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

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 _p ^SI. 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 _p ^SI>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.     

The CMSSM and NUHM1 in light of 7 TeV LHC, B s →μ + μ − and XENON100 data

We make a frequentist analysis of the parameter space of the CMSSM and NUHM1, using a Markov Chain Monte Carlo (MCMC) with 95 (221) million points to sample the CMSSM (NUHM1) parameter spaces. Our analysis includes the ATLAS search for supersymmetric jets?+? signals using ～5/fb of LHC data at 7 TeV, which we apply using PYTHIA and a Delphes implementation that we validate in the relevant parameter regions of the CMSSM and NUHM1. Our analysis also includes the constraint imposed by searches for BR(B _s →μ ⁺ μ ^?) by LHCb, CMS, ATLAS and CDF, and the limit on spin-independent dark matter scattering from 225 live days of XENON100 data. We assume M _h ～125 GeV, and use a full set of electroweak precision and other flavour-physics observables, as well as the cold dark matter density constraint. The ATLAS_5/fb constraint has relatively limited effects on the 68 and 95 % CL regions in the (m ₀,m _1/2) planes of the CMSSM and NUHM1. The new BR(B _s →μ ⁺ μ ^?) constraint has greater impacts on these CL regions, and also impacts significantly the 68 and 95 % CL regions in the (M _A ,tanβ) planes of both models, reducing the best-fit values of tanβ. The recent XENON100 data eliminate the focus-point region in the CMSSM and affect the 68 and 95 % CL regions in the NUHM1. In combination, these new constraints reduce the best-fit values of m ₀,m _1/2 in the CMSSM, and increase the global χ ² from 31.0 to 32.8, reducing the p-value from 12 % to 8.5 %. In the case of the NUHM1, they have little effect on the best-fit values of m ₀,m _1/2, but increase the global χ ² from 28.9 to 31.3, thereby reducing the p-value from 15 % to 9.1 %.     

Higgs and supersymmetry

Global frequentist fits to the CMSSM and NUHM1 using the MasterCode framework predicted M _h ?119 GeV in fits incorporating the (g?2) _μ constraint and ?126 GeV without it. Recent results by ATLAS and CMS could be compatible with a Standard Model-like Higgs boson around M _h ?125 GeV. We use the previous MasterCode analysis to calculate the likelihood for a measurement of any nominal Higgs mass within the range of 115 to 130 GeV. Assuming a Higgs mass measurement at M _h ?125 GeV, we display updated global likelihood contours in the (m ₀,m _1/2) and other parameter planes of the CMSSM and NUHM1, and present updated likelihood functions for $m_{\tilde{g}}, m_{\tilde{q}_{R}}We perform a determination of the strong coupling constant using the latest ATLAS inclusive jet cross section data, from proton?Cproton collisions at $\sqrt{s}=7~\mathrm{TeV}$ , and their full information on the bin-to-bin correlations. Several procedures for combining the statistical information from the different data inputs are studied and compared. The theoretical prediction is obtained using NLO QCD, and it also includes non-perturbative corrections. Our determination uses inputs with transverse momenta between 45 and 600?GeV, the running of the strong coupling being also tested in this range. Good agreement is observed when comparing our result with the world average at the Z-boson scale, as well as with the most recent results from the Tevatron.     

The CMSSM and NUHM1 after LHC Run 1

We analyze the impact of data from the full Run 1 of the LHC at 7 and 8 TeV on the CMSSM with \(\mu > 0\) and \(<0\) and the NUHM1 with \(\mu > 0\) , incorporating the constraints imposed by other experiments such as precision electroweak measurements, flavour measurements, the cosmological density of cold dark matter and the direct search for the scattering of dark matter particles in the LUX experiment. We use the following results from the LHC experiments: ATLAS searches for events with \({E\!\!/}_{T}\) accompanied by jets with the full 7 and 8 TeV data, the ATLAS and CMS measurements of the mass of the Higgs boson, the CMS searches for heavy neutral Higgs bosons and a combination of the LHCb and CMS measurements of \(\mathrm{BR}(B_s \rightarrow \mu ^+\mu ^-)\) and \(\mathrm{BR}(B_d \rightarrow \mu ^+\mu ^-)\) . Our results are based on samplings of the parameter spaces of the CMSSM for both \(\mu >0\) and \(\mu <0\) and of the NUHM1 for \(\mu > 0\) with 6.8 \(\times 10^6\) , 6.2 \(\times 10^6\) and 1.6 \(\times 10^7\) points, respectively, obtained using the MultiNest tool. The impact of the Higgs-mass constraint is assessed using FeynHiggs 2.10.0, which provides an improved prediction for the masses of the MSSM Higgs bosons in the region of heavy squark masses. It yields in general larger values of \(M_h\) than previous versions of FeynHiggs, reducing the pressure on the CMSSM and NUHM1. We find that the global \(\chi ^2\) functions for the supersymmetric models vary slowly over most of the parameter spaces allowed by the Higgs-mass and the \({E\!\!/}_{T}\) searches, with best-fit values that are comparable to the \(\chi ^2/\mathrm{dof}\) for the best Standard Model fit. We provide 95 % CL lower limits on the masses of various sparticles and assess the prospects for observing them during Run 2 of the LHC.     

Supersymmetry and dark matter in light of LHC 2010 and XENON100 data

We make frequentist analyses of the CMSSM, NUHM1, VCMSSM and mSUGRA parameter spaces taking into account all the public results of searches for supersymmetry using data from the 2010 LHC run and the XENON100 direct search for dark matter scattering. The LHC data set includes ATLAS and CMS searches for $\mathrm{jets} + {\not}E_{T}$ events (with or without leptons) and for the heavier MSSM Higgs bosons, and the upper limit on BR(B _s →μ ⁺ μ ^?) including data from LHCb as well as CDF and DØ. The absence of signals in the LHC data favours somewhat heavier mass spectra than in our previous analyses of the CMSSM, NUHM1 and VCMSSM, and somewhat smaller dark matter scattering cross sections, all close to or within the pre-LHC 68% CL ranges, but does not impact significantly the favoured regions of the mSUGRA parameter space. We also discuss the impact of the XENON100 constraint on spin-independent dark matter scattering, stressing the importance of taking into account the uncertainty in the π-nucleon σ term Σ _πN , which affects the spin-independent scattering matrix element, and we make predictions for spin-dependent dark matter scattering. Finally, we discuss briefly the potential impact of the updated predictions for sparticle masses in the CMSSM, NUHM1, VCMSSM and mSUGRA on future e ⁺ e ^? colliders.