Cosmological relic density from minimal supergravity with implications for collider physics

Stop coannihilation in the CMSSM and SubGUT models

Stop coannihilation may bring the relic density of heavy supersymmetric dark matter particles into the range allowed by cosmology. The efficiency of this process is enhanced by stop-antistop annihilations into the longitudinal (Goldstone) modes of the W and Z bosons, as well as by Sommerfeld enhancement of stop annihilations and the effects of bound states. Since the couplings of the stops to the Goldstone modes are proportional to the trilinear soft supersymmetry-breaking A-terms, these annihilations are enhanced when the A-terms are large. However, the Higgs mass may be reduced below the measured value if the A-terms are too large. Unfortunately, the interpretation of this constraint on the stop coannihilation strip is clouded by differences between the available Higgs mass calculators. For our study, we use as our default calculator FeynHiggs 2.13.0, the most recent publicly available version of this code. Exploring the CMSSM parameter space, we find that along the stop coannihilation strip the masses of the stops are severely split by the large A-terms. This suppresses the Higgs mass drastically for μ andA 0 > 0 , whilst the extent of the stop coannihilation strip is limited forA 0 < 0 and either sign of μ . However, in sub-GUT models, reduced renormalization-group running mitigates the effect of the large A-terms, allowing larger LSP masses to be consistent with the Higgs mass calculation. We give examples where the dark matter particle mass may reach ≳ 8  TeV.

The Constrained NMSSM with right-handed neutrinos

In this article, we demonstrate that the inclusion of right-handed neutrino superfields in the Next-to-Minimal Supersymmetric Standard Model (NMSSM) makes it possible to impose universality conditions on the soft supersymmetry-breaking parameters at the Grand Unification scale, alleviating many of the problems of the so-called Constrained NMSSM. We have studied the renormalization group equations of this model, showing that right-handed neutrinos greatly contribute to driving the singlet Higgs mass-squared parameter negative, which makes it considerably easier to satisfy the conditions for radiative electroweak symmetry breaking. The new fields also lead to larger values of the Standard Model Higgs mass, thus making it easier to reproduce the measured value. As a consequence, all bounds from colliders and low-energy observables can be fulfilled in wide areas of the parameter space. However, the relic density in these regions is generally too high requiring some form of late entropy production to dilute the density of the lightest supersymmetric particle.

Likelihood analysis of the minimal AMSB model

We perform a likelihood analysis of the minimal anomaly-mediated supersymmetry-breaking (mAMSB) model using constraints from cosmology and accelerator experiments. We find that either a wino-like or a Higgsino-like neutralino LSP, [Formula: see text], may provide the cold dark matter (DM), both with similar likelihoods. The upper limit on the DM density from Planck and other experiments enforces [Formula: see text] after the inclusion of Sommerfeld enhancement in its annihilations. If most of the cold DM density is provided by the [Formula: see text], the measured value of the Higgs mass favours a limited range of [Formula: see text] (and also for [Formula: see text] if [Formula: see text]) but the scalar mass [Formula: see text] is poorly constrained. In the wino-LSP case, [Formula: see text] is constrained to about [Formula: see text] and [Formula: see text] to [Formula: see text], whereas in the Higgsino-LSP case [Formula: see text] has just a lower limit [Formula: see text] ([Formula: see text]) and [Formula: see text] is constrained to [Formula: see text] in the [Formula: see text] ([Formula: see text]) scenario. In neither case can the anomalous magnetic moment of the muon, [Formula: see text], be improved significantly relative to its Standard Model (SM) value, nor do flavour measurements constrain the model significantly, and there are poor prospects for discovering supersymmetric particles at the LHC, though there are some prospects for direct DM detection. On the other hand, if the [Formula: see text] contributes only a fraction of the cold DM density, future LHC [Formula: see text]-based searches for gluinos, squarks and heavier chargino and neutralino states as well as disappearing track searches in the wino-like LSP region will be relevant, and interference effects enable [Formula: see text] to agree with the data better than in the SM in the case of wino-like DM with [Formula: see text].

Likelihood analysis of supersymmetric SU(5) GUTs

We perform a likelihood analysis of the constraints from accelerator experiments and astrophysical observations on supersymmetric (SUSY) models with SU(5) boundary conditions on soft SUSY-breaking parameters at the GUT scale. The parameter space of the models studied has seven parameters: a universal gaugino mass [Formula: see text], distinct masses for the scalar partners of matter fermions in five- and ten-dimensional representations of SU(5), [Formula: see text] and [Formula: see text], and for the [Formula: see text] and [Formula: see text] Higgs representations [Formula: see text] and [Formula: see text], a universal trilinear soft SUSY-breaking parameter [Formula: see text], and the ratio of Higgs vevs [Formula: see text]. In addition to previous constraints from direct sparticle searches, low-energy and flavour observables, we incorporate constraints based on preliminary results from 13 TeV LHC searches for jets + [Formula: see text] events and long-lived particles, as well as the latest PandaX-II and LUX searches for direct Dark Matter detection. In addition to previously identified mechanisms for bringing the supersymmetric relic density into the range allowed by cosmology, we identify a novel [Formula: see text] coannihilation mechanism that appears in the supersymmetric SU(5) GUT model and discuss the role of [Formula: see text] coannihilation. We find complementarity between the prospects for direct Dark Matter detection and SUSY searches at the LHC.

