Probing U(1) extensions of the MSSM at the LHC Run I and in dark matter searches
LAPTH, Université Savoie Mont Blanc, CNRS,
B.P.110, F-74941 Annecy-le-Vieux Cedex, France
University of Manchester, Oxford Road, Manchester, M13 9PL, United Kingdom
[2mm] Laboratoire de Physique Subatomique et de Cosmologie, Université Grenoble-Alpes, CNRS/IN2P3, 53 Avenue des Martyrs, 38026 Grenoble, France
[2mm] Skobeltsyn Institute of Nuclear Physics (SINP MSU), Lomonosov Moscow State University, 1(2) Leninskie gory, GSP-1, Moscow 119991, Russia
The U(1) extended supersymmetric standard model (UMSSM) can accommodate a Higgs boson at 125 GeV without relying on large corrections from the top/stop sector. After imposing LHC results on the Higgs sector, on -physics and on new particle searches as well as dark matter constraints, we show that this model offers two viable dark matter candidates, the right-handed (RH) sneutrino or the neutralino. Limits on supersymmetric partners from LHC simplified model searches are imposed using SModelS and allow for light squarks and gluinos. Moreover the upper limit on the relic abundance often favours scenarios with long-lived particles. Searches for a at the LHC remain the most unambiguous probes of this model. Interestingly, the -term contributions to the sfermion masses allow to explain the anomalous magnetic moment of the muon in specific corners of the parameter space with light smuons or left-handed (LH) sneutrinos. We finally emphasize the interplay between direct searches for dark matter and LHC simplified model searches.
- 1 Introduction
- 2 The model
- 3 The Higgs sector
- 4 Constraints on the model
- 5 Results
- 6 Impact of LHC searches for SUSY particles
- 7 Summary after LHC constraints
- 8 Couplings and signal strengths for the Higgses
- 9 Dark matter probes
- 10 Conclusion
- 11 Acknowledgements
- A Radiative corrections in the Higgs sector
The discovery by the ATLAS and CMS collaborations [1, 2, 3] of a 125 GeV Higgs boson whose properties are compatible with the standard model (SM) predictions coupled with the fruitless searches for new particles at Run I of the LHC [4, 5, 6, 7] has left the community with little guidance for which direction to search for new physics at the TeV scale. The dark matter (DM) problem remains a strong motivation for considering extensions of the SM, in particular supersymmetry.
In the minimal supersymmetric standard model (MSSM), the Higgs couplings are to a large extent SM-like, especially when the mass scales of the second Higgs doublet and/or of other new particles that enter the loop-induced Higgs couplings are well above the electroweak scale. This is to be expected in any model where the Higgs is responsible for electroweak symmetry breaking. The main challenge for the MSSM is however to explain a Higgs mass of 125 GeV. To achieve such a high mass requires large contributions from one-loop diagrams involving top squarks — in fact the loop contribution has to be of the same order as the tree-level contribution — thus introducing a large amount of fine-tuning [8, 9]. The fine-tuning is reduced in extensions of the minimal model containing an additional singlet scalar field [10, 11, 12, 13]. For example in the next-to-minimal supersymmetric standard model (NMSSM), terms in the superpotential give an extra tree-level contribution to the light Higgs mass, thus reducing the amount of fine-tuning required to reach . A doublet-singlet mixing can also modify significantly the tree-level couplings of the light Higgs. In the UMSSM, where the gauge group contains an extra U(1) symmetry, contributions from U(1) -terms in addition to those from the superpotential present in the NMSSM, can further increase the light Higgs mass [14, 15] reaching easily 125 GeV without a very large contribution from the stop sector. Furthermore, because the singlet mass is driven by the mass of the new gauge boson which is strongly constrained by LHC searches to be above the TeV scale [16, 17]111In this paper we concentrate on a above the electroweak scale, for scenarios with light see ., the tree-level couplings of the light Higgs are expected to be SM-like, in agreement with the latest results of ATLAS and CMS [19, 20]. This heavy was also found to increase the fine-tuning of supersymmetric models with U(1) extended gauge symmetry . Another nice feature of the UMSSM (as the NMSSM) is that the parameter, generated from the vacuum expectation value (vev) of the singlet field responsible for the breaking of the U(1) symmetry, is naturally at the weak scale. Finally, this model is well motivated within the context of superstring models [22, 23, 24, 25, 26] and grand unified theories [27, 28].
