Nonsimplified SUSY: \(\widetilde{\tau }\)coannihilation at LHC and ILC
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Abstract
If new phenomena beyond the Standard Model will be discovered at the LHC, the properties of the new particles could be determined with data from the HighLuminosity LHC and from a future linear collider like the ILC. We discuss the possible interplay between measurements at the two accelerators in a concrete example, namely a full SUSY model which features a small \( \widetilde{\tau }_1\)LSP mass difference. Various channels have been studied using the Snowmass 2013 combined LHC detector implementation in the Delphes simulation package, as well as simulations of the ILD detector concept from the Technical Design Report. We investigate both the LHC and the ILC capabilities for discovery, separation and identification of various parts of the spectrum. While some parts would be discovered at the LHC, there is substantial room for further discoveries at the ILC. We finally highlight examples where the precise knowledge about the lower part of the mass spectrum which could be acquired at the ILC would enable a more indepth analysis of the LHC data with respect to the heavier states.
1 Introduction
Supersymmetry (SUSY) [1, 2, 3, 4, 5, 6] is one of the best motivated theories beyond the Standard Model (SM). In the past, at LEP, Tevatron and the early LHC, results were mainly interpreted in the constrained minimal supersymmetric extension of the Standard Model (CMSSM) [7, 8], while later LHC search results are mostly presented in a simplified model approach [9, 10, 11]. Simplified models offer more flexibility for comparing to predictions of different theoretical models, though they might not describe reality well, as they usually contain only one decay with \(100\,\%\) branching ratio. In contrast, a real SUSY signal might comprise a large spectrum of SUSY particles and the higher states of the spectrum may have many decay modes leading to potentially long decay chains. This means that the simplified approach in general does not apply beyond the direct production of the nexttolightest SUSY particle (NLSP) and the interpretation of exclusion limits formulated in the simplified approach is nontrivial. Furthermore, also several production channels may be open, making SUSY the most serious background to itself. This becomes especially relevant for interpreting a future discovery of a nonSM signal.
Within the context of constrained models, the masses of the fermionpartner particles (sfermions) in kinematic reach of the ILC are excluded with high confidence. However, this exclusion is in most cases based on the strongly interacting sector, which in constrained models is coupled to the electroweak sector by GUTscale mass unification. Without the restriction of mass unification, the part of the spectrum which is of interest to electroweak and flavour precision observables as well as dark matter, i.e. which is decisive for the fit outcome, is not at all in conflict with LHC results. This applies in particular to the \(\widetilde{\tau }_1\) with a small mass difference from the LSP: although first limits on direct \(\widetilde{\tau }\) pair production from the LHC have been presented [15, 16], they rapidly lose sensitivity if the \(\widetilde{\tau }\) is not degenerate with the \(\widetilde{e}\) and \(\widetilde{\mu }\), and has a small mass difference from the LSP. In fact, the current limit on the \(\widetilde{\tau }\) without other assumptions on the mass difference from the LSP than that it is larger than \(m_{\tau }\) nor with any assumptions on the \(\widetilde{\tau }\) mixing angle comes from the DELPHI experiment at LEP and is \(M_{\widetilde{\tau }} > 26.3\) \(\,\text {GeV}\) [17, 18]. Due the key feature of a small \(\widetilde{\tau }\)LSP mass difference and the resulting sizeable \(\widetilde{\tau }\)coannihilation contribution the series of CPconserving model points considered here is called STC [19].
Motivated by solving the naturalness problem within the general MSSM [20, 21], the SUSY partner particles of thirdgeneration quarks in STC have been chosen to be lighter than those of the first and secondgeneration squarks. When the first and secondgeneration squarks and the gluino are rather heavy, \(\gtrsim \) \(2\,\text {TeV} \), the size of the total SUSY cross section at the LHC strongly depends on the mass of the lightest top squark. We therefore consider in particular two model points, called STC8 and STC10, whose physical spectra differ only by the mass parameter of the partners of the righthanded thirdgeneration squarks at a scale of 1\(\,\text {TeV}\). The mass parameter of the righthanded thirdgeneration squarks is set to 800 and 1000\(\,\text {GeV}\), resulting in physical masses of the top squark of \(m_{\widetilde{t}_1} \approx 740\,\text {GeV} \) and \(m_{\widetilde{t}_1} \approx 940\,\text {GeV} \), and of the bottom squark of \(m_{{\widetilde{\mathrm{b}}}_1} \approx 800\,\text {GeV} \) and \(m_{{\widetilde{\mathrm{b}}}_1} \approx 1000\,\text {GeV} \), respectively.
