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.     

Relating the CMSSM and SUGRA models with GUT-scale and super-GUT-scale supersymmetry breaking

While the constrained minimal supersymmetric standard model (CMSSM) with universal gaugino masses, m _1/2, scalar masses, m ₀, and A-terms, A ₀, defined at some high energy scale (usually taken to be the GUT scale) is motivated by general features of supergravity models, it does not carry all of the constraints imposed by minimal supergravity (mSUGRA). In particular, the CMSSM does not impose a relation between the trilinear and bilinear soft supersymmetry breaking terms, B ₀=A ₀?m ₀, nor does it impose the relation between the soft scalar masses and the gravitino mass, m ₀=m _3/2. As a consequence, tanβ is computed given values of the other CMSSM input parameters. By considering a Giudice–Masiero (GM) extension to mSUGRA, one can introduce new parameters to the Kähler potential which are associated with the Higgs sector and recover many of the standard CMSSM predictions. However, depending on the value of A ₀, one may have a gravitino or a neutralino dark matter candidate. We also consider the consequences of imposing the universality conditions above the GUT scale. This GM extension provides a natural UV completion for the CMSSM.     

Supersymmetric benchmarks with non-universal scalar masses or gravitino dark matter

We motivate, propose and examine a new set of benchmark supersymmetric scenarios, some of which have non-universal Higgs scalar masses (NUHM) and others have gravitino dark matter (GDM). The scalar masses in these proposed models are either considerably larger or smaller than the narrow range allowed for the same gaugino mass m_1/2 in the constrained MSSM (CMSSM) with universal scalar masses m₀ and neutralino dark matter. Unlike the CMSSM, the proposed NUHM and GDM models with larger m₀ may have large branching ratios for Higgs and/or Z production in the cascade decays of heavier sparticles, whose detection we discuss. The novel phenomenology of the GDM models depends on the nature of the next-to-lightest supersymmetric particle (NLSP), which has a lifetime exceeding 10⁴ s in the proposed benchmark scenarios. In one GDM scenario the NLSP is the lightest neutralino χ, and the supersymmetric collider signatures are similar to those in previous CMSSM benchmarks, but with a distinctive spectrum that would be challenging for the LHC and ILC. In the other GDM scenarios based on minimal supergravity (mSUGRA), the NLSP is the lighter stau slepton , with a lifetime between ∼10⁴ and 3×10⁶ s. Every supersymmetric cascade would end in a , which would have a distinctive time-of-flight signature. Slow-moving ’s might be trapped in a collider detector or outside it, and the preferred detection strategy would depend on the lifetime. We discuss the extent to which these mSUGRA GDM scenarios could be distinguished from gauge-mediated models.     

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.     

Flavoured co-annihilation

In minimal supergravity (mSUGRA) or CMSSM, one of the main co-annihilating partners of the neutralino is the lightest stau, $\tilde{\tau}_1$ . In the presence of flavour violation in the right-handed sector, the co-annihilating partner would be a flavour mixed state. The flavour effect is two-fold: (a) It changes the mass of $\tilde{\tau}_{1}$ , thus modifying the parameter space of the co-annihilation and (b) flavour violating scatterings could now contribute to the cross-sections in the early Universe. In fact, it is shown that for large enough ??~0.2, these processes would constitute the dominant channels in co-annihilation regions. The amount of flavour mixing permissible is constrained by flavour violating ?????? or ????e processes. For ??_RR mass insertions, the constraints from flavour violation are not strong enough in some regions of the parameter space due to partial cancellations in the amplitudes. In mSUGRA, the regions with cancelations within LFV amplitudes do not overlap with the regions of co-annihilations. In non-universal Higgs model (NUHM), however, these regions do overlap leading to significant flavoured co-annihilations. At the LHC and other colliders, these regions can constitute for interesting signals.     

Resurrecting no-scale supergravity phenomenology

In the context of phenomenological models in which the soft supersymmetry-breaking parameters of the MSSM become universal at some unification scale, M _in, above the GUT scale, M _GUT, it is possible that all the scalar mass parameters m ₀, the trilinear couplings A ₀ and the bilinear Higgs coupling B ₀ vanish simultaneously, as in no-scale supergravity. Using these no-scale inputs in a renormalisation-group analysis of the minimal supersymmetric SU(5) GUT model, we pay careful attention to the matching of parameters at the GUT scale. We delineate the region of M _in, m _1/2 and tan?β where the resurrection of no-scale supergravity is possible, taking due account of the relevant phenomenological constraints such as electroweak symmetry breaking, m _h ,b→s γ, the neutralino cold dark matter density Ω _χ h ² and g _μ ?2. No-scale supergravity survives in an L-shaped strip of parameter space, with one side having m _1/2?200 GeV, the second (orthogonal) side having M _in?5×10¹⁶ GeV. Depending on the relative signs and magnitudes of the GUT superpotential couplings, these may be connected to form a triangle whose third side is a hypotenuse at larger M _in, m _1/2 and tan?β, whose presence and location depend on the GUT superpotential parameters. We compare the prospects for detecting sparticles at the LHC in no-scale supergravity with those in the CMSSM and the NUHM.     

