Likelihood functions for supersymmetric observables in frequentist analyses of the CMSSM and NUHM1

Abstract

On the basis of frequentist analyses of experimental constraints from electroweak precision data, (g−2) _μ , B-physics and cosmological data, we investigate the parameters of the constrained MSSM (CMSSM) with universal soft supersymmetry-breaking mass parameters, and a model with common non-universal Higgs masses (NUHM1). We present χ ² likelihood functions for the masses of supersymmetric particles and Higgs bosons, as well as BR(b→s γ), BR(B _s →μ ⁺ μ ⁻) and the spin-independent dark-matter scattering cross section, σ ^SI _p . In the CMSSM we find preferences for sparticle masses that are relatively light. In the NUHM1 the best-fit values for many sparticle masses are even slightly smaller, but with greater uncertainties. The likelihood functions for most sparticle masses are cut off sharply at small masses, in particular by the LEP Higgs mass constraint. Both in the CMSSM and the NUHM1, the coannihilation region is favored over the focus-point region at about the 3-σ level, largely but not exclusively because of (g−2) _μ . Many sparticle masses are highly correlated in both the CMSSM and NUHM1, and most of the regions preferred at the 95% C.L. are accessible to early LHC running, though high-luminosity running would be needed to cover the regions allowed at the 3-σ levels. Some slepton and chargino/neutralino masses should be in reach at the ILC. The masses of the heavier Higgs bosons should be accessible at the LHC and the ILC in portions of the preferred regions in the (M _A ,tan β) plane. In the CMSSM, the likelihood function for BR(B _s →μ ⁺ μ ⁻) is peaked close to the Standard Model value, but much larger values are possible in the NUHM1. We find that values of σ ^SI _p >10⁻¹⁰ pb are preferred in both the CMSSM and the NUHM1. We study the effects of dropping the (g−2) _μ , BR(b→s γ), Ω _χ h ² and M _h constraints, demonstrating that they are not in tension with the other constraints.