\(\widetilde{\tau }\)coannihilation at the LHC has been studied before either in context of mSugra, relying on rather light gluinos with a mass of about 850 \(\,\text {GeV}\) [22, 23, 24], or more recently the very specific decay chain of \({\widetilde{t}}_1 \rightarrow {\overline{\mathrm{b}}} {\widetilde{\tau }}_1 {\widetilde{\nu _{\tau }}}\) [25], which has a branching ratio of less than 10 % in the full model investigated here, cf. Sect. 2.
Figure 1a introduces the full mass spectrum of the benchmark scenario STC8, while Fig. 1b zooms into the part of the spectrum accessible at the ILC with \(E_{\mathrm {cms}}=500\,\text {GeV} \). The lightest Higgs boson features SMlike branching ratios and has a mass in agreement with the LHC discovery within the typical theoretical uncertainty of \(\pm 3\,\text {GeV} \) on MSSM Higgsboson mass calculations.
The dashed lines in Fig. 1a indicate those decay chains of the various sparticles which have branching fractions of at least \(10\,\%\). The greyscale of the lines indicates the size of the branching ratio. Only very few particles, namely the first and second generation squarks, the sneutrinos and the lighter set of charged sleptons have decay modes with \(100\,\%\) branching ratio.
In particular the top and bottom squarks, but also the superpartners of the uncoloured bosons, called electroweakinos in the following, have various decay modes, none of them with a branching ratio larger than \(50\,\%\), but many with less than \(10\,\%\). This plethora of decay modes makes it challenging to separate the various production modes and identify each sparticle.

Which signature will lead to the first discovery of a discrepancy from the SM? How much integrated luminosity and operation time will be needed?

Which other signatures will be observable?

Which production modes of which sparticles contribute to this signal?

Can we tell how many sparticles are involved?

Which observables (masses, BRs, cross sections) can be measured and with which precision?

Can we show that it is SUSY?

Can the \(\widetilde{\chi }^0_1\) be identified as a Dark Matter particle?
2 Collider phenomenology of the STC scenarios
In this section we present the parameters of the benchmark models in more detail, summarising the masses of the most important SUSY particles, their production cross sections and branching ratios. Based on this information, the phenomenology at the LHC and ILC will be discussed.
A cornerstone of SUSY is that the couplings of the standardmodel particles and their supersymmetric partners are the same, so that on treelevel the production cross sections only depend on the masses and mixing angles of the produced and exchanged sparticles.
In the case of the LHC studies, we assumed \(E_{\mathrm {cms}}= \) 14\(\,\text {TeV}\) and an integrated luminosity up to 300 fb\(^{1}\). We also consider the highluminosity upgrade of the LHC, the HLLHC, assumed also to be running at \(E_{\mathrm {cms}}= \) 14\(\,\text {TeV}\), but delivering a total integrated luminosity of 3 ab\(^{1}\).
For the ILC studies, the conditions presented in the Technical Design Report (TDR) [26] were used. This means that the bulk of the data would be recorded at \(E_{\mathrm {cms}}= \) 500\(\,\text {GeV}\), with an integrated luminosity of 250 fb\(^{1}\) per year. We extrapolate our results to the running scenarios recently published by the Joint Working Group on ILC Beam Parameters [27]. Since the ILC beam energy is tunable, we also consider the option of running at different, lower energies, and performing energy scans around thresholds. Very important are the opportunities offered by the electron and positron beam polarisation, for which the baseline design of the ILC foresees absolute values of 80 and 30 %, respectively. As SUSY is a chiral theory, the possibility to have polarised initial conditions is a very powerful tool to disentangle different states, to enhance signal while reducing SM background, and to study helicitydependent predictions of the theory.
