Realistic Simplified Gaugino-Higgsino Models in the MSSM

Eur. Phys. J. C (2018) 78:209 https://doi.org/10.1140/epjc/s10052-018-5695-2

Special Article - Tools for Experiment and Theory

Realistic simpliﬁed gaugino-higgsino models in the MSSM

Benjamin Fuks1,2,3,a , Michael Klasen4,b, Saskia Schmiemann4,c, Marthijn Sunder4,d 1 Sorbonne Universités, Université Pierre et Marie Curie (Paris 06), UMR 7589, LPTHE, 75005 Paris, France 2 CNRS, UMR 7589, LPTHE, 75005 Paris, France 3 Institut Universitaire de France, 103 boulevard Saint-Michel, 75005 Paris, France 4 Institut für Theoretische Physik, Westfälische Wilhelms-Universität Münster, Wilhelm-Klemm-Straße 9, 48149 Münster, Germany

Received: 14 November 2017 / Accepted: 4 March 2018 / Published online: 13 March 2018 © The Author(s) 2018

Abstract We present simplified MSSM models for light Standard Model, feature gauge coupling unification at high neutralinos and charginos with realistic mass spectra and energy and generally include a natural explanation for the realistic gaugino-higgsino mixing, that can be used in exper- presence of dark matter in the universe. Consequently, super- imental searches at the LHC. The formerly used naive symmetry searches constitute a significant part of the LHC approach of defining mass spectra and mixing matrix ele- physics program. ments manually and independently of each other does not Up to now, no evidence for supersymmetry has been yield genuine MSSM benchmarks. We suggest the use of less found. Limits on the masses of the supersymmetric partners simplified, but realistic MSSM models, whose mass spectra of the Standard Model particles are consequently pushed and mixing matrix elements are the result of a proper matrix to higher and higher energy scales. Most of these results diagonalisation. We propose a novel strategy targeting the have, however, been derived either in the framework of the design of such benchmark scenarios, accounting for user- minimal supersymmetric realisation, known as the Minimal defined constraints in terms of masses and particle mixing. Supersymmetric Standard Model (MSSM) [1,2], or within We apply it to the higgsino case and implement a scan in the MSSM-inspired simplified models for new physics [3–6]. four relevant underlying parameters {μ, tan β, M1, M2} for a Simplified models are effective Lagrangian descriptions given set of light neutralino and chargino masses. We define minimally extending the Standard Model in terms of new a measure for the quality of the obtained benchmarks, that particles and interactions. They have been designed as use- also includes criteria to assess the higgsino content of the ful tools for the characterisation of new phenomena, allow- resulting charginos and neutralinos. We finally discuss the ing for the reinterpretation of the results in a straightforward distribution of the resulting models in the MSSM parameter manner thanks to a reduced set of degrees of freedom. In space as well as their implications for supersymmetric dark the context of MSSM-inspired simplified models, the experi- matter phenomenology. mental attention was initially mainly focused on the analysis of signatures that could originate from the strong production of squarks and gluinos, the corresponding cross sections 1 Introduction being expected to be larger by virtue of the properties of the strong interaction. LHC null results have implied that Supersymmetry (SUSY) is one of the most popular theo- severe constraints are now imposed on the masses of these ries beyond the Standard Model (SM) of particle physics. strongly interacting superpartners. In particular, the analysis Extending the Poincaré algebra by relating the fermionic and of about 36 fb−1 of LHC collision data at a centre-of-mass bosonic degrees of freedom of the theory, supersymmetry energy of 13 TeV pushes the lower bounds on these masses provides a solution to many of the shortcomings and limita- far into the multi-TeV regime [7–23]. Processes involving tions of the Standard Model. In particular, supersymmetric the production of a pair of electroweak superpartners (neu- theories solve the infamous hierarchy problem plaguing the tralinos, charginos and sleptons) have also been considered for some time. The electroweak nature of these processes a e-mail: [email protected] yields, however, smaller production rates and subsequently b e-mail: [email protected] softer bounds on the corresponding masses [23–26]. Neu- c e-mail: [email protected] d e-mail: [email protected] 123 209 Page 2 of 16 Eur. Phys. J. C (2018) 78 :209 tralinos, charginos and sleptons of a few hundreds of GeV In certain configurations, e.g. when the lightest states are are indeed still allowed by current data. nearly degenerate pure higgsinos and the gauginos are decou- We focus in this work on simplified models describing pled, this simple method works quite well. However, when electroweak gauginos and higgsinos and their dynamics. one targets next-to-minimal simplified models where a mass Recent searches of both ATLAS and CMS are in general splitting between the second-lightest state and its neighbours interpreted within the framework of two sets of simplified is introduced, some amount of mixing between the different models. In the first case, the Standard Model is extended gaugino and higgsino fields must be included in order to by a set of mass-degenerate pure wino states, and the lightest maintain viability with respect to the initial MSSM moti- superpartner is a pure bino state. The winos are then assumed vation. This concerns in particular identities guaranteed by to decay either into a system made of a bino and a weak gauge invariance and/or supersymmetry that could be vio- gauge or Higgs boson, regardless of the fact that these decays lated when one tweaks by hand masses and mixing matrix are strictly speaking not allowed by supersymmetric gauge elements, like in the above-mentioned wino set of simpli- invariance, or into a bino and jets or leptons via intermedi- fied models. Such non-minimal setups are already probed by ate off-shell sfermions. When the gaugino-higgsino mixing both LHC collaborations in their searches for supersymme- is not negligible and the mass splitting between the light- try [28,29]. It is therefore important to interpret the results in est states is sufficiently large, the decays to weak gauge and meaningful benchmark scenarios where supersymmetry and Higgs bosons become allowed and provide opportunities to gauge symmetries are preserved, allowing in this way only obtain bounds on the MSSM parameter space. The strength for theoretically-relevant interpretations. of the constraints then depends on the mixing and the mass In this work, we present simplified MSSM models for light splitting [27]. On the other hand, heavier higgsino-like elec- neutralinos and charginos with realistic mass spectra and troweakinos decay dominantly into lightest neutralinos and realistic gaugino-higgsino mixing, that can be used, e.g., in weak gauge bosons, thanks to their mixing with the gaugi- experimental searches at the LHC. Starting from the MSSM nos, but only if the channels are kinematically accessible. In without additional CP-violation, we design our simplified compressed mass scenarios, the corresponding experimen- model by decoupling all coloured superpartners as well as tal searches rely on the detection of the soft decay prod- the sleptons and the sneutrinos. The gaugino-higgsino sector ucts of the gauge bosons, e.g. low transverse-momentum is thus described, at tree-level, by four parameters that are the opposite-charge leptons of the same flavour (electrons or bino and wino mass parameters M1 and M2, the supersym- muons) [28,29]. The second set of models under considera- metric higgs(ino) off-diagonal mass parameter μ, and the tion is inspired by gauge-mediated supersymmetry breaking ratio of the vacuum expectation values of the neutral com- scenarios [30–36], in which the lightest superpartner is the ponents of the two Higgs doublets tan β. We then define a gravitino. This simplified model additionally contains two strategy to efficiently scan this four-dimensional parameter neutral and one charged higgsino state, which are quasi mass- space for given sets of light neutralino and chargino masses, degenerate. They hence decay into a gravitino and a neutral that also allows to maximise the gaugino or higgsino content, gauge or Higgs boson, together with possibly accompanying couplings to certain sparticles etc. This procedure therefore undetected soft objects. allows to find approximate solutions for simplified MSSM In all of the above approaches to MSSM-inspired sim- models that have a realistic and properly defined gaugino- plified models for the gaugino-higgsino sector, one naively higgsino sector in contrast to many of the overly simplified ignores all interrelationships between the masses of the neu- models studied so far. tralinos and the charginos and the features of the associated The remainder of this paper is organised as follows. We mixing matrices through their respective dependence on the first review in Sect. 2 the MSSM chargino-neutralino sector, free parameters in the MSSM Lagrangian. Starting from the discuss its analytic symmetries, and study the spectra and MSSM, the neutralinos and charginos that are not of interest decompositions of the physical states after numerical diag- are decoupled by imposing the corresponding mixing matrix onalisation of the neutralino and chargino mass matrices. In elements to be vanishing and their masses to be very large. Sect. 3, we describe our strategy to scan the four-dimensional On the other hand, the masses of the relevant neutralinos and MSSM parameter space, define a quality measure for the charginos are fixed by hand to the desired values, indepen- goodness of our fit to the desired simplified model, and indi- dently of the corresponding√ elements in the mixing matrices cate how our scan strategy can be generalised. In Sect. 4,we that are set to 0, 1, or ±1/ 2 (in the higgsino case). This present a case study for higgsino-like light neutralinos and approach is justified by the assumption that the MSSM has charginos, analyse their representation in the MSSM parame- sufficiently many free parameters to reproduce such a pattern ter space, and investigate the implications for the Higgs-stop closely enough, which is particularly true when one considers sector as well as the phenomenology of supersymmetric dark the extra freedoms originating from the loop corrections. matter. Our conclusions are given in Sect. 5.