The range of masses for the Higgs scalars and pseudoscalars were examined in a variety of singlet extension of the MSSM . The parameter space of a similar model with a new U(1) symmetry, the constrained SSM, compatible with the Higgs at 125 GeV as well as limits on the Higgs sector and providing a dark matter candidate was examined in . In this model the RH sneutrino does not have a U(1) charge and is expected to be very massive. The signal in a U(1) extended MSSM model was discussed in [30, 31] with emphasis on the region that leads to an increase in the two-photon signal. Additional non-standard decays of Higgs particles were found in [32, 33]. However, since the mass of the additional singlet Higgs is expected to be very large due to strong limits on the boson mass, it does not affect the property of the lightest Higgs which is hence expected to be SM-like. In the UMSSM model considered here RH sneutrinos can be charged under the additional U(1) symmetry, hence this model gives a new viable dark matter candidate in addition to the lightest neutralino as observed in . The properties of a RH sneutrino DM were also examined in the  and extensions of the MSSM . Note that in such models the sneutrino vev’s were found to play an important role in the vacuum stability . Furthermore the can contribute to the stabilization of the Higgs potential .
In this paper we explore the parameter space of the UMSSM (derived from ) that is compatible with both collider and dark matter observables. We include in particular the Higgs mass and signal strengths in all channels, LHC constraints on and on supersymmetric particles, new results from -physics, as well as the relic density and direct detection of dark matter. Specifically we take into account the most recent LHC results for supersymmetric particle searches based on simplified models using SModelS [39, 40]. This allows us to also highlight the signatures not well constrained by current searches despite a spectrum well below the TeV scale. One salient feature of the model is that large -term contributions can significantly reduce the mass of RH squarks thus splitting the u-type and d-type squarks and weakening the constraints on first generation squarks. Another feature, which is also found in the MSSM, is that the relic density upper limit favors a neutralino with a large higgsino or wino component as the lightest supersymmetric particle (LSP). Scenarios with a higgsino LSP can easily escape current search limits. For example simplified model limits from top squark searches rely on the assumption that one decay channel is dominant, while for higgsino LSP branching ratios into and can both be large, thus the mixed channels where each stop decay into a different final state are important. Since a higgsino or wino LSP may be associated with a chargino which is stable at the collider scale, we also impose the D0 and ATLAS limits originating from searches for long-lived particles. On the remaining parameter space, we then discuss the expected spectra of SUSY particles, the expectations for the signal strengths for the Higgses as well as dark matter observables in direct and indirect detection.
In general we do not attempt to explain the observed discrepancy with the standard model expectations in the muon anomalous magnetic moment. However, we highlight the region where the model can explain this discrepancy and investigate how it may escape simplified model limits from the LHC. The interplay between the muon anomalous magnetic moment constraint, LHC and DM limits was recently studied in the MSSM .
In contrast to previous studies [42, 34] we explore the impact of LHC8TeV results on Higgs and new particle searches from the 8 TeV run on scenarios with arbitrary U(1) originating from . Moreover we consider both the cases of a neutralino and a RH sneutrino dark matter. We further examine the implications of dark matter searches in these scenarios. An attractive feature of the model is the possibility to obtain GeV despite small values of . The phenomenology of Higgs and SUSY searches could thus differ from that of the much-studied MSSM.
This paper is organised as follows. In section 2 we describe the model. Section 3 is devoted to a detailed view of the Higgs sector. Section 4 presents the different constraints used in our study. Section 5 contains the results for several sectors of the model after applying a basic set of constraints mostly related to Higgs and -physics observables and after applying the DM relic abundance limits. Section 6 is dedicated to the application of the LHC simplified models searches on the remaining allowed parameter space of the UMSSM. Section 7 contains a summary of LHC constraints after Run I and suggestions on how to extend simplified models searches to further probe the model. Section 8 shows prospects for probing the Higgs sector and section 9 prospects from astroparticle searches. Our conclusions are presented in section 10.