2.1 Mass spectrum and decay modes
Sparticle masses for the models STC8 and STC10. The mass of the first two generation squarks (\(\widetilde{\mathrm{q}}\)) varies by a few GeV, their average mass is listed. We use \(\widetilde{\ell }\) when we refer to the first and second generation sleptons, while the third generation is listed separately
Sparticle  Mass (GeV)  Sparticle  Mass (GeV)  

STC8  STC10  STC8  STC10  
\(\widetilde{\mathrm{b}} _1\)  795  1008  \(\widetilde{\tau } _1\)  107  107 
\(\widetilde{\mathrm{b}} _2\)  1500  1500  \(\widetilde{\tau } _2\)  219  219 
\(\widetilde{\mathrm{t}} _1\)  736  944  \( \widetilde{\nu }_\tau \)  196  196 
\(\widetilde{\mathrm{t}} _2\)  1532  1537  \(\widetilde{\chi }^0_1\)  96  96 
\(\widetilde{\mathrm{g}}\)  2042  2042  \(\widetilde{\chi }^0_2\)  206  206 
\(\widetilde{\mathrm{q}} \)  2028  2028  \(\widetilde{\chi }^0_3\)  410  410 
\(\widetilde{\ell }_{\mathrm L}\)  212  212  \(\widetilde{\chi }^0_4\)  425  426 
\(\widetilde{\ell }_{\mathrm R}\)  131  131  \(\widetilde{\chi }^{\pm }_1\)  206  206 
\( \widetilde{\nu }_\mathrm {L}\)  198  198  \(\widetilde{\chi }^{\pm }_2\)  426  427 
Branching ratios (BR) of the gluinos and the third generation squarks in the models STC8 and STC10. Only branching ratios above 1 % are shown
Decay  BR (%)  Decay  BR (%)  

STC8  STC10  STC8  STC10  
\(\widetilde{\mathrm{g}} \rightarrow \mathrm{t} \widetilde{\mathrm{t}} _1\)  37.8  35.5  \(\widetilde{\mathrm{g}} \rightarrow \mathrm{b} \widetilde{\mathrm{b}} _1\)  39.1  36.9 
\(\widetilde{\mathrm{g}} \rightarrow \mathrm{t} \widetilde{\mathrm{t}} _2\)  11.5  13.8  \(\widetilde{\mathrm{g}} \rightarrow \mathrm{b} \widetilde{\mathrm{b}} _2\)  11.5  13.7 
\(\widetilde{\mathrm{t}} _1 \rightarrow \mathrm{t} \widetilde{\chi }^0_1 \)  13.2  9.9  \(\widetilde{\mathrm{b}} _1 \rightarrow \mathrm{b} \widetilde{\chi }^0_1 \)  58.2  51.4 
\(\widetilde{\mathrm{t}} _1 \rightarrow \mathrm{t} \widetilde{\chi }^0_2 \)  4.5  4.3  \(\widetilde{\mathrm{b}} _1 \rightarrow \mathrm{b} \widetilde{\chi }^0_2 \)  3.1  3.0 
\(\widetilde{\mathrm{t}} _1 \rightarrow \mathrm{t} \widetilde{\chi }^0_3 \)  22.4  24.3  \(\widetilde{\mathrm{b}} _1 \rightarrow \mathrm{b} \widetilde{\chi }^0_3 \)  10.7  12.1 
\(\widetilde{\mathrm{t}} _1 \rightarrow \mathrm{t} \widetilde{\chi }^0_4 \)  12.0  15.1  \(\widetilde{\mathrm{b}} _1 \rightarrow \mathrm{b} \widetilde{\chi }^0_4 \)  9.2  10.5 
\(\widetilde{\mathrm{t}} _1 \rightarrow \mathrm{b} \widetilde{\chi }^{+}_1 \)  10.8  9.8  \(\widetilde{\mathrm{b}} _1 \rightarrow \mathrm{t} \widetilde{\chi }^{}_1 \)  5.1  5.2 
\(\widetilde{\mathrm{t}} _1 \rightarrow \mathrm{b} \widetilde{\chi }^{+}_2 \)  37.1  36.5  \(\widetilde{\mathrm{b}} _1 \rightarrow \mathrm{t} \widetilde{\chi }^{}_2 \)  13.7  17.9 
Branching ratios (BR) of the sleptons in the models STC8 and STC10. We use \(\widetilde{\ell }\) when we refer to the first and second generation sleptons, while the third generation is listed separately