123 Eur. Phys. J. C (2018) 78 :209 Page 3 of 16 209

2 Theoretical definitions with The simplified model that we investigate in this work takes 1 v1 1 0 h1 = √ and h2 = √ , (4) the gaugino-higgsino sector from the MSSM in all its com- 2 0 2 v2 plexity, as it is defined by supersymmetry and gauge invariance. In other words, we compute all elements of the neu- the non-vanishing values of v1 and v2 giving rise to the spon- tralino and chargino mixing matrices and the physical mass taneous breaking of the electroweak symmetry, SU(2)L × spectrum through a proper diagonalisation of the relevant U(1)Y → U(1)EM. Since supersymmetry has not yet been mass matrices at tree level. In our procedure, the mass spec- observed, it must be a broken symmetry. As usual, we remain trum of the neutralinos and charginos is thus not treated agnostic of which mechanism is invoked to break supersym- independently from their couplings, as it has been done pre- metry, and thus explicitly include in the MSSM Lagrangian viously in (overly) simplified models. By decoupling other soft supersymmetry-breaking interaction terms that leave supersymmetric particles, the model does, however, still not the gauge symmetries intact and that do not introduce any become overly complex, and this partly justifies that we new quadratic divergences at the loop-level. Among the neglect higher-order effects. The latter are nevertheless not allowed supersymmetry breaking terms, the bino (B) and so relevant for our purpose, the idea being to design models wino (W) mass terms are the only ones relevant for our closely enough reproducible in the MSSM. work, MSSM 1 i 2.1 MSSM chargino-neutralino sector L =− M B B + M Wi W + h.c. +··· . (5) soft 2 1 2 In the MSSM and at tree-level, the gaugino-higgsino (or The chargino mass eigenvalues are obtained by diagonal- equivalently neutralino-chargino) sector is defined by four ising the chargino mass matrix X that can be extracted from parameters ( −, −) Eqs. (2) and (5). This matrix is given, in the iW H1 and ( +, +) iW H2 basis, by {μ, tan β, M , M }, (1) 1 2 √ M 2M sβ X = √ 2 W , (6) that are the off-diagonal Higgs(ino) mass parameter, the ratio 2MW cβ μ of the vacuum expectation values of the neutral components of the two doublets of Higgs fields and the two soft where MW stands for the mass of the W-boson and where we supersymmetry-breaking electroweak gaugino mass param- have introduced the cβ and sβ notations for the cosine and sine eters, respectively. of the β angle, respectively. This matrix can be diagonalised The μ parameter originates from the MSSM superpoten- by means of two unitary rotation matrices U and V, tial (WMSSM). It reads, when we assume that the superpotential contains only R-parity conserving terms, ∗ −1 diag(Mχ˜ ± , Mχ˜ ± ) = U XV , (7) 1 2 W = μ · − e · MSSM H1 H2 yijH1 Li E j where Mχ˜ ± < Mχ˜ ± are the masses of the two chargino 1 2 − d · − u · , states. The U and V mixing matrices respectively relate the yijH1 Qi D j yijQi H2U j (2) negatively-charged and positively-charged gaugino-higgsino (χ ±,χ±) basis to the physical chargino mass basis 1 2 , where H1 and H2 denote the two weak doublets of Higgs superfields. Q, L, and U, D and E are the two weak dou- − + χ iW− χ iW+ blets and three weak singlets of quark and lepton superfields, 1− = U − and 1+ = V . (8) χ H χ H+ respectively. Expanding the superpotential WMSSM in terms 2 d 2 u of the component fields of the various superfields, it includes in particular an off-diagonal mass term proportional to μ for Similarly, in the neutral sector the neutralino mass matrix the two higgsino fields H and H . The second parameter can be computed from Eqs. (2) and (5). This matrix can be 1 2 ( , 3, 0, 0) in Eq. (1) is defined as the ratio of the vacuum expectation written, in the i B iW H1 H2 basis, as values of the scalar components h1 and h2 of the two Higgs ⎛ ⎞ superfields M1 0 −MW tW cβ MW tW sβ ⎜ ⎟ ⎜ 0 M2 MW cβ −MW sβ ⎟ Y = ⎝ ⎠ , (9) v −MW tW cβ MW cβ 0 −μ tan β = 2 (3) β − β −μ v1 MW tW s MW s 0 123 209 Page 4 of 16 Eur. Phys. J. C (2018) 78 :209 where tW ≡ tan θW stands for the tangent of the electroweak where σ3 is the third Pauli matrix. In general, these two sign mixing angle. This symmetric matrix can be diagonalised by flips also lead to effects on the neutralino mass spectrum, means of a single unitary matrix N , unless one extends the transformation of Eq. (12)as