2 The model
The symmetry group of the model is and we assume that this model is derived from an underlying model. In this case the charges of each field of the model are parameterized by an angle as
The matter sector of the model contains, in addition to the chiral supermultiplets of the SM fermions, three families of new particles, each family containing : a RH neutrino, two Higgs doublets (), a singlet, and a colour (anti)triplet. While the complete matter sector is needed for anomaly cancellations, for simplicity we will assume that all exotic fields, with the exception of three RH neutrinos, two Higgs doublets and one singlet, are above a few TeV’s and can be neglected. Similarly in addition to the MSSM chiral multiplets we will only consider the chiral multiplets corresponding to these fields, that is the multiplet with a singlet and the singlino and another multiplet with RH neutrinos () and their supersymmetric partners, the sneutrinos, .
Finally the UMSSM model contains a new vector multiplet, with a new boson and the corresponding gaugino . The superpotential is the same as in the MSSM with but has additional terms involving the singlet,
where is the neutrino Yukawa matrix. The vev of , breaks the symmetry and induces a term
Note that for the symmetry cannot be broken by the singlet field since . Note also that the invariance of the superpotential under imposes a condition on the Higgs sector, namely . The soft-breaking Lagrangian of the UMSSM is
with the trilinear coupling , the mass term , the singlet mass term . The soft sneutrino mass term matrices and are taken to be diagonal in the family space. Note that our study is based on the UMSSM model with parameters defined at the electroweak scale, we make no attempt to check the validity of the model at a high scale. We now describe briefly the sectors of the model that will play a role in the considered observables.
2.1 Gauge bosons
The two neutral massive gauge bosons, and can mix both through mass and kinetic mixing [45, 42]. In the following we will neglect the kinetic mixing222The impact of the kinetic mixing on the Higgs boson mass and on the and DM phenomenology was examined in the extension of the MSSM in [46, 35, 47].. The electroweak and symmetries are broken respectively by the vev’s of the doublets, , and singlet, . The mass matrix reads
where , , and () is the cosinus (sinus) of the Weinberg angle. Diagonalisation of the mass matrix leads to two eigenstates
where the mixing angle is defined as
and the masses of the physical fields are
Precision measurements at the -pole and from low energy neutral currents provide stringent constraints on the mixing angle. Depending on the model parameters the constraints are below a few [48, 49]. The new gauge boson will therefore have approximately the same properties as the . As input parameters we choose the physical masses, GeV, and the mixing angle, . From these together with the coupling constants, we extract both the value of and the value of . Note that as in  we adopt the convention where both and are positive while (and then ) and can have both signs. From eqs. (2.7) and (2.9),
For each model the value of can be strongly constrained as a consequence of the requirement . For example for the case with and the value of has to be below 1. The reason is that for this choice of we have
For other choices of parameters the value of can be very large, (100). Another interesting relation is found for the case of small mass mixing between and namely . In this limit is determined from the charges only,
One might think that small values of are problematic for the Higgs boson mass since the MSSM-type tree-level contribution becomes very small. However, as we will see below, additional terms to the light Higgs mass and especially their dependence on can help raise its value to 125 GeV.
The important new feature in the sfermion sector is that the symmetry induces new -term contributions to the sfermion masses. These are added to the diagonal part of the usual MSSM sfermion matrix, and read
For large values of the new -term contribution can completely dominate the sfermion mass. Moreover this term can induce negative mass corrections, even driving the charged sfermion to be the LSP. Thus the requirement that the LSP be neutral (either the lightest neutralino or RH sneutrino) constrains the values of (unless one allows large soft masses for the sfermions). For example, for , the corrections to the d-squark and to LH slepton masses are negative, while for the corrections to the u-squark and RH slepton masses are negative. The latter implies that the u-type squarks (and in particular the lightest top squark) and the RH sleptons can be the Next-to-LSP (NLSP). Interestingly for the LH smuon/sneutrino can be sufficiently light to contribute significantly to the the anomalous magnetic moment of the muon and bring it in agreement with the data [51, 52].
In the UMSSM the neutralino mass matrix in the basis reads ( and )
Diagonalisation by a 66 unitary matrix leads to the neutralino mass eigenstates :
The chargino sector is identical to that of the MSSM.