Decay  BR (%)  Decay  BR (%)  

STC8  STC10  STC8  STC10  
\(\widetilde{\ell }_{\mathrm R}\rightarrow l \widetilde{\chi }^0_1 \)  100  100  \(\widetilde{\tau } _1 \rightarrow \tau \widetilde{\chi }^0_1 \)  100  100 
\(\widetilde{\ell }_{\mathrm L}\rightarrow l \widetilde{\chi }^0_1 \)  95.3  95.4  \(\widetilde{\tau } _2 \rightarrow \tau \widetilde{\chi }^0_1 \)  81.3  81.5 
\(\widetilde{\ell }_{\mathrm L}\rightarrow l \widetilde{\chi }^0_2 \)  1.7  1.6  \(\widetilde{\tau } _2 \rightarrow \tau \widetilde{\chi }^0_2 \)  3.4  3.4 
\(\widetilde{\ell }_{\mathrm L}\rightarrow \nu _{l} \widetilde{\chi }^{\pm }_1 \)  3.0  3.0  \(\widetilde{\tau } _2 \rightarrow \nu _{\tau } \widetilde{\chi }^{\pm }_1 \)  6.2  6.2 
\(\widetilde{\tau } _2 \rightarrow \widetilde{\tau }_1 Z\)  9.1  9.0  
\( \widetilde{\nu }_\ell \rightarrow \nu _{\ell } \widetilde{\chi }^0_1 \)  100  100  \( \widetilde{\nu }_\tau \rightarrow \nu _{\tau } \widetilde{\chi }^0_1 \)  94.2  94.6 
\(\widetilde{\nu } {\tau } \rightarrow \widetilde{\tau } _1 W\)  5.8  5.4 
The actual masses of the \(\widetilde{\mathrm {e}}_{\mathrm {L}}\) and \(\widetilde{\mu }_{\mathrm {L}}\) in STCx have been excluded by the ATLAS experiment for the case of 100 % branching ratio for the direct decay to the corresponding lepton and the LSP [30]. As can be seen in Table 3, the STCx branching ratios for these decays are quite close to \(100~\%\), thus this particular part of the spectrum is most likely excluded. It should be noted, however, that this large BR is a special case due to the small mass difference of only 6 GeV between the \(\widetilde{\ell }_{\mathrm L}\) and the \(\widetilde{\chi }^{\pm }_1\) / \(\widetilde{\chi }^0_2\), which leads to a strong phase space suppression for the cascade decays \(\widetilde{\ell }_{\mathrm L}\rightarrow l \widetilde{\chi }^0_2\) and \(\widetilde{\ell }_{\mathrm L}\rightarrow \nu _l \widetilde{\chi }^{\pm }_1\). With increasing mass difference, the branching ratio for the direct decay \(\widetilde{\ell }_{\mathrm L}\rightarrow l \widetilde{\chi }^0_1\) drops rapidly in favour of these cascade decays. Therefore, the results of this study remain highly relevant in the broader picture. Cases where the specific mass and branching ratio combination of the \(\widetilde{\ell }_{\mathrm L}\) plays a role will be pointed out.
The STCx masses of the righthanded sleptons are by far not excluded, although their BR to lepton and LSP is 100 %. This has to be attributed to their smaller mass difference from the LSP, which leads to softer leptons and thus a significantly smaller acceptance. Among the other slepton decays listed in Table 3, it is interesting to note that the \(\widetilde{\nu } _{\tau }\) features 5 % of visible decays to \(\widetilde{\tau } _1\)W.