∗ −1 → =− , N YN = diag (Mχ˜ 0 , Mχ˜ 0 , Mχ˜ 0 , Mχ˜ 0 ), (10) M1 M1 M1 1 2 3 4 → =− , M2 M2 M2 (14) where Mχ˜ 0 < Mχ˜ 0 < Mχ˜ 0 < Mχ˜ 0 stand for the masses μ → μ =−μ. 1 2 3 4 χ 0 = of the four neutralino states i with i 1, 2, 3 and 4. The mixing matrix N allows one to relate the four physical neu- The neutralino masses are thus left invariant by the trans- tralino mass eigenstates to the neutral higgsino and gaugino formation of Eq. (14), that modifies the neutralino mixing interaction eigenstates, matrix N as ⎛ ⎞ ⎛ ⎞ ⎛ ⎞ χ 0 i B 1000 1 ⎜ ⎟ ⎜χ 0⎟ ⎜iW3⎟ ⎜ 0100⎟ ⎜ 2 ⎟ = N ⎜ ⎟ . N → N = iN ⎝ ⎠ . (15) ⎝χ 0⎠ ⎝ 0 ⎠ (11) 00−10 3 Hd χ 0 0 000−1 4 Hu β Non-trivial analytic inversions of the gaugino mass matri- On different grounds, the inversion of tan , ces have been proposed in the past. Besides the knowl- 1 edge of three gaugino masses, typically those of one or two tan β →[tan β] = , (16) charginos and of two or one heavier neutralinos, they require tan β the choice of a value for tan β as well as additional infor- mation and/or numerical consistency checks to resolve sign also leaves the chargino and neutralino mass spectrum invari- U V ambiguities [37]. ant. The mixing matrices and are, however, interchanged, χ + χ − as are the decompositions of the Weyl fields i and i in terms of their gaugino and higgsino content, 2.2 Symmetry transformations 01 01 For a better understanding of the structure of the parameter U → U = V and V → V = U . (17) 10 10 space of our simplified model, we discuss in this subsec- tion two linear transformations of the mixing matrices that affect the electroweakino couplings, but leave their mass The total gaugino-higgsino content of the Dirac chargino spectrum unchanged. These symmetries hence allow us to spinors is, however, unaffected. As mentioned above, the deduce multiple benchmark scenarios fitting equally well a transformation of Eq. (16) also leaves the neutralino mass N preselected mass configuration and chargino and neutralino eigenvalues invariant. The neutralino mixing matrix is β decomposition in terms of gaugino and higgsino eigen- in contrast modified. The inversion of tan physically inter- 0 0 states. changes the roles of H1 and H2 , so that the decomposition of the neutralinos in terms of the two higgsino states is swapped We restrict our study to the case where the μ, M1 and with an extra sign flip, M2 parameters are real in order not to introduce additional sources of CP-violation in the theory. However, we keep ⎛ ⎞ the sign of these three mass parameters free, so that they can 1000 ⎜ ⎟ therefore be either positive or negative. The mass eigenvalues N → N = N ⎜ 0100⎟ . ⎝ − ⎠ (18) of the chargino mass matrix X only depend on the relative 0001 00−10 sign between the μ and M2 parameters. This means that the simultaneous flip of the signs of the M2 and μ parameters, 2.3 Mass spectra and gaugino-higgsino content → =− μ → μ =−μ, M2 M2 M2 and (12) As stated at the beginning of this section, the parameter leaves both chargino masses invariant. The chargino mixing space describing the MSSM gaugino-higgsino sector is four- μ β matrices are, however, impacted and transform as dimensional and specified by the parameters ,tan , M1 and M2. For convenience, we trade the gaugino mass parameters M1 and M2 for the relative mass differences δM2/|μ| U → U =−Uσ3 and V → V = Vσ3, (13) and δM1/M2 defined by 123 Eur. Phys. J. C (2018) 78 :209 Page 5 of 16 209

Fig. 1 Variation of the neutralino and chargino mass spectra for sce- colour-coding (with increased line width for better visibility) indicates narios featuring μ>0, as a function of |μ| (upper left), tan β (upper the bino (purple), wino (blue) and higgsino (red) content of the different right), δM2/|μ| (lower left) and δM1/M2 (lower right) when all other particles parameters are fixed to their reference value given in Eq. (20). The δ δ M2 M1 The results are shown in Figs. 1 and 2 for scenarios fea- M2 =|μ| 1 + and M1 = M2 1 + . |μ| M2 turing a positive and a negative μ parameter, respectively. In (19) these figures, we provide a global overview on how a variation of one of the model input parameters affects the mass The resulting mass spectrum and neutralino and chargino spectra and the neutralino and chargino decompositions in decompositions are related to these parameters in a complex terms of the gaugino and higgsino states. Starting from the and non-trivial manner, which makes it difficult to get a global reference scenario of Eq. (20), we vary either the μ parameter understanding of the response of the spectrum to a variation in (upper left panels of the figures), tan β (upper right panels of these parameters. Therefore, we explore the parameter space the figures), the ratio δM2/|μ| (lower left panels of the fig- in a systematic way by first defining a default scenario ures) or the ratio δM1/M2 (lower right panels of the figures). Although opposite choices for the sign of μ correspond to 1 δM δM |μ|=2M , tan β =2 ∨ , 2 =0 and 1 =0, different regions in the parameter space, they can potentially W |μ| M 2 2 lead to similar mass spectra (cf. the discussion in Sect. 2.2). (20) In the upper, middle and lower parts of each subfigure, we and then varying one of these parameters at a time. show the respective dependence of the bino (only for neutrali- 123 209 Page 6 of 16 Eur. Phys. J. C (2018) 78 :209

Fig. 2 Same as Fig. 1 for μ<0 nos), wino and higgsino content of each electroweakino state the mixing matrices that get imaginary, which thus affects on the considered model parameter. Trivially, we retrieve the the couplings. The original sign of the mass can be deduced fact that the chargino sector does not depend on the bino mass by examining the variation of the curves in Figs. 1 and 2.A parameter M1, and thus also not on δM1/M2. change of sign can be traced back to a curve hitting zero and The mixing pattern of the gaugino and higgsino states exhibiting a discontinuous local derivative. This conﬁgura- is driven by the off-diagonal elements in the mass matrices tion occurs when any of the μ, M1 and M2 mass parame- of Eqs. (6) and (9), which are all roughly proportional to ters is of O (MW ). Outside this range, two of the neutralinos the W-boson mass. Therefore, maximally mixed states arise always feature a dominant higgsino content, and their masses only when either |μ|, M1, M2, |±μ − M1|, |±μ − M2| or have opposite signs. The sign of the masses of the other two |M1 − M2| is of O(MW ) or smaller. Conversely, nearly pure neutralinos is driven by the sign of the M1 or M2 param- gaugino and higgsino states in the chargino sector occur for eters, depending on the dominant bino or wino nature of |μ| MW and |μ − M2| MW , while pure states in the the neutralinos under consideration, provided the mixing is neutralino sector additionally require also |−μ−M2| MW small. Moreover, one observes that the neutralino mass lines and |±μ − M1| MW . can only cross if the masses have opposite signs. Otherwise, The diagonalisation of the chargino and neutralino mass one gets an avoided crossing where the neutralino content is matrices can possibly yield negative mass eigenvalues. In exchanged. this case, they are made positive by absorbing the sign into