Maximal sfermion flavour violation in super-GUTs

We consider supersymmetric grand unified theories with soft supersymmetry-breaking scalar masses [Formula: see text] specified above the GUT scale (super-GUTs) and patterns of Yukawa couplings motivated by upper limits on flavour-changing interactions beyond the Standard Model. If the scalar masses are smaller than the gaugino masses [Formula: see text], as is expected in no-scale models, the dominant effects of renormalisation between the input scale and the GUT scale are generally expected to be those due to the gauge couplings, which are proportional to [Formula: see text] and generation independent. In this case, the input scalar masses [Formula: see text] may violate flavour maximally, a scenario we call MaxSFV, and there is no supersymmetric flavour problem. We illustrate this possibility within various specific super-GUT scenarios that are deformations of no-scale gravity.

Beyond the CMSSM without an accelerator: proton decay and direct dark matter detection

We consider two potential non-accelerator signatures of generalizations of the well-studied constrained minimal supersymmetric standard model (CMSSM). In one generalization, the universality constraints on soft supersymmetry-breaking parameters are applied at some input scale [Formula: see text]below the grand unification (GUT) scale [Formula: see text], a scenario referred to as 'sub-GUT'. The other generalization we consider is to retain GUT-scale universality for the squark and slepton masses, but to relax universality for the soft supersymmetry-breaking contributions to the masses of the Higgs doublets. As with other CMSSM-like models, the measured Higgs mass requires supersymmetric particle masses near or beyond the TeV scale. Because of these rather heavy sparticle masses, the embedding of these CMSSM-like models in a minimal SU(5) model of grand unification can yield a proton lifetime consistent with current experimental limits, and may be accessible in existing and future proton decay experiments. Another possible signature of these CMSSM-like models is direct detection of supersymmetric dark matter. The direct dark matter scattering rate is typically below the reach of the LUX-ZEPLIN (LZ) experiment if [Formula: see text] is close to [Formula: see text], but it may lie within its reach if [Formula: see text] GeV. Likewise, generalizing the CMSSM to allow non-universal supersymmetry-breaking contributions to the Higgs offers extensive possibilities for models within reach of the LZ experiment that have long proton lifetimes.

Supersymmetric dark matter after LHC run 1

Different mechanisms operate in various regions of the MSSM parameter space to bring the relic density of the lightest neutralino, [Formula: see text], assumed here to be the lightest SUSY particle (LSP) and thus the dark matter (DM) particle, into the range allowed by astrophysics and cosmology. These mechanisms include coannihilation with some nearly degenerate next-to-lightest supersymmetric particle such as the lighter stau [Formula: see text], stop [Formula: see text] or chargino [Formula: see text], resonant annihilation via direct-channel heavy Higgs bosons H / A, the light Higgs boson h or the Z boson, and enhanced annihilation via a larger Higgsino component of the LSP in the focus-point region. These mechanisms typically select lower-dimensional subspaces in MSSM scenarios such as the CMSSM, NUHM1, NUHM2, and pMSSM10. We analyze how future LHC and direct DM searches can complement each other in the exploration of the different DM mechanisms within these scenarios. We find that the [Formula: see text] coannihilation regions of the CMSSM, NUHM1, NUHM2 can largely be explored at the LHC via searches for [Formula: see text] events and long-lived charged particles, whereas their H / A funnel, focus-point and [Formula: see text] coannihilation regions can largely be explored by the LZ and Darwin DM direct detection experiments. We find that the dominant DM mechanism in our pMSSM10 analysis is [Formula: see text] coannihilation: parts of its parameter space can be explored by the LHC, and a larger portion by future direct DM searches.

