Constraining Electroweakinos in the Minimal Dirac Gaugino Model

Supersymmetric models with Dirac instead of Majorana gaugino masses have distinct phenomenological consequences. In this paper, we investigate the electroweakino sector of the Minimal Dirac Gaugino Supersymmetric Standard Model (MDGSSM) with regards to dark matter (DM) and collider constraints. We delineate the parameter space where the lightest neutralino of the MDGSSM is a viable DM candidate, that makes for at least part of the observed relic abundance while evading constraints from DM direct detection, LEP and lowenergy data, and LHC Higgs measurements. The collider phenomenology of the thus emerging scenarios is characterised by the richer electroweakino spectrum as compared to the Minimal Supersymmetric Standard Model (MSSM) -- 6 neutralinos and 3 charginos instead of 4 and 2 in the MSSM, naturally small mass splittings, and the frequent presence of long-lived particles, both charginos and/or neutralinos. Reinterpreting ATLAS and CMS analyses with the help of SModelS and MadAnalysis 5, we discuss the sensitivity of existing LHC searches for new physics to these scenarios and show which cases can be constrained and which escape detection. Finally, we propose a set of benchmark points which can be useful for further studies, designing dedicated experimental analyses and/or investigating the potential of future experiments.


Introduction
The lightest neutralino [1][2][3] in supersymmetric models with conserved R-parity has been the prototype for particle dark matter (DM) for decades, motivating a multitude of phenomenological studies regarding both astrophysical properties and collider signatures. The ever tightening experimental constraints, in particular from the null results in direct DM detection experiments, are however severely challenging many of the most popular realisations. This is in particular true for the so-called well-tempered neutralino [4] of the Minimal Supersymmetric Standard Model (MSSM), which has been pushed into blind spots [5] of direct DM detection. One sub-TeV scenario that survives in the MSSM is bino-wino DM [6][7][8][9], whose discovery is, however, very difficult experimentally [10][11][12].
It is thus interesting to investigate neutralino DM beyond the MSSM. While a large literature exists on this topic, most of it concentrates on models where the neutralinos -or gauginos in general -have Majorana soft masses. Models with Dirac gauginos (DG) have received much less attention, despite excellent theoretical and phenomenological motivations . The phenomenology of neutralinos and charginos ("electroweakinos" or "EW-inos") in DG models is indeed quite different from that of the MSSM. The aim of this work is therefore to provide up-to-date constraints on this sector for a specific realisation of DGs, within the context of the Minimal Dirac Gaugino Supersymmetric Standard Model (MDGSSM) The colourful states in DG models can be easily looked for at the LHC, even if they are "supersafe" compared to the MSSM -see e.g. [47,58,[60][61][62][63][64][65][66][67][68]. The properties of the Higgs sector have been well studied, and also point to the colourful states being heavy [38,56,59,[69][70][71]. However, currently there is no reason that the electroweak fermions must be heavy, and so far the only real contsraints on them have been through DM studies. Therefore we shall begin by revisiting neutralino DM, previously examined in detail in [72] (see also [73,74]), which we update in this work. We will focus on the EW-ino sector, considering the lightest neutralinõ χ 0 1 as the Lightest Supersymmetric Particle (LSP), and look for scenarios where theχ 0 1 is a good DM candidate in agreement with relic density and direct detection constraints. In this, we assume that all other new particles apart from the EW-inos are heavy and play no role in the phenomenological considerations.
While the measurement of the DM abundance and limits on its interactions with nucleii have been improved since previous analyses of the model, our major new contribution shall be the examination of up-to-date LHC constraints, in view of DM-collider complementarity. For example, certain collider searches are optimal for scenarios that can only over-populate the relic density of dark matter in the universe, so by considering both together we obtain a more complete picture.
Owing to the additional singlet, triplet and octet chiral superfields necessary for introducing DG masses, the EW-ino sector of the MDGSSM comprises six neutralinos and three charginos, as compared to four and two, respectively, in the MSSM. More concretely, one obtains pairs of bino-like, wino-like and higgsino-like neutralinos, with small mass splittings within the bino (wino) pairs induced by the couplings λ S (λ T ) between the singlet (triplet) fermions with the Higgs and higgsino fields. As we recently pointed out in [66], this can potentially lead to a long-livedχ 0 2 due to a small splitting between the bino-like states. Moreover, as we will see, one may also have long-livedχ The results of our study are presented in section 4. We first delineate the viable parameter space where the lightest neutralino of the MDGSSM is at least part of the DM of the universe, and then discuss consequences for collider phenomenology. Re-interpreting ATLAS and CMS searches for new physics, we characterise the scenarios that are excluded and those that escape detection at the LHC. In addition, we give a comparison of the applicability of a simplified models approach to the limits obtained with a full recasting. We also briefly comment on the prospects of the MATHUSLA experiment. In section 5 we then propose a set of benchmark points for further studies. A summary and conclusions are given in section 6.
The appendices contain additional details on the implementation of the parameter scan of the EW-ino sector (appendix A.2), and on the identification of parameter space wherein lie experimentally acceptable values of the Higgs mass (appendix A.3). Finally, in appendix A.4, we provide some details on the reinterpretation of a 139 fb −1 EW-ino search from ATLAS, which we developed for this study.

Classes of models
Models with Dirac gaugino masses differ in the choice of fields that are added to extend those of the MSSM, and also in the treatment of the R-symmetry. Both of these have significant consequences for the scalar ("Higgs") and EW-ino sectors. In this work, we shall focus on constraints on the EW-ino sector in the MDGSSM. Therefore, to understand the potential generality of our results, we shall here summarise the different choices that can be made in other models, before giving the details for ours.
To introduce Dirac masses for the gauginos, we need to add a Weyl fermion in the adjoint representation of each gauge group; these are embedded in chiral superfields S, T, O which are respectively a singlet, triplet and octet, and carry zero R-charge. Some model variants neglect a field for one or more gauge groups, see e.g. [28,75]; limits for those cases will therefore be very different.
The Dirac mass terms are written by the supersoft [16] operators where W iα are the supersymmetric gauge field strengths. It is possible to add Dirac gaugino masses through other operators, but this leads to a hard breaking of supersymmetry unless the singlet field is omitted -see e.g. [55]. On the other hand, whether we add supersoft operators or not, the difference appears in the scalar sector (the above operators lead to scalar trilinear terms proportional to the Dirac mass), so would not make a large difference to our results. There are then two classes of Dirac gaugino models: ones for which the R-symmetry is conserved, and those for which it is violated. If it is conserved, with the canonical example being the MRSSM, then since the gauginos all carry R-charge, the EW-inos must be exactly Dirac fermions. For a concise review of the EW sector of the MRSSM see [50]    that we discuss later. However, in that class of models the phenomenology is different to that described here. The second major class of models is those for which the R-symmetry is violated. This includes the minimal choices in terms of numbers of additional fields -the SOHDM [28], "MSSM without µ term" [76] and MDGSSM, as well as extensions with more fields, e.g. to allow unification of the gauge couplings, such as the CMDGSSM [69,74]. The constraints on the EW-ino sectors of these models should be broadly similar. Crucially in these models -in contrast to those where the EW-inos are exactly Dirac -the neutralinos are pseudo-Dirac Majorana fermions. This means that they come in pairs with a small mass splitting, in particular between the neutral partner of a bino or wino LSP and the LSP itself. This has significant consequences for dark matter in the model, as has already been explored in e.g. [72,74]: coannihilation occurs naturally. However, we shall also see here that it has significant consequences for the collider constraints: the decays fromχ 0 2 toχ 0 1 are generally soft and hard to observe, and lead to a long-lived particle in some of the parameter space.