123 Eur. Phys. J. C (2018) 78 :209 Page 7 of 16 209

The results presented in the upper left panels of Figs. 1 can also be included. Finally, we briefly reflect on possible and 2 confirm that when |μ|, and subsequently also M1 and generalisations of these strategies. M2, exceeds the W-boson mass scale, the overall magnitude of the electroweakino masses is solely set by |μ| and increases uniformly with it. In the special case correspond- 3.1 Parameter space exploration ing to δM2/|μ|=δM1/M2 = 0, the mass differences as well as the elecroweakino decompositions moreover become The observations made in the previous section allow for the identification of general characteristics of the gaugino- independent of |μ|. In contrast, variations of δM2/|μ| and higgsino parameter space that are useful for building realistic δM1/M2 influence the electroweakino mass differences, as shown in the lower panels of Figs. 1 and 2. These parameters benchmark scenarios. Following most of the experimental are thus those that will allow us to determine MSSM bench- studies at the LHC, we focus on configurations with only χ 0 χ 0 χ ± mark points defined by an overall mass scale and a given two light neutralinos ( 1 , 2 ) and a light chargino ( 1 ). For mass splitting between the superpartners. In particular, one illustrative purposes, we take the desired chargino mass Mχ± Δ 1 can obtain a spectrum where the lighter (heavier) states are as an input and ask for an equidistant mass splitting M21 of the two neutralinos, nearly pure higgsinos when δM2/|μ| 0(δM2/|μ| 0). Different values of tan β or δM1/M2 then raise or lower the value at which the turnover occurs. Similarly, varying both ΔM21 ΔM21 δ /|μ| δ / Mχ0 = Mχ± − and Mχ0 = Mχ± + . (21) M2 and M1 M2 allows one to obtain scenarios featur- 1 1 2 2 1 2 ing nearly pure bino or wino states as the heaviest or lightest states. Finally, as illustrated on the upper right panels of the figures, we observe that the tan β-dependence of the spectrum The scan procedure described in the following can, however, exhibits a peak or a dip at tan β = 1 with an amplitude that easily be generalised to other setups. In principle, we scan over all four parameters μ,tanβ, is typically smaller than about MW /2. Except this feature, the effect of tan β on the spectrum is small, which therefore M1 and M2, but we immediately reduce this parameter space allows us to use this parameter for small adjustments once on the basis of the transformations that leave the neutralino- all other parameters have been chosen. When tan β 1or chargino mass spectrum invariant. Regions of the parameter tan β 1, the dependence on tan β moreover vanishes. space that are not explored are then derived by transforming Thesignoftheμ parameter has little influence on the mass the mixing matrices as described in Sect. 2.2. As a conse- β ∈[ ; ] spectrum upon variations of |μ|, δM /|μ| or δM /M .Nega- quence, we only scan over the regions tan 1 100 and 2 1 2 > tive μ values only induce a more compressed spectrum com- M2 0. In contrast, the sign of the higgsino mass parame- μ pared to the case of a positive μ parameter. In the chargino ter can strongly affect the structure of the theory and the μ< sector, the opposite signs of μ and M in this case lead to an experimental signatures, so that we consider both 0 and 2 μ> unavoided crossing of the mass eigenvalues at tan β ∼ 1, as 0. As upper bounds on the absolute values of the mass well as to an opposite behavior when increasing or decreasing parameters, we impose 5 TeV, which we only raise when we < tan β with respect to 1. For μ<0, gaugino-higgsino mix- see that our results cluster near them. Values of M2 0 and β< β ings and eletroweakino mass splittings indeed increase with tan 1 are obtained with sign flips and a tan inversion, tan β variations, whilst they decrease for μ>0. In addition, as explained in Sect. 2.2. The three dimensionful parameters μ mixed bino/wino-states are rare and can only be obtained by , M1 and M2 are finally further constrained by the require- fine-tuning the parameters due to the non-existence of any ments on the desired gaugino/higgsino decomposition. direct bino/wino coupling in the Lagrangian. Moreover, wino As an illustration of the above strategy, we search for states mix more easily with higgsino states than bino states benchmark scenarios featuring a spectrum where the lightest states are all higgsino-like. The range of μ can then be as the hypercharge and weak couplings satisfy gY < g2,or restricted by observing (cf. Sect. 2.3) that the masses of neu- equivalently as sin θW < cos θW . tralinos and charginos with a dominant higgsino contribution lie in the range |μ|±O (MW ). The scan ranges are thus given 3 Scan strategy by In this section, we first select a strategy to explore the param- |μ|∈ min(Mχ± )−O(MW ), max(Mχ± )+O(MW ) , 1 1 eter space of the MSSM gaugino/higgsino sector in an effi- | |∈ ( ± )−O( ), , cient way. We then define criteria for acceptable benchmark M1 min Mχ MW 5TeV 1 (22) points that fit best a pre-defined mass spectrum of light neu- M2 ∈ min(Mχ± )−O(MW ), 5TeV , tralinos and charginos and discuss how additional require- 1 ments, such as a large higgsino content of these sparticles, tan β ∈[1, 100] , 123 209 Page 8 of 16 Eur. Phys. J. C (2018) 78 :209 δ ± with 1 Mχ = ± − fit =: 1 , d1 Mχ Mχ± ΔMχ± 1 1 ΔMχ± 1 1 (μ) ∈{−, +} ( ) ∈{−, +}, ΔM δ(ΔM ) sign and sign M1 (23) = 2 21 − fit − fit =: 21 , d2 Mχ0 Mχ± Δ(ΔM21) 2 2 1 Δ(ΔM21) 2 ΔM21 δ (ΔM21) ( ± ) ( ± ) = − fit − fit =: . and where min Mχ and max Mχ represent the minimal d3 M ± M 0 1 1 Δ(Δ ) χ χ Δ(Δ ) and maximal desired values for the light chargino mass. M21 2 1 1 M21 It is easy to see that an equidistant scan in these param- (26) eters is not very efficient. For instance, variations at large = = = values of tan β only weakly affect the spectrum and the A perfect fit then has d1 d2 d3 0, while the penalty gaugino/higgsino decompositions, since these depend on score of a configuration with respect to its nearest neighbour sin β and cos β rather than tan β. Also, a scan over multi- grid point is given by ple orders of magnitude for the gaugino mass parameters does not efficiently cover masses in the lower ranges where d2 + d2 + d2 score = 1 2 3 (27) |M1|, |M2|∼|μ|, where the masses of the higgsino-like 3 neutralinos and charginos are affected the most. We there- √ fore reparameterise the prior distributions in M1, M2 and with 1/3 ∼ 0.58 for a nearest neighbour grid point with a tan β as single outlier. We consider a configuration acceptable if