Collider Interplay for Supersymmetry, Higgs and Dark Matter

We discuss the potential impacts on the CMSSM of future LHC runs and possible [Formula: see text] and higher-energy proton-proton colliders, considering searches for supersymmetry via  [Formula: see text] events, precision electroweak physics, Higgs measurements and dark matter searches. We validate and present estimates of the physics reach for exclusion or discovery of supersymmetry via [Formula: see text] searches at the LHC, which should cover the low-mass regions of the CMSSM parameter space favoured in a recent global analysis. As we illustrate with a low-mass benchmark point, a discovery would make possible accurate LHC measurements of sparticle masses using the MT2 variable, which could be combined with cross-section and other measurements to constrain the gluino, squark and stop masses and hence the soft supersymmetry-breaking parameters [Formula: see text] and [Formula: see text] of the CMSSM. Slepton measurements at CLIC would enable [Formula: see text] and [Formula: see text] to be determined with high precision. If supersymmetry is indeed discovered in the low-mass region, precision electroweak and Higgs measurements with a future circular [Formula: see text] collider (FCC-ee, also known as TLEP) combined with LHC measurements would provide tests of the CMSSM at the loop level. If supersymmetry is not discovered at the LHC, it is likely to lie somewhere along a focus-point, stop-coannihilation strip or direct-channel A / H resonance funnel. We discuss the prospects for discovering supersymmetry along these strips at a future circular proton-proton collider such as FCC-hh. Illustrative benchmark points on these strips indicate that also in this case FCC-ee could provide tests of the CMSSM at the loop level.

The pMSSM10 after LHC run 1

We present a frequentist analysis of the parameter space of the pMSSM10, in which the following ten soft SUSY-breaking parameters are specified independently at the mean scalar top mass scale [Formula: see text]: the gaugino masses [Formula: see text], the first-and second-generation squark masses [Formula: see text], the third-generation squark mass [Formula: see text], a common slepton mass [Formula: see text] and a common trilinear mixing parameter A, as well as the Higgs mixing parameter [Formula: see text], the pseudoscalar Higgs mass [Formula: see text] and [Formula: see text], the ratio of the two Higgs vacuum expectation values. We use the MultiNest sampling algorithm with [Formula: see text]1.2 [Formula: see text] points to sample the pMSSM10 parameter space. A dedicated study shows that the sensitivities to strongly interacting sparticle masses of ATLAS and CMS searches for jets, leptons [Formula: see text][Formula: see text] signals depend only weakly on many of the other pMSSM10 parameters. With the aid of the Atom and Scorpion codes, we also implement the LHC searches for electroweakly interacting sparticles and light stops, so as to confront the pMSSM10 parameter space with all relevant SUSY searches. In addition, our analysis includes Higgs mass and rate measurements using the HiggsSignals code, SUSY Higgs exclusion bounds, the measurements of [Formula: see text] by LHCb and CMS, other B-physics observables, electroweak precision observables, the cold dark matter density and the XENON100 and LUX searches for spin-independent dark matter scattering, assuming that the cold dark matter is mainly provided by the lightest neutralino [Formula: see text]. We show that the pMSSM10 is able to provide a supersymmetric interpretation of [Formula: see text], unlike the CMSSM, NUHM1 and NUHM2. As a result, we find (omitting Higgs rates) that the minimum [Formula: see text] with 18 degrees of freedom (d.o.f.) in the pMSSM10, corresponding to a [Formula: see text] probability of 30.8 %, to be compared with [Formula: see text] in the CMSSM (NUHM1) (NUHM2). We display the one-dimensional likelihood functions for sparticle masses, and we show that they may be significantly lighter in the pMSSM10 than in the other models, e.g., the gluino may be as light as [Formula: see text]1250 [Formula: see text] at the 68 % CL, and squarks, stops, electroweak gauginos and sleptons may be much lighter than in the CMSSM, NUHM1 and NUHM2. We discuss the discovery potential of future LHC runs, [Formula: see text] colliders and direct detection experiments.

The NUHM2 after LHC Run 1

We make a frequentist analysis of the parameter space of the NUHM2, in which the soft supersymmetry (SUSY)-breaking contributions to the masses of the two Higgs multiplets, [Formula: see text], vary independently from the universal soft SUSY-breaking contributions [Formula: see text] to the masses of squarks and sleptons. Our analysis uses the MultiNest sampling algorithm with over [Formula: see text] points to sample the NUHM2 parameter space. It includes the ATLAS and CMS Higgs mass measurements as well as the ATLAS search for supersymmetric jets + [Formula: see text] signals using the full LHC Run 1 data, the measurements of [Formula: see text] by LHCb and CMS together with other B-physics observables, electroweak precision observables and the XENON100 and LUX searches for spin-independent dark-matter scattering. We find that the preferred regions of the NUHM2 parameter space have negative SUSY-breaking scalar masses squared at the GUT scale for squarks and sleptons, [Formula: see text], as well as [Formula: see text]. The tension present in the CMSSM and NUHM1 between the supersymmetric interpretation of [Formula: see text] and the absence to date of SUSY at the LHC is not significantly alleviated in the NUHM2. We find that the minimum [Formula: see text] with 21 degrees of freedom (dof) in the NUHM2, to be compared with [Formula: see text] in the CMSSM, and [Formula: see text] in the NUHM1. We find that the one-dimensional likelihood functions for sparticle masses and other observables are similar to those found previously in the CMSSM and NUHM1.