Electroweakinos in the MDGSSM
Here we shall summarise the important features of the EW-ino sector of the MDGSSM. Our notation and definitions are essentially identical to [72], to which we refer the reader for a more complete treatment.
The MDGSSM can be defined as the minimal extension of the MSSM allowing for Dirac gaugino masses. We add one adjoint chiral superfield for each gauge group, and nothing else: the field content is summarised in Table 1. We also assume that there is an underlying R-symmetry that prevents R-symmetry-violating couplings in the superpotential and supersymmetry-breaking sector, except for an explicit breaking in the Higgs sector through a (small) B µ term. This was suggested in the "MSSM without µ-term" [76] as such a term naturally has a special origin through gravity mediation; it is also stable under renormalisation group evolution, as the B µ term does not induce other R-symmetry violating terms.
The singlet and triplet fields can have new superpotential couplings with the Higgs, These new couplings may or may not have an underlying motivation from N = 2 supersymmetry, which has been explored in detail [59]. After electroweak symmetry breaking (EWSB), we obtain 6 neutralino and 3 chargino mass eigenstates (as compared to 4 and 2, respectively, in the MSSM). The neutralino mass matrix M N in the basis where s W = sin θ W , s β = sin β and c β = cos β; tan β = v u /v d is the ratio of the Higgs vevs; m DY and m D2 are the 'bino' and 'wino' Dirac mass parameters; µ is the higgsino mass term, and λ S and λ T are the couplings between the singlet and triplet fermions with the Higgs and higgsino fields. By diagonalising eq. (3), one obtains pairs of bino-like, wino-like and higgsinolike neutralinos, 1 with small mass splittings within the bino or wino pairs induced by λ S or λ T , respectively. For instance, if m DY is sufficiently smaller than m D2 and µ, we find mostly bino/U(1) adjointχ 0 1,2 as the lightest states with a mass splitting given by Alternative approximate formulae for the mass-splitting in other cases were also given in [72].
Turning to the charged EW-inos, the chargino mass matrix in the basis v This can give a higgsino-likeχ ± as in the MSSM, but we now have two wino-likeχ ± -the latter ones again with a small splitting driven by λ T . A wino LSP therefore consists of a set of two neutral Majorana fermions and two Dirac charginos, all with similar masses.
Note that in both eqs. (3) and (5), Majorana mass terms are absent, since we assume that the only source of R-symmetry breaking in the model is the B µ term. If we were to add Majorana masses for the gauginos, or supersymmetric masses for the singlet/triplet fields, then they would appear as diagonal terms in the above matrices (see e.g. [72] for the neutralino and chargino mass matrices with such terms included), and would generically lead to larger splitting of the pseudo-Dirac states.

Parameter scan
We now turn to the numerical analysis. Focusing solely on the EW-ino sector, the parameter space we consider is: The rest of the sparticle content of the MDGSSM is assumed to be heavy, with slepton masses fixed at 2 TeV, soft masses of the 1st/2nd and 3rd generation squarks set to 3 TeV and 3.5 TeV, respectively, and gluino masses set to 4 TeV. The rest of parameters are set to the same values as in [66]; in particular trilinear A-terms are set to zero. The mass spectrum and branching ratios are computed with SPheno v4.0.3 [77,78], using the DiracGauginos model [79] exported from SARAH [80][81][82][83]. This is interfaced to mi-crOMEGAs v5.2 [84][85][86] 2 for the computation of the relic density, direct detection limits and other constraints explained below. To efficiently scan over the EW-ino parameters, eq. (6), we implemented a Markov Chain Monte Carlo (MCMC) Metropolis-Hastings algorithm that walks towards the minimum of the negative log-likelihood function, − log(L), defined as Here, • χ 2 Ωh 2 is the χ 2 -test of the computed neutralino relic density compared to the observed relic density, Ωh 2 Planck = 0.12 [87]. In a first scan, this is implemented as an upper bound only, that is • p X1T is the p-value for the parameter point being excluded by XENON1T results [88]. The confidence level (CL) being given by 1 − p X1T , a value of p X1T = 0.1 (0.05) corresponds to 90% (95%) CL exclusion. To compute p X1T , the LSP-nucleon scattering cross sections are rescaled by a factor Ωh 2 /Ωh 2 Planck .
• m LSP is the mass of the neutralino LSP, added to avoid the potential curse of dimensionality. 3 In order to explore the whole parameter space, a small jump probability is introduced which prevents the scan from getting stuck in local minima of − log(L). We ran several Markov Chains from different, randomly drawn starting points; the algorithm is outlined step-by-step in Appendix A.2.
2 More precisely, we used a private pre-release version of micrOMEGAs v5.2, which does however give the same results as the official release. 3 Due to the exponential increase in the volume of the parameter space, one risks having too many points with an m LSP at the TeV scale. Current LHC searches are not sensitive to such heavy EW-inos.
The light Higgs mass, m h , also depends on the input parameters, and it is thus important to find the subset of the parameter space where it agrees with the experimentally measured value. Instead of including m h in the likelihood function, eq. (7), that guides the MCMC scan, we implemented a Random Forest Classifier that predicts whether a given input point has m h within a specific target range. As the desired range we take 120 < m h < 130 GeV, assuming m h ≃ 125 GeV can then always be achieved by tuning parameters in the stop sector. Points outside 120 < m h < 130 GeV are discarded. This significantly speeds up the scan. Details on the Higgs mass classifier are given in Appendix A.3.
In the various MCMC runs we kept for further analysis all points scanned over, which With the procedure outlined above, many points with very light LSP, in the mass range below m h /2 and even below m Z /2, are retained. We therefore added two more constraints a posteriori. Namely, we require for valid points that 6. ∆ρ lies within 3σ of the measured value ∆ρ exp = (3.9 ± 1.9) × 10 −4 [89], the 3σ range being chosen in order to include the SM value of ∆ρ = 0; 7. signal-strength constraints from the SM-like Higgs boson as computed with Lilith-2 [90] give a p-value of p Lilith > 0.05; this eliminates in particular points in which m LSP < m h /2, where the branching ratio of the SM-like Higgs boson into neutralinos or charginos is too large.
Points which do not fulfil these conditions are discarded. We thus collect in total 52550 scan points, which fulfil all constraints, as the basis for our phenomenological analysis.