score < 0.1, (28) M1 =±M 1 − , 2 which represents a reasonable compromise between scan = + , M2 M 1 (24) 2 time and accuracy: tan βmax √ tan β = tan β exp xβ ln min β δMχ± < 0.1 3ΔMχ± = 0.17ΔMχ± , tan min 1 1 1 δ( )(ΔM ) √ 21 < 0.1 3Δ(ΔM ) = 0.17Δ(ΔM ). (29) with 2 21 21 While this procedure allows us to find an approximately cor- Mmax rect chargino and neutralino mass spectrum, it still does not M = Mmin exp xM ln , Mmin maximise their average higgsino (or gaugino) content. This xM ∈ [0, 1] , (25) type of additional condition can be included by reweighting ∈ [−2, 2] , the score with xβ ∈ [0, 1] . ˜ fold < , scorenew scoreold (30) fnew In the expressions of Eqs. (24) and (25), the minimum and maximum values of tan β and M are dictated by the scan which balances accuracy of mass spectrum and decomposition for scores that are neither too small nor too large. In the range, with Mmin and Mmax referring both to M1 and M2.The case study of Sect. 4, f˜ represents the average higgsino con- scan time can be further reduced with an iterative procedure, ± tent of the light neutralinos χ 0, χ 0 and the light χ particles. where at each iteration the parameter range in |μ|, xM , , and 1 2 1 xβ is halved keeping the currently best parameters central. The total parameter space volume then shrinks each time by 3.3 Generalisation a factor of (1/2)4 = 1/16 with an additional factor of 1/2 The specific setup described above can be generalised by from the sign determination of M1 in the first iteration. modifying the desired mass spectrum of Eq. (21) to non- equidistant mass differences with the according adjustments 3.2 Benchmark selection in the conditions of Eq. (26). A qualitatively very distinct modification is the requirement of one-sided mass limits. The quality of our fit of the desired mass spectrum is param- Second, the maximisation of the higgsino content through eterised by the relative differences between the input masses the function f˜ and/or the reweighting condition in Eq. (30) and their fit values compared to the corresponding grid spac- can be replaced. A specific example would be the maximisa- ings ΔMχ± and Δ(ΔM21), tion of couplings to specific particles. In practice, a trial scan 1 123 Eur. Phys. J. C (2018) 78 :209 Page 9 of 16 209

Table 1 Targeted mass ranges, Mass/splitting Minimum (GeV) Maximum (GeV) Grid spacing (GeV) splittings and spacings for light higgsino-like neutralinos and Mχ± 90 400 3.1 charginos 1 ΔM21 1 100 1 often helps in defining more precisely acceptable configura- is inspired by the combined LEP limit of 92.4 GeV in the hig- tions and conditions that do not overly constrain the inter- gsino region for any lightest neutralino mass. This limit rises esting regions of parameter space. Scan ranges can often be to 103.5 GeV for mass splittings larger than 5 GeV [38,39]. guessed by using the observations made in Sect. 2.3. Repa- rameterisations as the one in Eq. (24) are moreover useful 4.2 Quality of the scan when scanning over multiple orders of magnitude in one or several parameters and can be optimised by studying the pos- The quality of our MSSM fits of these predefined desired terior distributions in the input parameters. scenarios can be evaluated in Fig. 3, where we show the distribution of scores defined in Eq. (27)forμ>0 (upper left) and μ<0 (upper right) as well as the average higgsino χ 0 χ 0 χ ± 4 Case study: Higgsino-like neutralinos and charginos contents of 1 , 2 and 1 (lower left and right, respectively). The size of the deviations between the targeted and In this section, we present a case study of a specific simpli- fitted physical masses can be deduced from the scores using fied MSSM model with a realistic neutralino-chargino sector, Eq. (29). whose general properties were discussed in Sect. 2. We then The score distributions in Fig. 3 indicate that in our spe- apply and test the parameter scan method presented in Sect. 3 cific case study, the mass splittings between light√ higgsinos and examine the properties of the underlying benchmark should not exceed MW for μ>0 and MZ · sW cW for points. Our case study has higgsino-like light neutralinos and μ<0. Large neutralino mass splittings ΔM21 mostly entail charginos with equidistant mass splitting and includes both higgsino contents of less than 70% and as low as ∼ 50% for signs of the higgsino mass parameter μ. the largest values of ΔM21. This result is nearly independent of the physical chargino mass Mχ± . 1 4.1 Definition of the simplified model In Fig. 4, we therefore show the higgsino content as a function of ΔM21 only for both μ>0 (blue crosses) and μ< As it is usually done in simplified models, we decouple the 0 (red diamonds). We find that it falls off quadratically sparticles that are not of direct relevance to our study, i.e. for mass splittings below roughly 25 GeV.For positive values μ squarks, gluinos, and non-SM Higgs particles, by setting their of , the fall-off then becomes linear beyond this value. masses to a sufficiently high value, here 1.5 TeV. Their phenomenological impact at the LHC is then negligible due to 4.3 MSSM scenarios limited kinematical phase space, suppressed virtual propaga- tors, and parton distribution functions that vanish at large par- In Fig. 5, we display the fitted MSSM parameters |μ| (a, ton momentum fractions. Decoupling sparticles with unreal- b), tan β (c, d), M1 (e, f) and M2 (g, h) for μ>0 and istically high mass values can result in numerical instabilities μ<0, respectively. Due to the limited sensitivity of the in the employed Monte Carlo generators, e.g. from miss- fit, the last three are shown logarithmically. In the following cancellations in higher-order corrections, and should be ing discussion of these figures, we focus on general trends, avoided. exceptional behaviour, and the amount of fine-tuning that is The targeted light neutralino and chargino mass spectra are necessary to reproduce the desired mass spectrum and hig- defined by a set of central light chargino masses Mχ± and gsino content. Statistically, fine-tuned models are unlikely to 1 correlated light neutralino masses that are split in an equidis- be realised in nature and are often taken as a hint for new, so tant way by ΔM21 (cf. Eq. (21)). Their ranges are constrained far poorly understood symmetries in physics. empirically through negative experimental searches for neu- The μ-parameter distributions found for μ<0 and μ> tralinos or charginos, whose masses must exceed the mass of 0 are shown in Fig. 5a, b, respectively. They confirm our 0 the Z -boson, and theoretically (cf. Sect. 2.3) to mass split- hypothesis that |μ| is mostly fixed by the chargino mass Mχ± . 1 tings of the two higgsino-like neutralinos that do not exceed The additional dependence on ΔM21 is characterised by 4 O(MW ). We therefore aim to fit the O(10 ) mass spectra in the ranges shown in Table 1 by scanning the parameter space ΔM21 as described in Sect. 3. The lower limit on the chargino mass |μ|=Mχ± + + μ MW , (31) 1 2 123 209 Page 10 of 16 Eur. Phys. J. C (2018) 78 :209

(a) score (μ>0) (b) score (μ<0)

0 0 ± Fig. 3 Scores and average higgsino contents of χ , χ and χ for the models found in our MSSM ﬁts of light chargino mass Mχ± and neutralino 1 2 1 1 mass splitting ΔM21. The dashed lines indicate that the latter are always smaller than O (MW ) (remember that MW = MZ cW )

where μ parameterises the deviations from these linear dependencies that are at most of O(MW ). For 95% of the models, μ lies within [−0.09, 0.08] for μ>0 and [−0.17, 0.0] for μ<0 with the largest deviations found in the region μ<0, ΔM21 20 GeV and Mχ± 170 GeV. 1 The two leading terms in Eq. (31) are thus accurate about 10 − 20 GeV. The tan β-parameter distributions found for μ<0 and μ>0 are shown in Fig. 5c, d, respectively. A general, though weak trend is that one obtains smaller tan β for larger ΔM21 for μ>0, but larger tan β for larger ΔM21 for μ<0. This corresponds to the opposite dependencies on tan β observed in the upper right parts of Figs. 1 and 2 in Sect. 2. The weak dependence of the spectrum for large values of tan β has been discussed before. As we can observe now, it appears in particular for μ<0orμ>0 and small ΔM , while the Fig. 4 Higgsino content as a function of ΔM21 for our ﬁt scenarios 21 with μ>0 (blue crosses) and μ<0 (red diamonds). In both cases allowed range of tan β becomes more limited for μ>0 and Δ < μ> it falls quadratically for M21 25 GeV. For 0, the fall-off is large neutralino mass splittings. linear beyond this value In Fig. 5e–h, the distributions of the gaugino mass parameters M1 and M2 are shown for both μ>0 and μ<0. The distributions of both parameters vary by almost two orders of