Relation between heat kernel method and scattering spectral method

Taking into account the available accelerator and astrophysical constraints, the mass of the lightest neutral Higgs boson h in the minimal supersymmetric extension of the Standard Model with universal soft supersymmetry-breaking masses (CMSSM) has been estimated to lie between 114 and ??130?GeV. Recent data from ATLAS and CMS hint that m _h ??125?GeV, though m _h ??119?GeV may still be a possibility. Here we study the consequences for the parameters of the CMSSM and direct dark matter detection if the Higgs hint is confirmed, focusing on the strips in the (m _1/2,m ₀) planes for different tan?? and A ₀ where the relic density of the lightest neutralino ?? falls within the range of the cosmological cold dark matter density allowed by WMAP and other experiments. We find that if m _h ??125?GeV focus-point strips would be disfavoured, as would the low-tan?? ${\tilde{\tau}}$ ?C?? and ${\tilde{t}}_{1} $ ?C?? coannihilation strips, whereas the ${\tilde{\tau}}$ ?C?? coannihilation strip at large tan?? and A ₀>0 would be favoured, together with its extension to a funnel where rapid annihilation via direct-channel H/A poles dominates. On the other hand, if m _h ??119?GeV more options would be open. We give parameterisations of WMAP strips with large tan?? and fixed A ₀/m ₀>0 that include portions compatible with m _h =125?GeV, and present predictions for spin-independent elastic dark matter scattering along these strips. These are generally low for models compatible with m _h =125?GeV, whereas the XENON100 experiment already excludes some portions of strips where m _h is smaller.     

What if supersymmetry breaking unifies beyond the GUT scale?

We study models in which soft supersymmetry-breaking parameters of the MSSM become universal at some unification scale, M _in, above the GUT scale, M _GUT. We assume that the scalar masses and gaugino masses have common values, m ₀ and m _1/2 respectively, at M _in. We use the renormalisation-group equations of the minimal supersymmetric SU(5) GUT to evaluate their evolutions down to M _GUT, studying their dependences on the unknown parameters of the SU(5) superpotential. After displaying some generic examples of the evolutions of the soft supersymmetry-breaking parameters, we discuss the effects on physical sparticle masses in some specific examples. We note, for example, that near-degeneracy between the lightest neutralino and the lighter stau is progressively disfavoured as M _in increases. This has the consequence, as we show in (m _1/2,m ₀) planes for several different values of tan?β, that the stau-coannihilation region shrinks as M _in increases, and we delineate the regions of the (M _in,tan?β) plane where it is absent altogether. Moreover, as M _in increases, the focus-point region recedes to larger values of m ₀ for any fixed tan?β and m _1/2. We conclude that the regions of the (m _1/2,m ₀) plane that are commonly favoured in phenomenological analyses tend to disappear at large M _in.     

Constraints on SUSY models from LEP

We consider a particular supersymmetric extension of the standard model involving a light singlet and explainingM _Weak?M _Planck naturally, without detailed assumptions about a GUT or supergravity sector. Imposingm _cl>45 GeV for the lightest chargino andm _H1>20 GeV for the lightest Higgs scalar, the model survives all other constraints due to recent LEP results; it predicts, however, supersymmetric and Higgs particles to be seen in the near future.     

Electroweak precision data and gravitino dark matter

Electroweak precision measurements can provide indirect information about the possible scale of supersymmetry already at the present level of accuracy. We review present day sensitivities of precision data in mSUGRA-type models with the gravitino as the lightest supersymmetric particle (LSP). The χ ² fit is based on M _W , sin² θ _eff, (g−2) _μ , BR(b → sγ) and the lightest MSSM Higgs boson mass, M _h . We find indications for relatively light soft supersymmetry-breaking masses, offering good prospects for the LHC and the ILC, and in some cases also for the Tevatron.      