Treatment of electroweakino decays
As argued above and will become apparent in the next section, many of the interesting scenarios in the MDGSSM feature the second neutralino and/or the lightest chargino very close in mass to the LSP. With mass splittings of O(1) GeV,χ decays intoχ 0,± 1 + γ become important. These decays were in the first case not implemented, and in the second not treated correctly in the standard SPheno/SARAH. We therefore describe below how these decays are computed in our analysis; the corresponding modified code is available online [91]. 4 Note that the precise calculation of the chargino and neutralino decays is important not only for the collider signatures (influencing branching ratios and decay lengths), but can also impact the DM relic abundance and/or direct detection cross sections. 4 We leave the decaysχ 0 i toχ ± j + pion(s) to future work.

Chargino decays into pions
When the mass splitting between chargino and lightest neutralino becomes sufficiently small, three-body decays via an off-shell W -boson,χ * start to dominate. However, when ∆m ≲ 1.5 GeV it is not accurate to describe the W * decays in terms of quarks, but instead we should treat the final states as one, two or three pions (with Kaon final states being Cabibbo-suppressed); and for ∆m < m π the hadronic channel is closed. Surprisingly, these decays have not previously been fully implemented in spectrum generators; SPheno contains only decays to single pions from neutralinos or charginos in the MSSM via an off-shell W or Z boson, and SARAH does not currently include even these. A full generic calculation of decays with mesons as final states for both charged and neutral EW-inos (and its implementation in SARAH) should be presented elsewhere; for this work we have adapted the results of [92][93][94] which include only the decay via an off-shell W: Herem − ,m 0 are the masses of theχ The couplings of the W-boson to the light quarks and the W mass are encoded in G F ; in SARAH we make the substitution is the coupling of the up and down quarks to the W-boson.
While the single pion decay can be simply understood in terms of the overlap of the axial current with the pion, the two-and three-pion decays proceed via exchange of virtual mesons which then decay to pions. The form factors for these processes are then determined by QCD, and so working at leading order in the electroweak couplings we can use experimental data for processes involving the same final states; in this case we can use τ meson decays. The two-pion decays are dominated by ρ and ρ ′ meson exchange, and the form factor F (q 2 ) was defined in eqs. (A3) and (A4) of [93]. The expressions for the Breit-Wigner propagator BW a of the a 1 meson (and not the a 2 meson as stated in [92][93][94]), which dominates 3π production, as well as for the three-pion phase space factor g(q 2 ) can be found in eqs. (3.16)-(3.18) of [95].
As in [92][93][94] we use the propagator without "dispersive correction," and so include a factor of  1.35 to compensate for the underestimate of τ − → 3πν τ decays by 35%. Note finally that the three-pion decay includes both π − π 0 π 0 and π − π − π + modes, which are assumed to be equal. In Figure 1 we compare our results to those of [92][93][94]  neutralinos, which can be easily tuned in mass relative to each other by changing the bino mass.
In Figure 2 we show the equivalent expressions in the case of interest for this paper, where there are no Majorana masses for the gauginos. We take tan β = 34.664, µ = 2 TeV, v T = −0.568 GeV, v S = 0.92 GeV, λ S = −0.2, 2λ T = 0.2687, m D2 = 200 GeV, and vary m DY between 210 and 221 GeV. We find identical behaviour for both models, except the overall decay rate is slightly different; and note that in this scenario we haveχ 0 2 almost degenerate withχ 0 1 , so we include decays ofχ ± 1 to both states of the pseudo-Dirac LSP. Finally, we implemented the decays of neutralinos to single pions via the expression where nowm 1,2 are the masses ofχ 0 1,2 and c L , c R are the couplings for the neutralinos to the Z-boson analogously defined as above; since the neutralino is Majorana in nature we must have c R = −c * L .

Neutralino decays into photons
In the MDGSSM, the mass splitting between the two lightest neutralinos is naturally small. 5 Therefore in a significant part of the parameter space the dominantχ 0 2 decay mode is the loop-induced processχ 0 2 →χ 0 1 + γ. This is controlled by an effective operator where is a Majorana spinor, and yields Our expectation (and indeed as we find for most of our points) is that |C 12 | ∼ 10 −5 -10 −6 GeV −1 . This loop decay process is calculated in SPheno/SARAH using the routines described in [96]. However, we found that the handling of fermionic two-body decays involving photons or gluons was not correctly handled in the spin structure summation. Suppose we have S-matrix elements M for a decay F (p 1 ) → F (p 2 ) + V (p 3 ) with a vector having wavefunction ε µ , then we can decompose the amplitudes according to their Lorentz structures (putting v i for the antifermion wavefunctions) as This is the decomposition made in SARAH which computes the values of the amplitudes {x i }. Now, if V is massless, and since M is an S-matrix element, the Ward identity requires (p 3 ) µ M µ = 0 (note that this requires that we include self-energy diagrams in the case of charged fermions), and this leads to two equations relating the {x i }: Here, m 1 and m 2 are the masses of the first and second fermion, respectively. Performing the spin and polarisation sums naively, we have the matrix spins, polarisations When we substitute in the Ward identities and re-express as just x 1 , x 2 we have spins, polarisations This matrix will yield real, positive-definite widths for any value of the matrix elements x 1 , x 2 , whereas this is not manifestly true for eq. (17). Therefore as of SARAH version 4.14.3 we implemented the spin summation for loop decay matrix elements given in eq. (18), i.e. in such decays we compute the Lorentz structures corresponding to x 1 , x 2 and ignore x 3 , x 4 . This applies to allχ