123 Eur. Phys. J. C (2018) 78 :209 Page 11 of 16 209

(a) |μ| (μ>0) (b) |μ| (μ<0)

(e) M1 (μ>0) (f) M1 (μ<0)

(g) M2 (μ>0) (h) M2 (μ<0)

Fig. 5 Fitted MSSM parameters |μ| (a, b), tan β (c, d), M1 (e, f)and masses below 92.4 GeV are excluded by LEP in the higgsino region M2 (g, h)forμ>0andμ<0, respectively. Due to the limited sen- for any lightest neutralino mass. This limit rises to 103.5 GeV for mass sitivity of the ﬁt, the last three are shown logarithmically. Chargino splittings larger than 5 GeV[38,39]

123 209 Page 12 of 16 Eur. Phys. J. C (2018) 78 :209

(a) ﬁne-tuning (μ>0) (b) ﬁne-tuning (μ<0)

Fig. 6 Upper figures: logarithmic representation of the fine-tuning ranges for μ>0(c)andμ<0(d). Chargino masses below 92.4 GeV level of simplified light higgsino models in terms of the relative accept- are excluded by LEP in the higgsino region for any lightest neutralino able ranges of the underlying MSSM parameters for μ>0(a)and mass. This limit rises to 103.5 GeV for mass splittings larger than 5 μ<0(b). Large negative numbers therefore indicate large fine-tuning. GeV [38,39] Lower figures: number of boundary violations of the initial parameter magnitude and roughly inversely to the neutralino mass split- region to identify the resulting light gaugino states as mixed ting ΔM12. We parameterise the fitted gaugino mass param- binos and higgsinos, allows for the approximate analytic eters M1 and M2 by diagonalization of the reduced three-dimensional neutralino mass matrix [40]. We already observed this increased mixing Δ 2 in Fig. 4, where the higgsino content fell linearly for sizeable M21 MW , = ± − + . M1 2 Mχ M1,2 (32) mass splittings ΔM21. 1 2 ΔM21 Models that reproduce similar physical masses or mixings, This expression does not reproduce the correlation of but originate from very different, sometimes isolated fundamental parameters, signal the presence of fine-tuning. We ΔM21 and tan β discussed above and is thus less accurate than our parameterisation of |μ| in Eq. (31). In quantify this fine-tuning by multiplying for each benchmark |μ| particular, the parameters , that parameterise devia- the variations of the fundamental parameters , M1, M2 M1,2 β tions from the two leading terms, lie in the large ranges and tan leading to acceptable scores (below 0.1) and then ∈[. , . ], [ . , . ] μ> ∈ dividing by the corresponding total ranges as defined in Eq. M1,2 0 18 0 82 1 26 2 42 for 0 and M1,2 [0.10, 3.05], [0.82, 1.43] for μ<0 and for 95% of the mod- (22). The result is shown in Fig. 6a, b for positive and negative μ els. This is due to the known fact that pure higgsinos, often values of , respectively. Due to the logarithmic representation, large negative numbers correspond to large fine-tuning. associated with M1,2 μ, have small mass splittings, so that the requested spectrum is not very sensitive to the exact It occurs more often for large mass splittings and/or positive values of μ confirming that conversely pure higgsino sce- values of the gaugino masses. The region of |μ|M1,but narios usually have small mass splittings and are then less M2 |μ|, known as the “well-tempered bino/higgsino” 123 Eur. Phys. J. C (2018) 78 :209 Page 13 of 16 209 sensitive to specific choices e.g. of M1, M2 or tan β. Further- for positive and negative values of μ, respectively. As is more, in some cases acceptable models also lie outside the well known, a light SM-like Higgs boson of mass 125 GeV parameter ranges given in Eq. (22). The number of such ini- requires in general a light stop with a mass below or around tial boundary violations is displayed in Fig. 6c, d, again for 1 TeV and a large stop mass splitting of at least 1 TeV. μ>0 and μ<0, respectively. As one can see, acceptable models in larger regions of the parameter space exist often 4.5 Implications on dark matter for (nearly) mass degenerate light neutralinos, where large M , allow for compressed higgsino mass spectra, and in the 1 2 An important motivation for supersymmetry is its predic- case μ<0, where tan β can be very large. tion of a classic WIMP (weakly interacting massive particle) dark matter candidate, the lightest neutralino. The 4.4 The Higgs-stop sector relic abundance of dark matter in the universe has been determined very precisely by the Planck collaboration to be The large MSSM parameter space allows one (at least at Pl 2 Ωχ h = 0.1199 ± 0.0027 [42]. We therefore compare the tree-level) to decouple squarks, gluinos and sleptons without relic density ΩMO predicted for light higgsino MSSM mod- any impact on the gaugino-higgsino sector. Care is, however, χ els by the public code micrOMEGAs [43] to the observed required for the decoupling of the higgs-stop sector due to one in Fig. 7a, b for μ>0 and μ<0. The main observation the large impact of stop radiative corrections on the mass here is the appearance of the χ 0χ 0 → W +W − threshold. of the observed SM-like Higgs boson, that has to match the 1 1 When this process is kinematically allowed, the annihilation measured value of 125 GeV.In the absence of stop mixing, the cross section of χ 0 increases, and therefore the dark matter squared CP-even and CP-odd neutral Higgs boson masses 1 relic abundance decreases. Close to (above) this threshold, are related to the top quark mass m and the stop mass m ˜ t t the cross section is sufficiently small to explain (at least par- through [41] tially) the measured dark matter relic abundance. In Fig. 7c, d we show the ratios of predicted direct detection cross sec- G m4 m2 2 + 2 = 2 + 2 + √3 F t t˜ , m 0 m 0 m 0 MZ ln (33) tions over the Xenon1T exclusion limits [44]. In the higgsino h H A 2π 2s2 m2 β t mass range of MZ to 400 GeV studied here, the cross sections predicted by micrOMEGAs decrease with the mass split- where G F is the Fermi constant. This entails ting from 10−6 to 10−11 pb. Since the Xenon1T experiment Xe1T −10 √ has recently reached a sensitivity of σχ ∼ 10 pb for 2π 2s2 2 2 β 2 − 2 WIMP masses of about 100 GeV, only cross sections below mt˜ mt exp 4 mh0 MZ (34) 3G F mt the black line and very small mass splittings are still allowed. However, since searches at the LHC and in direct detection ∈[ , ] for m H 0 m A0 or mt˜ 885 GeV 1330 GeV , as long experiments depend on different sets of assumptions, both are as tan β>2. The full additional parameter space for the complementary, and they should both be taken into account. Higgs-stop sector includes the squared off-diagonal Higgs In the dark matter context, the potential LHC constraints 2 mass parameter m12, the soft SUSY-breaking mass parame- on the considered models include both results from direct 2 2 ters m ˜ and m ˜ , and the trilinear coupling At , all taken to searches for supersymmetry and for dark matter in general, Q3 tR be real to avoid new sources of CP-violation. A scan over like when using monojet probes that are expected to be golden this additional parameter space for a given MSSM higgsino handles on compressed electroweakino spectra [45]. Models model with fixed μ and tan β and full stop mixing leads to a with light gravitinos imply, of course, a very different dark successful decoupling of the heavy Higgs bosons. The cor- matter phenomenology. responding regions in the CP-odd neutral Higgs mass and the physical stop masses are