The extent of the stop coannihilation strip

Many supersymmetric models such as the constrained minimal supersymmetric extension of the Standard Model (CMSSM) feature a strip in parameter space where the lightest neutralino [Formula: see text] is identified as the lightest supersymmetric particle, the lighter stop squark [Formula: see text] is the next-to-lightest supersymmetric particle (NLSP), and the relic [Formula: see text] cold dark matter density is brought into the range allowed by astrophysics and cosmology by coannihilation with the lighter stop squark [Formula: see text] NLSP. We calculate the stop coannihilation strip in the CMSSM, incorporating Sommerfeld enhancement effects, and we explore the relevant phenomenological constraints and phenomenological signatures. In particular, we show that the [Formula: see text] may weigh several TeV, and its lifetime may be in the nanosecond range, features that are more general than the specific CMSSM scenarios that we study in this paper.

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 [Formula: see text] and [Formula: see text] and the NUHM1 with [Formula: see text], 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 [Formula: see text] 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 [Formula: see text] and [Formula: see text]. Our results are based on samplings of the parameter spaces of the CMSSM for both [Formula: see text] and [Formula: see text] and of the NUHM1 for [Formula: see text] with 6.8[Formula: see text], 6.2[Formula: see text] and 1.6[Formula: see text] 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 [Formula: see text] than previous versions of FeynHiggs, reducing the pressure on the CMSSM and NUHM1. We find that the global [Formula: see text] functions for the supersymmetric models vary slowly over most of the parameter spaces allowed by the Higgs-mass and the [Formula: see text] searches, with best-fit values that are comparable to the [Formula: see text] 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.

Supersymmetric fits after the Higgs discovery and implications for model building

The data from the first run of the LHC at 7 and 8 TeV, together with the information provided 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, provide important constraints on supersymmetric models. Important information is provided by the ATLAS and CMS measurements of the mass of the Higgs boson, as well as the negative results of searches at the LHC for events with [Formula: see text] accompanied by jets, and the LHCb and CMS measurements of [Formula: see text]. Results are presented from frequentist analyses of the parameter spaces of the CMSSM and NUHM1. The global [Formula: see text] functions for the supersymmetric models vary slowly over most of the parameter spaces allowed by the Higgs mass and the [Formula: see text] search, with best-fit values that are comparable to the [Formula: see text] for the standard model. The 95 % CL lower limits on the masses of gluinos and squarks allow significant prospects for observing them during the LHC runs at higher energies.

Implications of improved Higgs mass calculations for supersymmetric models

We discuss the allowed parameter spaces of supersymmetric scenarios in light of improved Higgs mass predictions provided by FeynHiggs 2.10.0. The Higgs mass predictions combine Feynman-diagrammatic results with a resummation of leading and subleading logarithmic corrections from the stop/top sector, which yield a significant improvement in the region of large stop masses. Scans in the pMSSM parameter space show that, for given values of the soft supersymmetry-breaking parameters, the new logarithmic contributions beyond the two-loop order implemented in FeynHiggs tend to give larger values of the light CP-even Higgs mass, [Formula: see text], in the region of large stop masses than previous predictions that were based on a fixed-order Feynman-diagrammatic result, though the differences are generally consistent with the previous estimates of theoretical uncertainties. We re-analyse the parameter spaces of the CMSSM, NUHM1 and NUHM2, taking into account also the constraints from CMS and LHCb measurements of [Formula: see text]and ATLAS searches for [Formula: see text] events using 20/fb of LHC data at 8 TeV. Within the CMSSM, the Higgs mass constraint disfavours [Formula: see text], though not in the NUHM1 or NUHM2.

Lower limits on R-parity-violating couplings in supersymmetric models with light squarks

We interpret the results of searches for strongly interacting massive particles to place absolute lower limits on R-parity-violating couplings for squarks with mass (m(q) below 100 GeV. Recent searches for anomalous isotopes require that there be a baryon-number-violating or lepton-number-violating coupling larger than 10(-22)-10(-21) if m(q)>18 GeV. Using data from searches for stable particles at the CERN Large Electron Positron Collider (LEP) we demonstrate that this lower limit increases by 14 orders of magnitude, to an R-parity-violating coupling larger than 10(-8)-10(-7) for any squarks of mass less than 90 GeV. In the presence of an R-parity-violating coupling of this magnitude, neutralinos cannot explain the dark matter density in the Universe.