Properties of viable scan points
We are now in the position to discuss the results from the MCMC scans. We begin by considering the properties of theχ 0 1 as a DM candidate. Figure 3(a) shows the bino, wino and higgsino composition of theχ 0 1 when only an upper bound on Ωh 2 is imposed; all points in the plot also satisfy XENON1T (p X1T > 0.1) and all other constraints listed in section 3.1. We see that cases where theχ 0 1 is a mixture of all states (bino, wino and higgsino) are excluded, while cases where it is a mixture of only two states, with one component being dominant, can satisfy all constraints. Also noteworthy is that there are plenty of points in the low-mass region, m LSP < 400 GeV. Figure 3(b) shows the points where theχ 0 1 makes for all the DM abundance. This, of course, imposes much stronger constraints. In general, scenarios with strong admixtures of two or more EW-ino states are excluded and the valid points are confined to the corners of (almost) pure bino, wino or higgsino. Similar to the MSSM, the higgsino and especially the wino DM cases are heavy, with masses ≳ 1 TeV, and only about a 5% admixture of another interaction eigenstate; in the wino case, the MCMC scan gave only one surviving point within the parameter ranges scanned over. Light masses are found only for bino-like DM; in this case there can also be slightly larger admixtures of another state: concretely we find up to about 10% wino or up to 35% higgsino components.  As mentioned, we assume that all other sparticles besides the EW-inos are heavy. Hence, co-annihilations of EW-inos which are close in mass to the LSP must be the dominating processes to achieve Ωh 2 of the order of 0.1 or below. The relation between mass, bino/wino/higgsino nature of the LSP, relic density and mass difference to the next-to-lightest sparticle (NLSP) is illustrated in Figure 4. The three panels of this figure show m LSP vs. Ωh 2 for the points from Figure 3(a), where the LSP is > 50% bino, wino, or higgsino, respectively. The NLSP-LSP mass difference is shown in colour, while different symbols denote neutral and charged NLSPs. Two things are apparent besides the dependence of Ωh 2 on mχ0 1 for the different scenarios: 1. All three cases feature small NLSP-LSP mass differences. For a wino-like LSP, this mass difference is at most 3 GeV. For bino-like and higgsino-like LSPs it can go up to nearly 25 GeV, though for most points it is just few GeV.
2. The NLSP can be neutral or charged, that is in all three cases we can have mass orderings χ For bino-like LSP points outside the Z and Higgs-funnel regions, a small mass difference between the LSP and NLSP is however not sufficient-co-annihilations with other nearby states are required to achieve Ωh 2 ≤ 0.132. Indeed, as shown in Figure 5, we have m D2 ≈ m DY , with typically m D2 /m DY ≈ 0.9-1.4, over much of the bino-LSP parameter space outside the funnel regions. This leads to bino-wino co-annihilation scenarios like also found in the MSSM. The scattered points with large ratios m D2 /m DY have µ ≈ m DY , i.e. a triplet of higgsinos close to the binos. Outside the funnel regions, the bino-like LSP points therefore feature mχ ± 1 − mχ0 1 ≲ 30 GeV and mχ0 3,4 − mχ0 1 ≲ 60 GeV in addition to mχ0 2 − mχ0 1 ≲ 20 GeV. For completeness we also give the maximal mass differences found within triplets (quadruplets) of higgsino (wino) states in the higgsino (wino) LSP scenarios. Concretely we have mχ0 2 − mχ0 1 ≲ 15 GeV and mχ ± 1 − mχ0 1 ≲ 50-10 GeV (decreasing with increasing mχ0 1 ) in the (a) LSP more than 50% bino. (b) LSP more than 50% wino.
(c) LSP more than 50% higgsino. higgsino LSP case. In the wino LSP case, GeV (though mostly below 10 GeV). However, as noted before, either mass ordering, mχ0 2 < mχ ± 1 or mχ ± 1 < mχ0 2 is possible. An important point to note is that the mass differences are often so small that the NLSP (and sometimes even the NNLSP) becomes long-lived on collider scales, i.e. it has a potentially visible decay length of cτ > 1 mm. This is illustrated in Figure 6, which shows in the left panel the mean decay length of the LLPs as function of their mass difference to the LSP. Longlived charginos will lead to charged tracks in the detector, while long-lived neutralinos could potentially lead to displaced vertices. However, given the small mass differences involved, the decay products of the latter will be very soft. The right panel in Figure 6 shows the importance of the radiative decay of long-livedχ    From the collider point of view, the bino-like DM region is perhaps the most interesting one, as it has masses below a TeV. We find that, in this case, the NLSP is always theχ 0 2 with mass differences mχ0 2 − mχ0 1 ranging from about 0.2 GeV to 16 GeV. As already pointed in [72,73], this small mass splitting helps achieve the correct relic density throughχ   . This is shown explicitly in the right panel of the same figure. Concretely, we have mχ ± 1 − mχ0 1 ≲ 30 GeV and mχ0 3,4 − mχ0 1 ≈ 10-60 GeV. Often, that is when the LSP has a small wino admixture, theχ ± 2 is also close in mass. In most cases mχ ± 1 < mχ0 3 although the opposite case also occurs. All in all this creates peculiar compressed EW-ino spectra; they are similar to the bino-wino DM scenario in the MSSM, but there are LT/ 2 in SARAH convention. scattering cross sections on protons, with the p-value from XENON1T indicated in colour. While the bulk of the points has cross sections that should be testable in future DM direct detection experiments, there are also a few points with cross sections below the neutrino floor. We note in passing that the scattering cross section on neutrons (not shown) is not exactly the same in this model but can differ from that on protons by few percent.

LHC constraints
Let us now turn to the question of how the DG EW-ino scenarios from the previous subsection can be constrained at the LHC. Before reinterpreting various ATLAS and CMS SUSY searches, it is important to point out that the cross sections for EW-ino production are larger in the MDGSSM than in the MSSM. For illustration, Figure 9 compares the production cross sections for pp collisions at 13 TeV in the two models. The cross sections are shown as a function of the wino mass parameter, with m D2 = 1.2 m DY (M 2 = 1.2 M 1 ) for the MDGSSM (MSSM); the other parameters are µ ≃ 1400 GeV, tan β ≃ 10, λ S ≃ −0.29 and 2λ T ≃ −1.40. While LSP-LSP production is almost the same in the two models, chargino-neutralino and charginochargino production is about a factor 3-5 larger in the MDGSSM, due to the larger number of degrees of freedom.