∈[ , ] (μ > ), 5 Conclusion m A0 992 4386 GeV 0 m ˜ ∈[ , ] (μ > ), t1 752 1481 GeV 0 (35) Simpliﬁed SUSY models have become a popular tool for ˜ ∈[ , ] (μ > ), mt2 1607 2487 GeV 0 model-independent searches at the LHC. Recently, the LHC experiments ATLAS and CMS have also applied this and approach to light neutralinos and charginos with predeﬁned physical mass spectra and pure gaugino or higgsino content. ∈[ , ] (μ < ), m A0 1063 3925 GeV 0 We have emphasised in this paper that these models can vio- ˜ ∈[ , ] (μ < ), mt1 809 1212 GeV 0 (36) late physical principles such as supersymmetry, gauge invari- ˜ ∈[ , ] (μ < ). ance, or the consistent combination of production cross sec- mt2 1840 2413 GeV 0 123 209 Page 14 of 16 Eur. Phys. J. C (2018) 78 :209

MO Pl MO Pl (a) log10(Ωχ /Ωχ )(μ>0) (b) log10(Ωχ /Ωχ )(μ<0)

MO MO (c) log10(σχ )(μ>0) (d) log10(σχ )(μ<0)

Fig. 7 Upper figures: logarithmic ratio of predicted and observed relic sion limits for the direct detection of higgsino dark matter for μ>0 abundance of light higgsino dark matter for μ>0(a)andμ<0(b). (c)andμ<0(d) Lower figures: ratios of predicted cross sections and Xenon1T exclu- tions and decay branching ratios and that they must therefore led to viable scenarios. As expected, squarks, gluinos, and be embedded in full MSSM models, whose relevant four- sleptons could be decoupled to 1.5 TeV, as could the heavier dimensional parameter space is spanned by μ,tanβ, M1 and Higgs bosons without spoiling the reproduction of a SM- M2. like light Higgs boson of mass 125 GeV. The latter required, Exploiting the symmetries of the neutralino and chargino however, a light stop of mass below or around 1 TeV with its mass matrices, we diagonalised them and discussed the lead- heavier partner split by at least 1 TeV.The observed dark mat- ing and sub-leading dependencies of the resulting physical ter relic density could be reproduced close to the threshold of mass spectra and decompositions on these parameters. We neutralino annihilation into pairs of W-bosons, whereas for then devised an efficient scan strategy for the full parameter higher masses the higgsinos can only represent a fraction of space given a desired physical mass spectrum and introduced the observed dark matter. The corresponding direct detection a measure for the quality of our full MSSM reproduction of cross sections are within reach of current experiments such this spectrum, that could also include criteria such as a max- as Xenon1T. imal gaugino or higgsino component or couplings to specific While we have indicated how our strategy can be gener- sparticles. As a case study, we investigated the MSSM reali- alised to other scenarios such as those with non-equidistant sations of light higgsinos, finding an upper bound on the pos- mass splitting of the light neutralinos and chargino or those sible mass splitting among the lightest neutralinos of O(MW ) with specific couplings of gauginos, higgsinos and other spar- and a lower bound on the higgsino content of about 70%. We ticles, specific studies of these other scenarios are beyond the saw that large mass splittings required a more substantial scope of the present work and should be performed with a level of fine-tuning, whereas for small mass splittings even detailed application in mind. larger regions of parameter space than those scanned by us