Several studies have analysed the properties of the neutralino sector in the UMSSM [53, 54], in particular as concerns the neutralino LSP as a viable DM candidate [55, 56]. In the weak scale model, the LSP can be any combination of bino/Higgsino/wino/singlino and bino’. However, as we will show, the LSP is never pure bino’, the pure bino and singlino tend to be overabundant while pure higgsino and wino lead to under abundance of DM.
3 The Higgs sector
The Higgs sector of the UMSSM consists of three CP-even Higgs bosons , two charged Higgs bosons and one CP-odd Higgs boson .
The Higgs potential is a sum of F-, D- and soft supersymmetry breaking-terms belonging to the UMSSM Lagrangian : , where
At the minimum of the potential , the neutral Higgs fields are expanded as
while the charged Higgs :
with the Goldstone boson.
The minimization conditions of are 
The tree-level mass-squared matrices for the CP-even and CP-odd Higgs bosons can be written in the basis using the relations
where and . For the neutral CP-even Higgs bosons the relations are
For the CP-odd sector the mass matrix
The charged Higgs mass at tree-level reads
The radiative corrections to the Higgs sector are given in appendix A.
The lightest Higgs is usually SM like but can be heavier than in the MSSM. Indeed the tree-level lightest Higgs boson mass squared, which can be approximated by 
receives three types of additional contributions as compared to the MSSM. The first one proportional to is also found in the NMSSM, the second one comes from the additional U(1) gauge coupling and the last arises from a combination of pure UMSSM and NMSSM terms. The first term is not expected to play as important a role as in the NMSSM since is small. This is because is inversely proportional to the vev of the singlet Higgs field which is in turn related to the mass of new gauge boson, see eqs. (2.3) and (2.6). The strong dependence of the latter two terms on the charges means that the size of the tree-level contribution to the Higgs mass will mostly depend on the value of . We illustrate this taking the limit of small mass mixing between the two bosons as given in eq. (2.13). Figure 2 shows that in this limit does not exceed the MSSM upper bound and that its value depends strongly on . The maximum is reached for which corresponds to or = 1. A smaller value for the maximum is found for lower values of since the last term in eq. (3.10) then gives a larger negative contribution to the tree-level mass. Furthermore, the tree-level mass tends to be suppressed for small values since these are linked to small values of and thus to a small contribution from the NMSSM term. This behaviour shown in figure 2 is mostly observed for TeV and TeV. In the general case with non-zero mixing, a large tree-level contribution can be obtained for a wider range of parameters and a mass of 125 GeV for the lightest Higgs boson can easily be reached even with a small contribution from one-loop corrections that comes predominantly from the stop/top sector, as in the MSSM.
Typically the Higgs spectrum will consist of a standard model like light Higgs, a heavy mostly doublet scalar which is almost degenerate with the pseudoscalar and the charged Higgs, and a predominantly singlet Higgs boson. The latter can be either or , depending on the values of the free parameters of the model, in particular and . The singlet Higgs is never because its mass depends on which is large due to the lower bound on .
4 Constraints on the model
4.1 Higgs physics
For the Higgs sector we require that the light333 Strictly speaking it is also possible that the Higgs at 125 GeV corresponds to , however we did not find such points in the scan. Higgs mass lies in the range allowing for a theoretical uncertainty around 2 GeV. We impose constraints on the Higgs sector keeping only points allowed by HiggsBounds-4.1.3  and by HiggsSignals-1.2.0  at 95% C.L (-value above 0.05). We also use constraints contained in NMSSMTools, in particular the one on the heavy Higgs search in the decay mode that rules out some of the large region.
Note that the Yukawa couplings evaluated at the SUSY scale which enter the computation of the Higgs boson masses must remain perturbative. We require that all Yukawa couplings stay below at the SUSY scale. This condition will impose restrictions on both the small and the very large values (recall that is not a free parameter of the model). Yukawa couplings within the perturbative limit can nevertheless induce a very large width for some of the Higgs states, since we work in the context of elementary Higgs particles we impose the condition .