Constraints from prompt searches SModelS
We start by checking the constraints from searches for promptly decaying new particles with SModelS [97][98][99][100]. The working principle of SModelS is to decompose all signatures occurring in a given model or scenario into simplified model topologies, also referred to as simplified model spectra (SMS). Each SMS is defined by the masses of the BSM states, the vertex structure, and the SM and BSM final states. After this decomposition, the signal weights, determined in terms of cross-sections times branching ratios, σ × BR, are matched against a database of LHC results. SModelS reports its results in the form of r-values, defined as the ratio of the theory prediction over the observed upper limit, for each experimental constraint that is matched in the database. All points for which at least one r-value equals or exceeds unity (r max ≥ 1) are considered as excluded. The SLHA files produced with SPheno in our MCMC scan contain the mass spectrum and decay tables. For evaluating the simplified model constraints with SModelS, also the LHC cross sections at s = 8 and 13 TeV are needed. They are conveniently added to the SLHA files by means of the SModelS-micrOMEGAs interface [85], which moreover automatically produces the correct particles.py file to declare the even and odd particle content for SModelS. Once the cross sections are computed, the evaluation of LHC constraints in SModelS takes a few seconds per point, which makes it possible to check the full dataset of 52.5k scan points.
The results are shown in Figures 10 and 11. The left panels in Figure 10 show the points excluded by SModelS (r max ≥ 1), in the plane of mχ0 1 vs. mχ0 3,4 (top left) and mχ ± j vs. mχ0 3,4 (bottom left), the difference betweenχ 0 3,4 not being discernible on the plots. Points with binolike or higgsino-like LSPs are distinguished by different colours and symbols: light blue dots for bino-like LSP points and magenta/pink triangles for higgsino-like LSP points. There are no excluded points with wino-like LSPs.
As can be seen, apart from two exceptions, all bino LSP points excluded by SModelS lie in the Z or h funnel region and have almost mass-degenerateχ show the excluded points, r max ≥ 1, in the mχ0 1 vs. mχ0 3,4 (top) and mχ ± j vs. mχ0 3,4 (bottom) planes, with bino-like or higgsino-like LSP points distinguished by different colours and symbols as indicated in the plot labels. The right panels show the same mass planes but distinguish the signatures, which are responsible for the exclusion, by different colours/symbols (again, see plot labels); moreover the region with r max ≥ 0.5 is shown in yellow, and that covered by all scan points in grey.
to about 750 GeV for wino-likeχ 3 ) below about 500 GeV. In terms of soft terms, the excluded bino LSP points have m D2 < 750 GeV or µ < 400 GeV, while the excluded higgsino LSP points have µ < 200 GeV and m D2 < 500 GeV (see Figure 11).
The right panels of Figures 10 and 11 show the same mass and parameter planes as the left panels but distinguish the signatures, which are responsible for the exclusion, by different colours/symbols. We see that W H + E miss T simplified model results exclude only bino-LSP points in the h-funnel region, but can reach up to mχ0 3,4 ≲ 750 GeV; all these points have

MadAnalysis 5
One disadvantage of the simplified model constraints is that they assume that charginos and neutralinos leading to W Z signatures are mass degenerate. SModelS allows a small deviation from this assumption, butχ ± iχ 0 j production with sizeable differences between mχ ± i and mχ0 j will not be constrained. Moreover, the simplified model results from [101][102][103][104] are cross section upper limits only, which means that different contributions to the same signal region cannot be combined (to that end efficiency maps would be necessary [98]). It is therefore interesting to check whether full recasting based on Monte Carlo event simulation can extend the limits derived with SModelS.
Here we use the recast codes [105][106][107] for Run 2 EW-ino searches available in MadAnalysis 5 [108][109][110][111].  For these analyses we again treat the two lightest neutralino states as LSPs, assuming the transitionχ 0 2 →χ 0 1 is too soft as to be visible in the detector. For the CMS 35.9 fb −1 analyses, we simulate all possible combinations ofχ 0 1,2 with the heavy neutralinos, charginos, and pair production of charginos; while to recast the analysis of [102] we must simulate pp →χ ± iχ 0 j>2 + njets, where n is between zero and two. The hard process is simulated in MadGraph5_aMC@NLO [115] v2.6 and passed to Pythia 8.2 [116] for showering. MadAnalysis 5 handles the detector simulation with Delphes 3 [117] with different cards for each analysis, and then computes exclusion confidence levels (1 − CL s ), including the combination of signal regions for the multi-lepton analysis. For the two 35.9 fb −1 analyses we simulate 50k events, and the whole simulation takes more than an hour per point on an 8-core desktop PC. For the ATLAS 139 fb −1 analysis, we simulate 100k events (because of the loss of efficiency in merging jets, and targeting only b-jets from the Higgs and in particular the leptonic decay channel of the W ) and each point requires 3 hours.
The reach of collider searches depends greatly on the wino fraction of the EW-inos. Winos have a much higher production cross section than higgsinos or binos, and thus we can divide the scan points into those where m D2 is "light" and "heavy." The results are shown in Figure 12. They show the distribution of points in our scan in the mχ0 1 − mχ0 3 plane. In our model, there is always a pseudo-Dirac LSP, so the lightest neutralinos are nearly degenerate; for a higgsino-or wino-like LSP the lightest chargino is nearly degenerate with the LSP. However, mχ0 3 gives the location of the next lightest states, irrespective of the LSP type. In this plane we show the points that we tested using MadAnalysis 5, and delineate the region encompassing all excluded points.
For "light" m D2 < 900 GeV, nearly all tested points in the Higgs funnel are excluded by [102] up to mχ 3 = 800 GeV; the Z-funnel is excluded for mχ 3 ≲ 300 GeV. Otherwise we can find excluded points in the region mχ0 1 ≲ 200 GeV, mχ0 3 ≲ 520 GeV. While for small mχ0 3 − mχ0 1 the ATLAS-SUSY-2019-08 search [102] is not effective, at large values of mχ0 3 some points are excluded by this analysis, and others still by CMS-SUS-16-039 [112] and/or CMS-SUS-16-048 [114]. We note here that the availability of the covariance matrix for signal regions A of [112] is quite crucial for achieving a good sensitivity. It would be highly beneficial to have more such (full or simplified) likelihood data that allows for the combination of signal regions! For "heavy" m D2 > 700 GeV, 9 we barely constrain the model at all: clearly Z-funnel points are excluded up to about mχ0 3 = 260 GeV; but we only find excluded points for mχ0 1 ≲ 100 GeV, mχ 3 ≲ 300 GeV. Hence one of the main conclusions of this work is that higgsino/bino mixtures in this model, where m D2 > 700 GeV, are essentially unconstrained for mχ0 1 ≳ 120 GeV.
In general, as in [66], one may expect a full recast in MadAnalysis 5 to be much more powerful than a simplified models approach. However, comparing the results from MadAnalysis 5 to those from SModelS, a surprisingly good agreement is found between the r-values from like searches (such as the W H + E miss T channel in the same analysis). 10 Indeed, from comparing  [112]; in terms of the ratio r MA5 of predicted over excluded (visible) cross sections, this corresponds to r MA5 = 0.67 and 0.71, so somewhat lower than the values from SModelS.
• The W H + E miss T signal for the two example points above splits up into several components (corresponding to different mass vectors) in SModelS, which each give r-values of roughly 0.3 but cannot be combined. The recast of ATLAS-SUSY-2019-08 [102] with MadAnalysis 5, on the other hand, takes the complete signal into account and gives 1 − CL s = 0.77 for the first and 0.96 for the second point. 9 The regions are only not disjoint so that we can include the entire constrained reach of the Higgs funnel in the "light" plot; away from the Higgs funnel there would be no difference in the "light" m D2 plot if we took m D2 < 700 GeV. 10 We shall see this explicitly for some benchmark scenarios in section 5.
• The points excluded with MadAnalysis 5 but not with SModelS typically contain complex spectra with all EW-inos below about 800 GeV, which all contribute to the signal.
• Most tested points away from the Higgs funnel region, which are excluded with Mad-Analysis 5 but not with SModelS, have r max > 0.8.
• There also exist points which are excluded by SModelS but not by the recasting with MadAnalysis 5. In these cases the exclusion typically comes from the CMS EW-ino combination [104]; detailed likelihood information would be needed to emulate this combination in recasting codes.
It would be interesting to revisit these conclusions once more EW-ino analyses are implemented in full recasting tools, but it is clear that, since adding more luminosity does not dramatically alter the constraints, the SModelS approach can be used as a reliable (and much faster) way of constraining the EW-ino sector; and that the constraints on EW-inos in Dirac gaugino models are still rather weak, particularly for higgsino LSPs where the wino is heavy.