123 Eur. Phys. J. C (2018) 78 :209 Page 15 of 16 209

Acknowledgements We thank W. Adam, C. Heidegger, B. Schneider 15. CMS Collaboration, A.M. Sirunyan et. al., Search for supersymme- and L. Shchutska for useful discussions. This work has been supported try in pp collisions at sqrt(s) = 13 TeV in the single-lepton final state by the ANR under contracts ANR-11-IDEX-0004-02 and ANR-10- using the sum of masses of large-radius jets. arXiv:1705.04673 LABX-63, the BMBF under contract 05H15PMCCA, the CNRS under 16. CMS Collaboration, A.M. Sirunyan et. al., Search for new phenom- contract PICS 150423, and the DFG through the Research Training ena with the MT2 variable in the all-hadronic final state produced Network 2149 “Strong and weak interactions – from hadrons to dark in proton-proton collisions at sqrt(s) = 13 TeV. arXiv:1705.04650 matter”. 17. CMS Collaboration, A.M. Sirunyan et. al., Search for supersymmetry in events with one lepton and multiple jets exploiting the angular Open Access This article is distributed under the terms of the Creative correlation between the lepton and√ the missing transverse momen- Commons Attribution 4.0 International License (http://creativecomm tum in proton-proton collisions at s = 13 TeV. arXiv:1709.09814 ons.org/licenses/by/4.0/), which permits unrestricted use, distribution, 18. CMS Collaboration, A.M. Sirunyan et. al., Search for physics and reproduction in any medium, provided you give appropriate credit beyond the standard model in events with two leptons of same to the original author(s) and the source, provide a link to the Creative sign, missing√ transverse momentum, and jets in proton–proton Commons license, and indicate if changes were made. collisions at s = 13 TeV. Eur. Phys. J. C 77(9), 578 (2017). Funded by SCOAP3. arXiv:1704.07323 19. CMS Collaboration, A.M. Sirunyan et. al., Search for supersymmetry in events with at least one photon, missing transverse momentum, and large transverse event activity in proton-proton collisions References at sqrt(s) = 13 TeV. arXiv:1707.06193 20. CMS Collaboration, A.M. Sirunyan et. al., Search for direct pro- 1. H.P. Nilles, Supersymmetry, supergravity and particle physics. duction of supersymmetric partners of the√ top quark in the all-jets Phys. Rep. 110, 1–162 (1984) final state in proton-proton collisions at s = 13 TeV. JHEP 10, 2. H.E. Haber, G.L. Kane, The search for supersymmetry: probing 005 (2017). arXiv:1707.03316 physics beyond the standard model. Phys. Rep. 117, 75–263 (1985) 21. CMS Collaboration, A.M. Sirunyan et. al., Search for the pair pro- 3. J. Alwall, M.-P. Le, M. Lisanti, J.G. Wacker, Model-independent duction of third-generation squarks with two-body decays to a bot- jets plus missing energy searches. Phys. Rev. D 79, 015005 (2009). tom or charm quark and a neutralino in proton-proton collisions at arXiv:0809.3264 sqrt(s) = 13 TeV. arXiv:1707.07274 4. J. Alwall, P. Schuster, N. Toro, Simplified models for a first char- 22. CMS Collaboration, A.M. Sirunyan√ et. al., Search for top squark acterization of new physics at the LHC. Phys. Rev. D 79, 075020 pair production in pp collisions at s = 13 TeV using single lepton (2009). arXiv:0810.3921 events. JHEP 10, 019 (2017). arXiv:1706.04402 5. LHC New Physics Working Group Collaboration, D. Alves, Sim- 23. CMS Collaboration, A.M. Sirunyan et. al., Search for new phenom- plified models for LHC new physics searches. J. Phys. G 39, 105005 ena in final states with two opposite-charge, same-flavor leptons,√ (2012). arXiv:1105.2838 jets, and missing transverse momentum in pp collisions at s = 6. L. Calibbi, J.M. Lindert, T. Ota, Y. Takanishi, LHC tests of light 13 TeV. arXiv:1709.08908 neutralino dark matter without light sfermions. JHEP 11, 106 24. ATLAS Collaboration, M. Aaboud et. al.,√ Search for the direct pro- (2014). arXiv:1410.5730 duction of charginos and neutralinos in s = 13 TeV pp collisions 7. ATLASCollaboration, M. Aaboud et. al., Search for a scalar partner with the ATLAS detector. arXiv:1708.07875 of the top√ quark in the jets plus missing transverse momentum final 25. CMS Collaboration, A.M. Sirunyan et. al., Search for electroweak state at s=13 TeV with the ATLAS detector. arXiv:1709.04183 production of charginos and neutralinos√ in multilepton final states 8. ATLAS Collaboration, M. Aaboud et. al., Search for supersym- in proton-proton collisions at s = 13 TeV. arXiv:1709.05406 metryineventswithb-tagged√ jets and missing transverse momen- 26. CMS Collaboration, A.M. Sirunyan√ et. al., Search for higgsino pair tum in pp collisions at s = 13 TeV with the ATLAS detector. production in pp collisions at s = 13 TeV in final states with large arXiv:1708.09266 missing transverse momentum and two Higgs bosons decaying via 9. ATLAS Collaboration, M. Aaboud et. al., Search for squarks H → bb. arXiv:1709.04896 and gluinos in events with√ an isolated lepton, jets and missing 27. A. Bharucha, S. Heinemeyer, F. Pahlen von der, Direct chargino- transverse momentum at s = 13 TeV with the ATLAS detector, neutralino production at the LHC: interpreting the exclusion lim- arXiv:1708.08232 its in the complex MSSM. Eur. Phys. J. C 73(11), 2629 (2013). 10. ATLAS Collaboration, M. Aaboud et. al., Search for direct√ top arXiv:1307.4237 squark pair production in final states with two leptons in s = 13 28. ATLAS Collaboration, M. Aaboud et. al., Search for electroweak TeV pp collisions with the ATLAS detector. arXiv:1708.03247 production of supersymmetric√ states in scenarios with compressed 11. ATLAS Collaboration, M. Aaboud et. al., Search for supersym- mass spectra at s = 13 TeV with the ATLAS detector. metryinfinalstateswithtwosame-signorthreeleptonsandjets√ arXiv:1712.08119 using36fb−1 of s = 13 TeV pp collision data with the ATLAS 29. CMS Collaboration, A.M. Sirunyan et. al., Search for new physics detector. JHEP 09, 084 (2017). arXiv:1706.03731 in events with two soft oppositely charged leptons√ and missing 12. ATLAS Collaboration, M. Aaboud et. al., Search for direct top transverse momentum in proton-proton collisions at s = 13 TeV. squark pair production in events√ with a Higgs or Z boson, and arXiv:1801.01846 missing transverse momentum in s = 13 TeV pp collisions with 30. M. Dine, W. Fischler, A phenomenological model of particle the ATLAS detector. JHEP 08, 006 (2017). arXiv:1706.03986 physics based on supersymmetry. Phys. Lett. 110B, 227–231 13. ATLAS Collaboration, M. Aaboud et. al., Search for new phenom- (1982) ena with large jet multiplicities and missing transverse momentum 31. C.R. Nappi, B.A. Ovrut, Supersymmetric extension of the SU(3) x using large-radius jets and flavour-tagging at ATLAS in 13 TeV pp SU(2) x U(1) model. Phys. Lett. 113B, 175–179 (1982) collisions. arXiv:1708.02794 32. L. Alvarez-Gaume, M. Claudson, M.B. Wise, Low-energy super- 14. CMS Collaboration, A.M. Sirunyan et. al., Search for supersymme- symmetry. Nucl. Phys. B 207, 96 (1982) try in multijet events with missing transverse momentum in proton- 33. M. Dine, A.E. Nelson, Dynamical supersymmetry break- proton collisions at 13 TeV. Phys. Rev. D 96(3), 032003 (2017). ing at low-energies. Phys. Rev. D 48, 1277–1287 (1993). arXiv:1704.07781 arXiv:hep-ph/9303230 123 209 Page 16 of 16 Eur. Phys. J. C (2018) 78 :209

34. M. Dine, A.E. Nelson, Y. Shirman, Low-energy dynamical super- 40. N. Arkani-Hamed, A. Delgado, G.F. Giudice, The well- symmetry breaking simpliﬁed. Phys. Rev. D 51, 1362–1370 (1995). tempered neutralino. Nucl. Phys. B 741, 108–130 (2006). arXiv:hep-ph/9408384 arXiv:hep-ph/0601041 35. M. Dine, A.E. Nelson, Y.Nir, Y.Shirman, New tools for low-energy 41. M. Drees, R. Godbole, P. Roy, Theory and phenomenology of Spar- dynamical supersymmetry breaking. Phys. Rev. D 53, 2658–2669 ticles: an account of four-dimensional N=1 supersymmetry in high- (1996). arXiv:hep-ph/9507378 energy physics (World Scientiﬁc, Singapore, 2004) 36. G.F. Giudice, R. Rattazzi, Theories with gauge mediated 42. Planck Collaboration, P.A.R. Ade, N. Aghanim, C. Armitage- supersymmetry breaking. Phys. Rep. 322, 419–499 (1999). Caplan, M. Arnaud, M. Ashdown, F. Atrio-Barandela, J. Aumont, arXiv:hep-ph/9801271 C. Baccigalupi, B. et al., Planck 2013 results. XVI. Cosmological 37. J.L. Kneur, G. Moultaka, Inverting the supersymmetric standard parameters. A& A 571, A16 (2014). arXiv:1303.5076 model spectrum: from physical to Lagrangian gaugino parameters. 43. D. Barducci, G. Belanger, J. Bernon, F. Boudjema, J. Da Silva, S. Phys. Rev. D 59, 015005 (1999). arXiv:hep-ph/9807336 Kraml, U. Laa, A. Pukhov, Collider limits on new physics within 38. LEP2 SUSY Working Group Collaboration, Combined lep micrOMEGAs4.3. arXiv:1606.03834 chargino results up to 208 gev for low dm (2002). http:// 44. XENON Collaboration, E. Aprile et. al., First Dark Matter Search lepsusy.web.cern.ch/lepsusy/www/inoslowdmsummer02/ Results from the XENON1T Experiment. arXiv:1705.06655 charginolowdm_pub.html 45. P. Schwaller, J. Zurita, Compressed electroweakino spectra at the 39. Particle Data Group Collaboration, K.A. Olive et. al., Review of LHC. JHEP 03, 060 (2014). arXiv:1312.7350 particle physics. Chin. Phys. C 38, 090001 (2014)

123