Branching ratios (BR) of the charginos and neutralinos in the models STC8 and STC10
Decay  BR (%)  Decay  BR (%)  

STC8  STC10  STC8  STC10  
\(\widetilde{\chi }^{+}_1 \rightarrow \widetilde{\mu } ^+_\mathrm{R}\nu _{\mu }\)  0.2  0.2  \(\widetilde{\chi }^0_2 \rightarrow \widetilde{\mathrm{e}} _\mathrm{R}^{\pm }\)e\(^{\mp }\)  2.1  2.1 
\(\widetilde{\chi }^{+}_1 \rightarrow \widetilde{\tau } _1 \nu _{\tau }\)  67.9  67.5  \(\widetilde{\chi }^0_2 \rightarrow \widetilde{\mu }_\mathrm{R} ^{\pm } \mu ^{\mp }\)  2.1  2.2 
\(\widetilde{\chi }^{+}_1 \rightarrow \widetilde{\nu } _\mathrm{e}\)e\(^+\)  6.6  6.8  \(\widetilde{\chi }^0_2 \rightarrow \widetilde{\tau } _1^{\pm } \tau ^{\mp }\)  73.2  72.9 
\(\widetilde{\chi }^{+}_1 \rightarrow \widetilde{\nu } _{\mu } \mu ^+\)  6.6  6.8  \(\widetilde{\chi }^0_2 \rightarrow \widetilde{\nu } _\mathrm{e} \nu _\mathrm{e} \)  5.7  5.8 
\(\widetilde{\chi }^{+}_1 \rightarrow \widetilde{\nu } _{\tau } \tau ^+\)  11.3  11.5  \(\widetilde{\chi }^0_2 \rightarrow \widetilde{\nu } _{\mu } \nu _{\mu } \)  5.7  5.8 
\(\widetilde{\chi }^{+}_1 \rightarrow \widetilde{\chi }^0_1 \mathrm{W}^{+} \)  7.2  7.0  \(\widetilde{\chi }^0_2 \rightarrow \widetilde{\nu } _{\tau } \nu _{\tau } \)  9.5  9.7 
\(\widetilde{\chi }^0_2 \rightarrow \widetilde{\chi }^0_1 \mathrm{Z} \)  1.2  1.1  
\(\widetilde{\chi }^{+}_2 \rightarrow \widetilde{\mathrm{e}} ^+_\mathrm{L}\nu _\mathrm{e}\)  4.6  4.6  \(\widetilde{\chi }^0_3 \rightarrow \widetilde{\chi }^{\pm }_1 \mathrm{W} ^{\mp } \)  58.3  58.4 
\(\widetilde{\chi }^{+}_2 \rightarrow \widetilde{\mu } ^+_\mathrm{L}\nu _{\mu }\)  4.6  4.6  \(\widetilde{\chi }^0_3 \rightarrow \widetilde{\chi }^0_1 \mathrm{Z} \)  10.3  10.2 
\(\widetilde{\chi }^{+}_2 \rightarrow \widetilde{\tau } _2 \nu _{\tau }\)  5.1  5.1  \(\widetilde{\chi }^0_3 \rightarrow \widetilde{\chi }^0_2 \mathrm{Z} \)  23.2  23.2 
\(\widetilde{\chi }^{+}_2 \rightarrow \widetilde{\nu } _\mathrm{e}\)e\(^+\)  1.7  1.7  \(\widetilde{\chi }^0_3 \rightarrow \widetilde{\chi }^0_1 \mathrm{h}^0 \)  2.2  2.2 
\(\widetilde{\chi }^{+}_2 \rightarrow \widetilde{\nu } _{\mu } \mu ^+\)  1.7  1.7  \(\widetilde{\chi }^0_3 \rightarrow \widetilde{\chi }^0_2 \mathrm{h}^0 \)  1.2  1.2 
\(\widetilde{\chi }^{+}_2 \rightarrow \widetilde{\nu } _{\tau } \tau ^+\)  2.5  2.5  \(\widetilde{\chi }^0_4 \rightarrow \widetilde{\tau } _2^{\pm } \tau ^{\mp }\)  3.2  3.2 
\(\widetilde{\chi }^{+}_2 \rightarrow \widetilde{\chi }^0_1 \mathrm{W}^{+} \)  7.8  7.7  \(\widetilde{\chi }^0_4 \rightarrow \widetilde{\nu } _\mathrm{e} \nu _\mathrm{e} \)  4.3  4.3 
\(\widetilde{\chi }^{+}_2 \rightarrow \widetilde{\chi }^0_2 \mathrm{W}^{+} \)  28.3  28.3  \(\widetilde{\chi }^0_4 \rightarrow \widetilde{\nu } _{\mu } \nu _{\mu } \)  4.3  4.3 
\(\widetilde{\chi }^{+}_2 \rightarrow \widetilde{\chi }^{+}_1 \mathrm{Z} \)  25.0  25.0  \(\widetilde{\chi }^0_4 \rightarrow \widetilde{\nu } _{\tau } \nu _{\tau } \)  4.3  4.3 
\(\widetilde{\chi }^{+}_2 \rightarrow \widetilde{\chi }^0_1 \mathrm{h}^0 \)  18.8  18.8  \(\widetilde{\chi }^0_4 \rightarrow \widetilde{\chi }^{\pm }_1 \mathrm{W} ^{\mp } \)  51.9  52.0 