Constraints from searches for long-lived particles
As mentioned in section 4.1, a relevant fraction (about 20%) of the points in our dataset contain LLPs. Long-lived charginos, which occur in about 14% of all points, can be constrained by Heavy Stable Charged Particles (HSCP) and Disappearing Tracks (DT) searches. Displaced vertex (DV) searches could potentially be sensitive to long-lived neutralinos; in our case however, the decay products of long-lived neutralinos are typically soft photons, and there is no ATLAS or CMS analysis which would be sensitive to these.
We therefore concentrate on constraints from HSCP and DT searches. They can conveniently be treated in the context of simplified models. For HSCP constraints we again use SModelS, which has upper limit and efficiency maps from the full 8 TeV [118] and early 13 TeV (13 fb −1 ) [119] CMS analyses implemented. (The treatment of LLPs in SModelS is described in detail in Refs. [99,120].) A new 13 TeV analysis for 36 fb −1 is available from ATLAS [121], but not yet included in SModelS; we will come back to this below.
For the DT case, the ATLAS [122] and CMS [123] analyses for 36 fb −1 provide 95% CL upper limits on σ × BR in terms of chargino mass and lifetime on HEPData [124,125]. Here, σ × BR stands for the cross section of direct production of charginos, which includes χ ± 1χ  There is also a new CMS DT analysis [126], which presents full Run 2 results for 140 fb −1 . At the time of our study, this analysis did not yet provide any auxiliary (numerical) material 11 This is 95 < mχ± 1 < 600 GeV and 0.05 < τχ± 1 < 4 ns (15 < cτχ± 1 < 1200 mm) for the ATLAS analysis [122], and 100 < mχ± 1 < 900 GeV and 0.067 < τ χ± 1 < 333.56 ns (20 < cτχ± 1 < 100068 mm) for the CMS analysis [123].   for reinterpretation. We therefore digitised the limits curves from Figures 1a-1d of that paper, and used them to construct linearly interpolated limit maps which are employed in the same way as described in the previous paragraph. Since the interpolation is based on only four values of chargino lifetimes, τχ ± 1 = 0.33, 3.34, 33.4 and 333 ns, this is however less precise than the interpolated limits for 36 fb −1 . The results are shown in Figure 13 in the plane of chargino mass vs. mean decay length; on the left for points with long-lived charginos, on the right for point with long-lived charginos and neutralinos. Red points are excluded by the HSCP searches implemented in SModelS: orange points are excluded by DT searches. The HSCP limits from [118,119] eliminate basically all long-lived chargino scenarios with cτχ± ≳ 1 m up to about 1 TeV chargino mass. The exclusion by the DT searches [122,123] covers 10 mm ≲ cτχ ± 1 ≲ 1 m and mχ ± 1 up to about 600 GeV; this is only slightly extended to higher masses by our reinterpretation of the limits of [126].
To verify the HSCP results from SModelS and extend them to 36 fb −1 , we adapted the code for recasting the ATLAS analysis [121] written by A. Lessa and hosted at https://github. com/llprecasting/recastingCodes. This requires simulating hard processes of single/double chargino LLP production with two additional hard jets, which was performed at leading order with MadGraph5_aMC@NLO. The above code then calls Pythia 8.2 to shower and decay the events, and process the cuts. It uses experiment-provided efficiency tables for truth-level events rather than detector simulation, and therefore does not simulate the presence of a magnetic field. However, the code was validated by the original author for the MSSM chargino case and found to give excellent agreement.
We wrote a parallelised version of the recast code to speed up the workflow (which is available upon request); the bottleneck in this case is actually the simulation of the hard process (unlike for the prompt recasting case in the previous section), and our sample was simulated on one desktop. We show the result in Figure 14. For decay lengths cτχ ± 1 > 1 m, the exclusion is very similar to that from SModelS, only slightly extending it in the mχ ± 1 ≈ 1-

Future experiments: MATHUSLA
We also investigated the possibility of seeing events in the MATHUSLA detector [127], which would be built O(100)m from the collision point at the LHC, and so would be able to detect neutral particles that decay after such a long distance. Prima facie this would seem ideal to search for the decays of long-lived neutralino NLSPs; pseudo-Dirac states should be excellent candidates for this (indeed, the possibility of looking for similar particles if they were of O(GeV) in mass at the SHiP detector was investigated in [128]). However, in our case the only states that have sufficient lifetime to reach the detector have mass splittings of O(10) MeV (or less), and decaysχ 0 2 →χ 0 1 + γ vastly dominate, with a tiny fraction of decays to electrons.
In the detectors in the roof of MATHUSLA the photons must have more than 200 MeV (or 1 GeV for electrons) to be registered. Moreover, it is anticipated to reconstruct the decay vertex in the decay region, requiring more than one track; in our case only one track would appear, and much too soft to trigger a response. Hence, unless new search strategies are employed, our long-livedχ 0 2 will escape detection.

