to capture all of the multiple solutions, CMSSM phenomenological analyses are incomplete.

21 pages, 7 figures; v2: some clarifications and minor changes, matches journal version

References in corpus (6)

• Observation of a new boson at a mass of 125 GeV with the CMS experiment at the LHC
• Search for new physics in the multijet and missing transverse momentum final state in proton-proton collisions at sqrt(s) = 8 TeV
• Search for new physics in the multijet and missing transverse momentum final state in proton-proton collisions at sqrt(s) = 7 TeV
• Natural Priors, CMSSM Fits and LHC Weather Forecasts
• Search for squarks and gluinos with the ATLAS detector in final states with jets and missing transverse momentum using 20.3 $f{b}^{-1}$ of $\sqrt{s}$ = 8 TeV proton-proton collision data
• Higgs Boson Mass, Proton Decay, Naturalness and Constraints of LHC and Planck Data

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• Anapole moment of the lightest neutralino in the cMSSM
• Investigating Multiple Solutions in the Constrained Minimal Supersymmetric Standard Model
• Effects of supersymmetric threshold corrections on the Yukawa matrix unification
• Multiple solutions in supersymmetry and the Higgs
• Investigating multiple solutions to boundary value problems in constrained minimal and non-minimal SUSY models
• Top-down and bottom-up excursions beyond the Standard Model: The example of left-right symmetries in supersymmetry