4.2 Collider searches for
One of the main constraint on this model comes from the direct collider searches for a boson in the two-lepton decay channel. The best limits have been obtained at the LHC by the ATLAS  and CMS  collaborations for collisions at a center-of-mass energy of 8 TeV. In  limits were obtained with an integrated luminosity of 19.7 fb (20.6 fb) in the dielectron (dimuon) channel and lead to TeV for , assuming only SM decay modes. Such limits however depend on the couplings of the , hence on . To reinterpret this limit for any value of , we first simulate Monte Carlo signals for production using the same Monte Carlo generator and PDF set as in , respectively Pythia 8.165  and MSTW2008LO , for a large set of values. We get results compatible with with the ones derived in  as well as the one obtained by the CMS collaboration . Then we interpolate our limits for any possible choice of . Note that the coupling of to the standard model fermions also weakly depends on . We have checked that this dependence does not modify significantly the limits and are well below PDF uncertainties . Furthermore in the UMSSM the can decay into supersymmetric particles, RH neutrinos and Higgs bosons, thus reducing the branching ratio into leptons. The limits on the mass are therefore weakened [64, 65, 66, 67]. To take this effect into account we determine in a second step the modified leptonic branching ratio for each point in our scan, and re-derive the corresponding limit.
For any value of we restrict the scan to . In addition, the mixing between and can be constrained by the parameter . This observable, which measures the deviation of the -parameter of the standard model from unity, receives a specific UMSSM tree-level contribution because is no longer purely the boson. In the limit where , which is the case for the TeV scale , this new contribution reads 
We compute for each point in the parameter space using a micrOMEGAs routine which also contains leading one-loop third generation sfermions and leading two-loop QCD contributions. We impose the upper bound .
4.3 Collider searches for SUSY particles
First we impose generic constraints from LEP on neutralinos, charginos, sleptons and squarks. For the latter we ignore the possibility of very compressed spectra and use the generic limit at 103 GeV. Lighter compressed squarks can in any case be constrained from LHC monophoton searches [70, 71] and monojet analyses .
The most powerful and comprehensive constraints on supersymmetric partners have been obtained by ATLAS and CMS using the data collected at 7 and 8 TeV. Searches were performed for a wide variety of channels and results were presented both in the framework of specific models, such as the MSSM, and in the context of simplified model spectra (SMS). Here we use the SMS results to find the main constraints on the UMSSM. We base our analysis on SModelS v1.0.1 [39, 40], a tool designed to decompose the signal of an arbitrary BSM model into simplified model topologies and to test it against LHC bounds. The version used includes more than 60 SMS results from both ATLAS and CMS.
The input to SModelS are SLHA files that contain the full mass spectrum, decay tables as well as production cross sections. The input files, including tree-level production cross sections, are generated using micrOMEGAs_4.1.5 , for strongly produced particles, SModelS then calls NLL-fast [74, 75, 76, 77, 78, 79, 80] to compute the k-factor at NLO+NLL order. Subsequently the code decomposes the full model into simplified model components, and calculates the weight (production cross section times branching ratio, ) for each topology. To limit computing time, topologies with small weights are not considered in the decomposition. As a minimum weight we have used a cutoff of fb. The resulting list is then confronted with the SModelS database, for any matching result is compared against the experimental upper limit. If no matching results are found the point is labeled as not tested. This may happen for several reasons, either all cross sections are below in which case the decomposition will not return any entries, there is no matching simplified model result in the database, or the mass vector of the new particles lies outside the experimental grids for all applicable SMS results. Since soft decay products cannot be detected, in this analysis we disregard vertices where the mass splitting between the mother and daughter SUSY particles is less than 5 GeV. A fully invisible decay at the end of a decay chain is compressed, the corresponding mother SUSY particle is then treated as an effective LSP.
Note that topologies that contain long-lived charged particles corresponding to mm are not tested against SMS results within SModelS. However searches for long-lived particles leaving charged tracks in the detector have been performed at the Tevatron  and the LHC [82, 83] and were interpreted in the context of long-lived charginos or in the context of the pMSSM . When the neutralino LSP is dominantly wino, typically, the NLSP chargino will be stable at the collider scale. We have therefore considered the D0 and ATLAS upper limits for points with charginos in the mass range GeV and GeV, and decay lengths m and m respectively. We have not included the limits from CMS as these cannot be simply reinterpreted for direct production of chargino pairs . Long-lived gluinos or squarks are also possible, we have not considered these cases since the interpretation of a given experimental analysis relies on the modeling of R-hadrons, thus introducing large uncertainties. Moreover we have not implemented current limits on long-lived staus as these rarely occur in the parameter space considered.