Benchmark points
In this section we present a few sample points which may serve as benchmarks for further studies, designing dedicated experimental analyses and/or investigating the potential of future experiments. Parameters, masses, and other relevant quantities are listed in Tables 2 and 3.      Moreover, the total relevant EW-ino production cross section is only 41 fb at s = 13 TeV, compared to ≈ 2.6 pb for Point 2. Therefore, again, no relevant constraints are obtained from the current LHC searches. In particular, SModelS does not give any constraints from EW-ino searches but reports 34 fb as missing topology cross section, 64% of which go on account of W * (→ 2 jets or lν) + γ + E miss T

signatures.
Point 4 (SPhenoDiracGauginos_2231) has bino and wino masses of the order of 600 GeV similar to Point 3, but features a smallerχ We also note that theχ 0 2 is long-lived with a mean decay length of about 0.5 m. However, given the tiny mass difference to theχ 1079 GeVχ The LHC production cross sections are however very low for such heavy EW-inos, below 1 fb at 13-14 TeV. This is clearly a case for the high luminosity (HL) LHC, or a higher-energy machine.
Point 7 (SPhenoDiracGauginos_37) is another higgsino DM point with mχ0 1 ≃ 1.1 TeV but small, sub-GeV mass splittings between the higgsino-like states, mχ0 2 − mχ0 1 ≃ 120 MeV and mχ ± 1 − mχ0 1 ≃ 400 MeV. Co-annihilations betweenχ 1159 GeVχ 1327 GeVχ The SLHA files for these 10 points, which can be used as input for MadGraph, mi-crOMEGAs or SModelS are available via Zenodo [130]. The main difference between the SLHA files for MadGraph5_aMC@NLO or micrOMEGAs is that the MadGraph5_aMC@NLO ones have complex mixing matrices, while the micrOMEGAs ones have real mixing matrices and thus neu-tralino masses can have negative sign. The SModelS input files consist of masses, decay tables and cross sections in SLHA format but don't include mixing matrices. The CalcHEP model files for micrOMEGAs are also provided at [130]. The UFO model for MadGraph5_aMC@NLO is available at [79], and the SPheno code at [91].

Conclusions
Supersymmetric models with Dirac instead of Majorana gaugino masses have distinct phenomenological features. In this paper, we investigated the electroweakino sector of the Minimal Dirac Gaugino Supersymmetric Standard Model. The MDGSSM can be defined as the minimal Dirac gaugino extension of the MSSM: to introduce DG masses, one adjoint chiral superfield is added for each gauge group, but nothing else. The model has an underlying R-symmetry that is explicitly broken in the Higgs sector through a (small) B µ term, and new superpotential couplings λ S and λ T of the singlet and triplet fields with the Higgs. The resulting EW-ino sector thus comprises two bino, four wino and three higgsino states, which mix to form six neutralino and three chargino mass eigenstates (as compared to four and two, respectively, in the MSSM) with naturally small mass splittings induced by λ S and λ T . All this has interesting consequences for dark matter and collider phenomenology. We explored the parameter space where theχ 0 1 is a good DM candidate in agreement with relic density and direct detection constraints, updating previous such studies. The collider phenomenology of the emerging DM-motivated scenarios is characterised by the richer EW-ino spectrum as compared to the MSSM, naturally small mass splittings as mentioned above, and the frequent presence of long-lived charginos and/or neutralinos.
We worked out the current LHC constraints on these scenarios by re-interpreting SUSY and LLP searches from ATLAS and CMS, in both a simplified model approach and full recasting using Monte Carlo event simulation. While HSCP and disappearing track searches give quite powerful limits on scenarios with charged LLPs, scenarios with mostly E miss T signatures remain poorly constrained. Indeed, the prompt SUSY searches only allow the exclusion of (certain) points with an LSP below 200 GeV, which drops to about 100 GeV when the winos are heavy. This is a stark contrast to the picture for constraints on colourful sparticles, and indicates that this sector of the theory is likely most promising for future work. We provided a set of 10 benchmark points to this end.
We also demonstrated the usefulness of a simplified models approach for EW-inos, in comparing it to a full recasting. While cross section upper limits have the in-built shortcoming of not being able to properly account for complex spectra (where several signals overlap), the results are close enough to give a good estimate of the excluded region. This is particularly true since it is a much faster method of obtaining constraints, and the implementation of new results is much more straightforward (and hence more complete and up-to-date). Moreover, the constraining power could easily be improved if more efficiency maps and likelihood information were available and implemented. This holds for both prompt and LLP searches.
We note in this context that, while this study was finalised, ATLAS made pyhf likelihood files for the 1l + H(→ bb) + E miss T EW-ino search [102] available on HEPData [131] in addition to digitised acceptance and efficiency maps. We appreciate this very much and are looking forward to using this data in future studies. To go a step further, it would be very interesting if the assumption mχ ± 1 = mχ0 2 could be lifted in the simplified model interpretations.
Furthermore, the implementation in other recasting tools of more analyses with the full ≈ 140 fb −1 integrated luminosity from Run 2 would be of high utility in constraining the EW-ino sector. Here, the recasting of LLP searches is also a high priority, as theories with such particles are very easily constrained, with the limits reaching much higher masses than for searches for promptly decaying particles. A review of available tools for reinterpretation and detailed recommendations for the presentation of results from new physics searches are available in [132].
Last but not least, we note that the automation of the calculation of particle decays when there is little phase space will also be a fruitful avenue for future work.
Funding information This work was supported in part by the IN2P3 through the projects "Théorie -LHCiTools" (2019) and "Théorie -BSMGA" (2020). This work has also been done within the Labex ILP (reference ANR-10-LABX-63) part of the Idex SUPER, and received financial state aid managed by the Agence Nationale de la Recherche, as part of the programme Investissements d'avenir under the reference ANR-11-IDEX-0004-02, and the Labex "Institut Lagrange de Paris" (ANR-11-IDEX-0004-02, ANR-10-LABX-63) which in particular funded the scholarship of SLW. SLW has also been supported by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) under grant 396021762 -TRR 257. MDG acknowledges the support of the Agence Nationale de Recherche grant ANR-15-CE31-0002 "HiggsAutomator." HRG is funded by the Consejo Nacional de Ciencia y Tecnología, CONACyT, scholarship no. 291169.

A.1 Electroweakinos in the MRSSM
In this appendix we provide a review of the EW-ino sector of the MRSSM in our notation, to contrast with the phenomenology of the MDGSSM.
The MRSSM [19] is characterised by preserving a U (1) R-symmetry even after EWSB. To allow the Higgs fields to obtain vacuum expectation values, they must have vanishing Rcharges, and we therefore need to add additional partner fields R u,d so that the higgsinos can obtain a mass (analogous to the µ-term in the MSSM). The relevant field content is summarised in Table 4. The superpotential of the MRSSM is Names Spin 0, Here we define the triplet as Notably the model has an N = 2 supersymmetry if The above definitions are common to e.g. [38,59,72] and can be translated to the notation of [50] via The Higgs fields as well as the triplet and singlet scalars have R-charges 0, so their fermionic partners all have R-charge −1. The R u,d fields have R-charges 2, so the R-higgsinos have Rcharge 1. Together with the "conventional" bino and wino fields, which also have R-charge 1, this gives 2 × four Dirac spinors with opposite R-charges. After EWSB, the EW gauginos and (R-)higgsinos thus form four Dirac neutralinos with mass-matrix The above mass matrix looks very similar to that of the MSSM in the case of N = 2 supersymmetry! On the other hand, for the charginos, although there are eight Weyl spinors, these organise into four Dirac spinors, and again into two pairs with opposite R-charges. So we have The MRSSM therefore does not entail naturally small splittings between EW-ino states. However, if the R-symmetry is broken by a small parameter, then this situation is reversed: small mass splittings would appear between each of the Dirac states.