CBBN in the CMSSM

Catalyzed big bang nucleosynthesis (CBBN) can lead to overproduction of ⁶Li in gravitino dark matter scenarios in which the lighter stau is the lightest standard model superpartner. Based on a treatment using the state-of-the-art result for the catalyzed ⁶Li production cross section, we update the resulting constraint within the framework of the constrained minimal supersymmetric standard model (CMSSM). We confront our numerical findings with recently derived limits on the gaugino mass parameter m_1/2 and the reheating temperature T_R. PACS  12.60.Jv; 95.35.+d     

Constraints on supersymmetry from LHC data on SUSY searches and Higgs bosons combined with cosmology and direct dark matter searches

The ATLAS and CMS experiments did not find evidence for Supersymmetry using close to 5/fb of published LHC data at a center-of-mass energy of 7 TeV. We combine these LHC data with data on $B^{0}_{s}\to \mu^{+}\mu^{-}$ (LHCb experiment), the relic density (WMAP and other cosmological data) and upper limits on the dark matter scattering cross sections on nuclei (XENON100 data). The excluded regions in the constrained Minimal Supersymmetric SM (CMSSM) lead to gluinos excluded below 1270 GeV and dark matter candidates below 220 GeV for values of the scalar masses (m ₀) below 1500 GeV. For large m ₀ values the limits of the gluinos and the dark matter candidate are reduced to 970 GeV and 130 GeV, respectively. If a Higgs mass of 125 GeV is imposed in the fit, the preferred SUSY region is above this excluded region, but the size of the preferred region is strongly dependent on the assumed theoretical error.     

Some phenomenological consequences of the super higgs effect

To the combined system of supergravity ofN=1 and the Higgs multiplet (a scalar multiplet) is coupled a complex scalar multiplet as a simplified representative of the matter. An order-of-magnitude estimate is attempted on the masses and the couplings of the gravitino and other fields.     

Updated post-WMAP benchmarks for supersymmetry

We update a previously-proposed set of supersymmetric benchmark scenarios, taking into account the precise constraints on the cold dark matter density obtained by combining WMAP and other cosmological data, as well as the LEP and constraints. We assume that R parity is conserved and work within the constrained MSSM (CMSSM) with universal soft supersymmetry-breaking scalar and gaugino masses m₀ and m_1/2. In most cases, the relic density calculated for the previous benchmarks may be brought within the WMAP range by reducing slightly m₀, but in two cases more substantial changes in m₀ and m_1/2 are made. Since the WMAP constraint reduces the effective dimensionality of the CMSSM parameter space, one may study phenomenology along WMAP lines in the (m_1/2, m₀) plane that have acceptable amounts of dark matter. We discuss the production, decays and detectability of sparticles along these lines, at the LHC and at linear e ⁺ e^- colliders in the sub- and multi-TeV ranges, stressing the complementarity of hadron and lepton colliders, and with particular emphasis on the neutralino sector. Finally, we preview the accuracy with which one might be able to predict the density of supersymmetric cold dark matter using collider measurements.Received: 2 September 2003, Published online: 4 February 2004     

Supersymmetric dark matter,catalyzed BBN,and heavy moduli in mSUGRA with gravitino LSP and stau NLSP

In mSUGRA model we assume that gravitino, the LSP, plays the role of cold dark matter in the universe, while the lightest stau, the NLSP, catalyzes primordial BBN reconciling the discrepancy between theory and observations. We have taken into account all gravitino production mechanisms, namely decay from heavy scalar fields, decay from the NLSP, and from the thermal bath. We find that the dark matter constraint is incompatible with the lower bound on the reheating temperature.     

Constraints on the MSSM from the Higgs sector

We discuss the constraints on supersymmetry in the Higgs sector arising from LHC searches, rare B decays and dark matter direct detection experiments. We show that constraints derived on the mass of the lightest h ⁰ and the CP-odd A ⁰ bosons from these searches are covering a larger fraction of the SUSY parameter space compared to searches for strongly interacting supersymmetric particle partners. We discuss the implications of a mass determination for the lightest Higgs boson in the range 123<M _h <127?GeV, inspired by the intriguing hints reported by the ATLAS and CMS Collaborations, as well as those of a non-observation of the lightest Higgs boson for MSSM scenarios not excluded at the end of 2012 by LHC and direct dark matter searches and their implications on LHC SUSY searches.     

Masses and couplings of the lightest Higgs bosons in (M + 1)SSM

We study the upper limits on the mass of the lightest and second lightest CP even Higgs bosons in the (M + 1)SSM, the MSSM extended by a gauge singlet. The dominant two loop contributions to the effective potential are included, which reduce the Higgs masses by GeV. Since the coupling R of the lightest Higgs scalar to gauge bosons can be small, we study in detail the relations between the masses and couplings of both lightest scalars. We present upper bounds on the mass of a ”strongly” coupled Higgs (R < 1/2) as a function of lower experimental limits on the mass of a ”weakly” coupled Higgs (R < 1/2). With the help of these results, the whole parameter space of the model can be covered by Higgs boson searches. Received: 7 September 1999 / Published online: 12 July 2002