\(\widetilde{\chi }^0_4 \rightarrow \widetilde{\chi }^0_1 \mathrm{Z} \)  2.3  2.2  
\(\widetilde{\chi }^0_4 \rightarrow \widetilde{\chi }^0_2 \mathrm{Z} \)  2.0  2.0  
\(\widetilde{\chi }^0_4 \rightarrow \widetilde{\chi }^0_1 \mathrm{h}^0 \)  6.7  6.7  
\(\widetilde{\chi }^0_4 \rightarrow \widetilde{\chi }^0_2 \mathrm{h}^0 \)  15.8  15.9 
Table 4 lists the decay modes of the electroweakinos. The largest branching ratios of about 70 % occur for \(\widetilde{\chi }^{\pm }_1 \rightarrow \widetilde{\tau } _1 \nu _{\tau }\) and \(\widetilde{\chi }^0_2 \rightarrow \widetilde{\tau } _1 \tau \), both always followed by \(\widetilde{\tau } _1 \rightarrow \tau \widetilde{\chi }^0_1 \). Since the \(\widetilde{\tau } _1\) NLSP is only about \(10\,\text {GeV} \) more massive than the \(\widetilde{\chi }^0_1 \) LSP, the \(\tau \) leptons from the \(\widetilde{\tau } _1\) are typically very soft, making these decays challenging to detect. Although the mass splitting between \(\widetilde{\chi }^0_2 \) (\(\widetilde{\chi }^{\pm }_1 \)) and LSP is large enough to allow decays to onshell Z (\(\mathrm{W}^{\pm }\)) bosons, these decay modes occur only at the level of a few percent due to the presence of the light sleptons. Electroweakino production with cascade decays via sleptons has been searched for by ATLAS [15, 16] and CMS [31]. While these searches are sensitive to the mass ranges studied here if either (a) decays proceed democratically via all three lepton flavours or (b) exclusively via a \(\widetilde{\tau } \), but with a mass halfway between chargino1/neutralino2 and the LSP, they rapidly lose sensitivity if the decays proceed predominantly via a light \(\widetilde{\tau } _1\) with a small mass difference, as is the case here. Thus, neither the light sleptons nor the \(\widetilde{\tau } _2\) of the STC scenarios have been probed by the LHC to date.
The heavier neutralinos \(\widetilde{\chi }^0_3 \) and \(\widetilde{\chi }^0_4 \), however, feature sizeable branching ratios to \(\widetilde{\chi }^{\pm }_1 \mathrm{W}^{\pm } \) of about 60 and 50 %, respectively, while the \(\widetilde{\chi }^{\pm }_2 \) decays most frequently to \(\widetilde{\chi }^0_2 \mathrm{W}^{\pm } \), \(\widetilde{\chi }^{\pm }_1 \)Z and \(\widetilde{\chi }^{\pm }_1 \)h\(^0\) with branching fractions of about 30, 25 and 20 %, respectively. Thus, although the \(\widetilde{\tau } _1\) is the NLSP, in particular the heavier electroweakinos have sizeable branching fractions to other final states than the notoriously difficult \(\tau \)lepton. This also means that signatures with electrons or muons in the final state can originate either from slepton or electroweakino production.
2.2 Production cross sections at the LHC
Production cross sections for the benchmark model STC8 at LHC with \(E_{\mathrm {cms}}=14\,\text {TeV} \). The leading order (LO), nexttoleading order (NLO) and the Kfactor between LO and NLO are shown