4.4 Flavour physics
Indirect constraints coming from the flavour sector, especially those involving -Mesons, play an important role in defining the allowed parameter space of supersymmetric models, e.g. [85, 86, 87, 88]. The constraints imposed on the model are listed in Table 2, though we do not in general require agreement with the measured value of . We do however highlight the specific regions consistent with the measured value of the muon anomalous magnetic moment. These mostly correspond to regions with a light LH smuon/sneutrino as mentioned in section 2.2. To compute these observables, we have adapted the NMSSMTools routine to the UMSSM, for more details see . The most powerful constraints are and for small values of while and are also important to constrain some large values of . We also compute but this channel does not give additional constraints. Uncertainties coming from CKM matrix elements, rare decays, hadronic parameters and theory are taken into account when computing the observables listed in Table 2, see . The most important uncertainties in our computation of flavour observables are theoretical (10%) and from the CKM element .
|[0.70, 1.58]10 |
|[2.99, 3.87]10 |
|[1.6, 4.2]10 |
|[17.805, 17.717] ps |
|[0.504, 0.516] ps |
|[7.73, 42.14]10 [51, 52, 96]|
4.5 Dark matter
The value of the dark matter relic density has recently been measured precisely by the Planck collaboration and a combination of Planck power spectra, Planck lensing and other external data leads to 
We will impose only the 2 upper bound from eq. (4.2) on the value of the relic density. That is we assume that either there is another component of dark matter or that there exists some regeneration mechanism that can bring the dark matter within the range favoured by Planck [98, 99].
This measurement puts a strong constraint on the parameter space of the UMSSM whether the dark matter candidate is the lightest neutralino or the supersymmetric partner of the right-handed neutrino. Since the three RH sneutrinos have the same coupling to all other particles in the model we assume for simplicity that the third generation sneutrino is the lightest. In previous studies it was shown that the favoured mass for the RH sneutrino LSP was near , although much lighter sneutrinos could also be found, especially near or when coannihilation was present . As in the MSSM the lightest neutralino covers a large range of mass, the main new features being the possibility of a singlino LSP [100, 101, 102] and the possibility for this singlino to have a non-negligeable bino’ component. Typical MSSM features can also be observed as the example of wino LSP annihilating efficiently into ’s and strongly degenerate in mass with chargino NLSP. However sometimes the mass degeneracy between the NLSP and the LSP can be sufficiently small to give an absolutely stable charged NLSP. When focusing on relic density constraints we will systematically discard these configurations.
One of the strongest constraint on DM arises from direct detection. We implement the upper limit from the LUX collaboration  taking micrOMEGAs default values for the quark coefficients in the nucleons. This upper limit strongly constrains the scenarios where the LSP is GeV). Another relevant constraint is the one from FermiLAT searches for DM annihilation from the dwarf spheroidal satellite galaxies of the Milky Way where limits obtained for DM annihilation into and can constrain scenarios with DM masses below 100 GeV .
|[0, 2] TeV||[-2, 2] TeV|
|[2.2, 7] TeV||[-4, 4] TeV|
|[-20, 20] TeV||[0.4, 12] TeV|
|[-/2, /2] rad||[0, 4] TeV|
|[-, ] rad||173.34 1 GeV |
After imposing universality for the sfermion masses of the first and second generation and fixing the trilinear coupling of the first two generation sfermions to 0 GeV, the UMSSM features 24 free parameters. The range used for these parameters in the scans are listed in Table 3. In addition we have allowed the top mass to vary. We perform a random scan over the free parameters and impose first the set of basic constraints described from section 4.1 to section 4.3 : the Higgs mass and couplings allowed by HiggsBounds, HiggsSignals and our modified NMSSMTools routines, perturbative Yukawas for top and bottom quarks, agreement with LEP limits on sparticles and LHC limits on the and finally a neutral LSP. We then include the constraints from -physics mentioned in section 4.4. Another scan is done to highlight the regions of parameter space which give sufficient New Physics contribution to . For this we restrict the soft masses of the second generation of sleptons to [0, 2] TeV and we impose all constraints given in section 4.4.