A.3 Higgs mass classifier
A common drawback for the efficiency of phenomenological parameter scans, is finding the subset of the parameter space where the Higgs mass m h is around the experimentally measured value. Our case is not the exception, as m h depends on all the input variables considered in our study. This is clear for µ, the mass term in the scalar potential, and tan β, the ratio between the vevs. For the soft terms, the dependence becomes apparent when one realises that in DG models, the Higgs quartic coupling receives corrections of the form where m SR and m T P are the tree-level masses of the singlet and triplet scalars, respectively, and are given large values to avoid a significant suppression on the Higgs mass 15 .
To overcome this issue, we have implemented Random Forest Classifiers (RFCs) that predict, from the initial input values, if the parameter point has a m h inside (p in ) or outside (p out ) the desired our 120 < m h < 130 GeV range. A sample of 50623 points was chosen so as to have an even distribution of inside/outside range points. The data was then divided as training and test data in a 67:33 split. We trained the classifier using the RFC algorithm in the scikit-learn python module with 150 trees in the forest (n_estimators=150).
The obtained mean accuracy score for the trained RFC was 93.75%. However, we are interested in discarding as many points with m h outside of range as possible while keeping all the p in ones. To do so we have rejected only the points with a 70% estimated probability of being p out . In this way, we obtained an improved 98.8% on the accuracy for discarding p out points while still rejecting 86% of them. The cut value of estimated probability for p out was chosen as an approximately optimal balance between accuracy and rejection percentage. Above the 70% value there is no significant improvement in the accuracy, but the rejection percentage depreciates. This behaviour is schematised in Figure 15, where the estimated probability of p out is shown as a function of m h .
Finally, to estimate the overall improvement on the scan efficiency, we multiplied the percentage of real p out (roughly 88%) by the p out rejection percentage (86%) and obtained an overall 75% rejection percentage. Hence, the inclusion of the classifier yields a scan approximately four times faster.

A.4 Recast of ATLAS-SUSY-2019-08
ATLAS reported a search in final states with E miss T , 1 lepton (e or µ) and a Higgs boson decaying into bb, with 139 fb −1 in [102]. This is particularly powerful for searching for winos with a lighter LSP (such as a bino or higgsino) and so we implemented a recast of this analysis in MadAnalysis 5 [108][109][110][111]. The analysis targets electroweakinos produced in the combination of a chargino and a heavy neutralino, where the neutralino decays by emitting an on-shell Higgs, and the chargino decays by emitting a W -boson, i.e. W H + E This search should be particularly effective when other supersymmetric particles (such as sleptons and additional Higgs fields) are heavy. Given constraints on heavy Higgs sectors and colourful particles, it is rather model independent and difficult to evade in a minimal model. The ATLAS collaboration made available substantial additional data via HEPData at [131], in particular including detailed cutflows and tables for the exclusion curves, which are essential for validating our recast code.
The implementation in MadAnalysis 5 follows the cuts of [102] and implements the lepton isolation and a jet/lepton removal procedure as described in that paper directly in the analysis. Jet reconstruction is performed using fastjet [133] in Delphes 3 [117], where b-tagging and lepton/jet reconstruction efficiencies are taken from a standard ATLAS Delphes 3 card used in other recasting analyses [134][135][136][137]. The analysis was validated by comparing signals generated for the same MSSM simplified scenario as in [102]: this consists of a degenerate wino-like chargino and heavy neutralino, together with a light bino-like neutralino. The analysis requires two or three signal jets, two of which must be b-jets (to target the Higgs decay); the signal is simulated by a hard process of p, p →χ   Table 5: Number of events expected in each signal region in [102] (columns labelled "ATLAS") against result from recasting in MadAnalysis 5 (columns labelled "MA") for different parameter points. The quoted error bands are Monte Carlo uncertainties, but the cross-section uncertainties can also reach 10% for some regions.
In the validation, up to 2 hard jets are simulated at leading order in MadGraph5_aMC@NLO, the parton shower is performed in Pythia 8.2, and the jet merging is performed by the MLM algorithm using MadGraph5_aMC@NLO defaults. In addition, to select only leptonic decays of the W -boson, and b-quark decays of the Higgs, the branching ratios are modified in the SLHA file (with care that Pythia does not override them with the SM values) and the signal cross-sections weighted accordingly: this improves the efficiency of the simulation by a factor of roughly 8, since the leptonic branching ratio of the W is 0.2157 and the Higgs decays into b-quarks 58.3% of the time. A detailed validation note will be presented elsewhere, including detailed cutflow analysis and a reproduction of the exclusion region with that found in [102]. Here we reproduce the expected (according to the calculated cross-section and experimental integrated luminostiy) final number of events passing the cuts for the "exclusive" signal regions, for the three benchmark points where cutflows are available in table 5, where an excellent agreement can be seen. For each point, 30k events were simulated, leading to small but non-negligible Monte-Carlo uncertainties listed in the table.

Application to the MDGSSM
To apply this analysis to our model, firstly we treat both the lightest two neutralino states as LSP states; we must also simulate the production of all heavy neutralinos (χ 0 i , i > 2) and charginos in pairs. It is no longer reasonable to select only leptonic decays of the W , because we can have several processes contributing to the signal. Indeed, in our case, we can have both for example. Therefore we do not modify the decays of the electroweakinos in the SLHA files, and simulate p, p →χ ± i≥1 ,χ 0 j≥3 + njets, n ≤ 2 as the hard process in MadGraph5_aMC@NLO, before showering with Pythia 8.2 and passing to the analysis as before.
We have not produced an exclusion contour plot for this analysis comparable to the MSSM case in [102], because a heavy wino with a light bino always leads to an excess of dark matter unless the bino is near a resonance. We should generally expect the reach of the exclusion to be better than for the MSSM, due to the increase in cross section from pseudo-Dirac states; since we can only compare our results directly for points on the Higgs-funnel, for mχ 1 ≈ m h /2, we find a limit on the heavy wino mass of about 800 GeV in our model, compared to 740 GeV in the MSSM.