Process  LO (fb)  NLO (fb)  \(K_\mathrm{NLO/LO}\) 

pp \(\rightarrow \) \(\widetilde{\mathrm{g}}\) \(\widetilde{\mathrm{g}}\)  0.18  0.67  3.58 
pp \(\rightarrow \) \(\widetilde{\mathrm{q}}\) \(\widetilde{\mathrm{q}}\)  5.1  6  1.16 
pp \(\rightarrow \) \(\widetilde{\mathrm{q}}\) \(\widetilde{\mathrm{g}}\)  3  5.4  1.80 
pp \(\rightarrow \) \(\widetilde{\mathrm{q}}\) \(\bar{\widetilde{\mathrm{q}}}\)  16.4  25.4  1.54 
pp \(\rightarrow \) \(\widetilde{\mathrm{b}} _1 \widetilde{\mathrm{b}} _1\)  22.8  38.3  1.67 
pp \(\rightarrow \) \(\widetilde{\mathrm{b}} _2 \widetilde{\mathrm{b}} _2\)  0.2  0.37  1.90 
pp \(\rightarrow \) \(\widetilde{\mathrm{t}} _1 \widetilde{\mathrm{t}} _1\)  37.7  62.7  1.66 
pp \(\rightarrow \) \(\widetilde{\mathrm{t}} _2 \widetilde{\mathrm{t}} _2\)  0.16  0.31  1.94 
pp \(\rightarrow \) \(\widetilde{\ell }_{\mathrm L}\) \(\widetilde{\ell }_{\mathrm L}\)  15.5  19.4  1.25 
pp \(\rightarrow \) \(\widetilde{\ell }_{\mathrm R}\) \(\widetilde{\ell }_{\mathrm R}\)  32.4  41.8  1.29 
pp \(\rightarrow \) \(\widetilde{\nu _{\ell }}\) \(\widetilde{\nu _{\ell }}\)  19.4  24.6  1.26 
pp \(\rightarrow \) \(\widetilde{\ell }\) \(\widetilde{\nu _{\ell }}\)  63.3  79.6  1.26 
pp \(\rightarrow \) \(\widetilde{\tau } _1\) \(\widetilde{\tau } _1\)  59.1  77.4  1.30 
pp \(\rightarrow \) \(\widetilde{\tau } _2\) \(\widetilde{\tau } _2\)  11.7  14.6  1.24 
pp \(\rightarrow \) \(\widetilde{\tau } _1\) \(\widetilde{\tau } _2\)  34.7  44.7  1.28 
pp \(\rightarrow \) \(\widetilde{\nu _{\tau }}\) \(\widetilde{\nu _{\tau }}\)  20.4  25.9  1.26 
pp \(\rightarrow \) \(\widetilde{\tau }\) \(\widetilde{\nu _{\tau }}\)  73.9  93.6  1.26 
pp \(\rightarrow \) \(\widetilde{\chi }^0_1 \widetilde{\chi }^0_1 \)  0.34  0.42  1.25 
pp \(\rightarrow \) \(\widetilde{\chi }^{0}_{i}\) \(\widetilde{\chi }^{0}_{j}\) (except \(\widetilde{\chi }^0_1 \widetilde{\chi }^0_1 \))  15.8  19.6  1.24 
pp \(\rightarrow \) \(\widetilde{\chi }^{\pm }_1 \widetilde{\chi }^{\pm }_1 \)  585  747  1.28 
pp \(\rightarrow \) \(\widetilde{\chi }^{\pm }_{k}\) \(\widetilde{\chi }^{\pm }_{m}\) (except \(\widetilde{\chi }^{\pm }_1 \widetilde{\chi }^{\pm }_1 \))  17.3  20.2  1.17 
pp \(\rightarrow \) \(\widetilde{\chi }^{0}_{1}\) \(\widetilde{\chi }^{\pm }_{1}\)  10.0  12.9  1.29 
pp \(\rightarrow \) \(\widetilde{\chi }^{0}_{1}\) \(\widetilde{\chi }^{\pm }_{2}\)  1.07  1.36  1.27 
pp \(\rightarrow \) \(\widetilde{\chi }^{0}_{2}\) \(\widetilde{\chi }^{\pm }_{1}\)  1170  1492  1.28 
pp \(\rightarrow \) \(\widetilde{\chi }^{0}_{2}\) \(\widetilde{\chi }^{\pm }_{2}\)  3.51  4.33  1.23 
pp \(\rightarrow \) \(\widetilde{\chi }^{0}_{3}\) \(\widetilde{\chi }^{\pm }_{1}\)  6.10  7.63  1.25 
pp \(\rightarrow \) \(\widetilde{\chi }^{0}_{3}\) \(\widetilde{\chi }^{\pm }_{2}\)  22.0  27.0  1.25 
pp \(\rightarrow \) \(\widetilde{\chi }^{0}_{4}\) \(\widetilde{\chi }^{\pm }_{1}\)  3.45  4.25  1.25 
pp \(\rightarrow \) \(\widetilde{\chi }^{0}_{4}\) \(\widetilde{\chi }^{\pm }_{2}\)  24.4  29.8  1.25 