For all points that satisfy these sets of constraints in both scans, around , we found that the maximum tree-level mass for the Higgs reached only GeV and was above the mass only for mixing angles , see figure (a)a. Thus a contribution from the radiative corrections in the stop/top sector is still required to reach a Higgs mass of 125 GeV. Nevertheless the full range of values of is allowed. Small values of require a large value of to compensate the small MSSM-like tree-level contribution to the light Higgs mass, see figure (b)b. This also means that , hence , cannot be too large given the range assumed for the parameter, see eq. (2.3). Radiative corrections from the top/stop sector are expected to be large for since the top Yukawa coupling increases as , which explains why a larger range for is allowed when .
It is well known that large one-loop corrections from the stop sector require heavy stops and/or large mixing . The mixing parameter is indeed found to be large when TeV while heavy stops (associated with large ) allow no mixing, see figure (a)a. The heavier the the larger the minimal value for the scale where zero mixing is allowed.
The spectrum for supersymmetric particles differs significantly from the case of the MSSM and NMSSM, depending on the choice of charges. The lightest stop mass can be as light as 300 GeV for (figure (b)b), this value corresponds to the largest negative contribution to the stop mass from the -term, see section 2.2. When the lightest stop is at least 670 GeV. Similar values are found for both LH and RH up-type squarks, modulo mixing effects. Such light squark masses are well within the range of exclusion of LHC searches within the MSSM, hence the need to reinvestigate the impact of these searches within the UMSSM discussed in the next section. The mass receives a large negative -term contribution for . For this value it can be as light as allowed by LEP (103 GeV), see figure (d)d. For the RH d-squark is above the TeV scale while the LH one can be light since . This implies also that a light sbottom, say below 500 GeV, can be found for either value of , see figure (c)c. In one case it is mostly LH and in the other RH. Note that an increase in the lower limit on the mass will lead to larger squark masses except for the specific values of where one gets a very large -term contribution. Finally, the gluino mass is determined by , hence can also be well below the TeV scale.
The impact of the flavour constraints is best displayed in the plane, see figure 5. As expected and are the most important constraints in our scans and exclude a large part of the parameter space when , through the charged Higgs contribution . The contribution from Double Penguin diagrams to these observables enable exclusion of a few scenarios at large . and are important for scenarios at very large but they mostly fail to exclude points, especially for cases where the mass of heavy neutral and charged MSSM-like Higgs bosons is above several TeVs. Finally the New Physics contribution to the deviation of the -parameter from unity exclude only few points, mostly from the sfermion contributions. Actually the pure UMSSM contribution shown in eq. (4.1) can barely reach for the allowed values for and and is then negligible. Note that, as we will see in the next section, specific regions of the parameter space give large enough contributions to the anomalous magnetic moment of the muon.
Special conditions are required to get agreement with the value of . Indeed the discrepancy between the theoretical and experimental value requires a large contribution from New Physics. In the UMSSM this comes in particular from diagrams involving smuon (LH sneutrino) and neutralino (chargino) exchange. A large UMSSM contribution requires either a light smuon/LH sneutrino or an enhanced Yukawa for the muon. The latter is found at very large values of , see figure (a)a. A light LH smuon mass arises for corresponding to a large negative -term contribution as explained in section 2.2. Future collider limits on the mass, say above 5 TeV, will severely constrain scenarios for positive values of that are in agreement with the latest value of , see figure (b)b. Note that the distribution of points in the plane is similar to the one found in the general scan where consistency with the muon anomalous magnetic moment is not required, except that heavier sleptons are allowed in that case.
5.2 Dark matter relic abundance
In this model the LSP can either be a neutralino or a RH sneutrino. The annihilation properties of the neutralino LSP are determined by its composition (figure 7). As in the NMSSM, the pure bino or singlino LSP is typically overabundant unless it can benefit from a resonance enhancement. Note that in this model the Higgs singlet is very heavy so that resonant annihilation of a singlino through the Higgs singlet works only for heavy singlinos444For an analysis of a scenario with a light singlino DM see .. The dominantly singlino LSP is found only for masses above 250 GeV. Some admixture of a higgsino/wino component or coannihilation processes can however reduce the relic density to for any mass. Coannihilation can occur with gluinos or other gauginos as well as with sfermions. As in the MSSM the dominantly higgsino or wino LSP annihilates very efficienty into gauge boson pairs and therefore leads to an under-abundance of dark matter unless the higgsino (wino) LSP mass is roughly above 1 (1.5) TeV. Note that the component of the LSP is never dominant, because the vev of the singlet, which mostly drives the mass of the and the , eq. (2.15), is always above 6 TeV. For , and are both shifted towards large masses whereas for the singlino benefit from a seesaw-type mechanism which allows a singlino LSP down to 250 GeV. This close relation between and is illustrated in figure 8.
We note that the fraction of points that satisfy the Planck upper bound is much higher in the scan where we impose the constraint on than in the general scan. The main reason is that it is easier to satisfy the relic density upper bound with a bino LSP when the sleptons are light.
Sneutrino dark matter is typically overabundant as sneutrino annihilation channels are not very efficient. Agreement with the upper bound set by Planck requires either or as found in . The latter case requires above the TeV scale when considering current limits on the mass, here we consider DM below 2 TeV. Annihilation into or pairs through Higgs boson exchange was also found to be efficient enough for GeV . However this process, which depends mostly on the singlet nature of the Higgs boson exchanged, will not give a large enough contribution if the lower limit on increases as shown in figure 9. Sneutrino LSP masses in the range GeV are also allowed if some coannihilation mechanism, involving e.g. the lightest neutralino or other sfermions, helps reduce the relic abundance. The low density of points in this region (see figure 9) reflects the fact that the importance of such coannihilation processes require the adjustment of uncorrelated parameters in the model.
6 Impact of LHC searches for SUSY particles
After having imposed the basic constraints, flavour constraints and an upper bound on the relic density (corresponding to the upper limit of eq. (4.2)), we next consider the impact of LHC searches for SUSY particles based on SMS results and using SModelS. To analyse the impact of the SMS results we group the points into four categories. Points excluded by SModelS are labeled as excluded, points where the SMS results apply but the cross section is below the experimental upper limit are labeled as not excluded. Points where no SMS result applies, as explained in section 4.3, are labeled as not tested. Finally points with long-lived particles cannot yet be tested in SModelS. Points that are not excluded are then examined in more details to determine the signatures that could best be used to further probe them with upcoming data. We divide the study in three steps. First, we consider scenarios with a neutralino LSP and find that the most stringent constraints on supersymmetric particles are obtained for light gluino or light squarks [6, 106, 107]. Second, we concentrate on points compatible with the measurements of the muon anomalous magnetic moment and that still have a neutralino LSP. This dedicated scan provides a significant number of points with light sfermions and allows us to ascertain the impact of slepton searches. Finally we investigate scenarios with a RH sneutrino LSP, among these we do not characterize the ones that are compatible with the muon because of the small number of points involved. The possibilities to probe all points with long-lived charginos are considered separately in section 6.4 regardless of the dark matter candidate. Our results for the constraints on the SUSY spectra are presented in section 7 where we combine all sets.
6.1 Neutralino LSP
In most points with a neutralino LSP, the LSP is actually either dominantly wino or higgsino, see figure 7. Points with a wino LSP are however mostly not considered in the SModelS v1.0.1 analysis because they lead to long-lived charginos. Therefore the most common configuration for the supersymmetric spectra relevant for SMS results is one with three dominantly higgsino particles with similar masses : the LSP, the second neutralino and the lightest chargino. Moreover since the jets/leptons produced in the decay of the chargino (second neutralino) to the LSP are too soft to be detected the chargino (second neutralino) will often lead to a missing (MET) signature. We will see that this has important consequences when using the SMS results. In particular hardly any points can be excluded from electroweakinos searches as only few can exploit the decay channel into real gauge/Higgs boson. Furthermore we do not find constraints from decays into leptons via sleptons since sleptons are rarely light.
6.1.1 Gluino constraints
In figure 10 we show points with a neutralino LSP in the LSP and gluino mass plane for gluino masses up to GeV. On the left we show excluded points in red and allowed points in blue, moreover we indicate points with long-lived sparticles that cannot be tested in SModelS v1.0.1 in green and points not tested for the other reasons mentioned before in grey. The right panel indicates the topology giving the strongest constraint for each excluded point.