Cross sections of the processes in the model STC10 at LHC with \(E_{\mathrm {cms}}=14\,\text {TeV} \). Only cross sections significantly different from those of STC8 given in Table 5 are listed. The leading order (LO), nexttoleading order (NLO) and the Kfactor between LO and NLO are shown
Process  LO (fb)  NLO (fb)  \(K_\mathrm{NLO/LO}\) 

pp \(\rightarrow \) \(\widetilde{\mathrm{b}} _1 \widetilde{\mathrm{b}} _1\)  4.4  7.7  1.74 
pp \(\rightarrow \) \(\widetilde{\mathrm{t}} _1 \widetilde{\mathrm{t}} _1\)  7.08  12.0  1.72 
Production cross sections for the benchmark model STC8 at the ILC, for different degrees of beam polarisation. The ILC TDR beam spectrum is used with a nominal centreofmass energy is 500\(\,\text {GeV}\). All channels accessible at this energy are shown. Channels with no detectable final states are marked with \((*)\). In addition, the cross section for \( {\, e}^+ {e}^ \rightarrow \widetilde{\mathrm{e}}_{\mathrm{R}} ^+\widetilde{\mathrm{e}}_{\mathrm{L}} ^ (\widetilde{\mathrm{e}}_{\mathrm{L}} ^+\widetilde{\mathrm{e}}_{\mathrm{R}} ^)\) is 335.85 fb for \(\mathcal {P}_{R,R}\)(\(\mathcal {P}_{L,L}\)); for all other processes the cross section vanishes for both \(\mathcal {P}_{L,L}\) and \(\mathcal {P}_{R,R}\)
Process  \(\mathcal {P}_{R,L}\) (fb)  \(\mathcal {P}_{L,R}\) (fb)  \(\mathcal {P}_{+80,30}\) (fb)  \(\mathcal {P}_{80,+30}\) (fb) 

\( {\, e}^+ {e}^ \rightarrow \widetilde{\chi }^0_1\widetilde{\chi }^0_1(*)\)  1203.57  34.47  705.29  62.29 
\( {\, e}^+ {e}^ \rightarrow \widetilde{\chi }^{\pm }_1\widetilde{\chi }^{\mp }_1\)  0.38  259.37  9.30  151.74 
\( {\, e}^+ {e}^ \rightarrow \widetilde{\chi }^0_1\widetilde{\chi }^0_2\)  11.97  206.67  14.24  121.32 
\( {\, e}^+ {e}^ \rightarrow \widetilde{\chi }^0_2\widetilde{\chi }^0_2\)  0.03  115.71  4.07  67.69 
\( {\, e}^+ {e}^ \rightarrow \widetilde{\mathrm{e}}_{\mathrm{L}} \widetilde{\mathrm{e}}_{\mathrm{L}} \)  8.01  84.07  7.63  49.46 
\( {\, e}^+ {e}^ \rightarrow \widetilde{\mathrm{e}}_{\mathrm{R}} \widetilde{\mathrm{e}}_{\mathrm{R}} \)  1313.73  52.32  770.36  76.59 
\( {\, e}^+ {e}^ \rightarrow \widetilde{\mu }_\mathrm{L} \widetilde{\mu }_\mathrm{L} \)  8.05  39.11  6.08  23.16 
\( {\, e}^+ {e}^ \rightarrow \widetilde{\mu }_\mathrm{R} \widetilde{\mu }_\mathrm{R} \)  222.47  52.23  131.97  38.34 
\( {\, e}^+ {e}^ \rightarrow \widetilde{\nu }_\tau \widetilde{\nu }_\tau \)  16.93  22.02  10.67  13.47 
\( {\, e}^+ {e}^ \rightarrow \widetilde{\nu }_e \widetilde{\nu }_e(*)\)  15.86  973.97  43.37  570.33 
\( {\, e}^+ {e}^ \rightarrow \widetilde{\nu }_\mu \widetilde{\nu }_\mu (*)\)  15.93  20.71  10.04  12.67 
\( {\, e}^+ {e}^ \rightarrow \widetilde{\tau }_1 \widetilde{\tau }_1 \)  244.33  77.61  145.65  53.95 
\( {\, e}^+ {e}^ \rightarrow \widetilde{\tau }_1 \widetilde{\tau }_2 \)  5.46  7.10  3.44  4.34 
\( {\, e}^+ {e}^ \rightarrow \widetilde{\tau }_2 \widetilde{\tau }_2 \)  7.14  26.10  5.09  15.52 
\( {\, e}^+ {e}^ \rightarrow \widetilde{\mathrm{e}}_{\mathrm{L}} \widetilde{\mathrm{e}}_{\mathrm{R}} \)  0.00  0.00  127.62  127.62 
The top squark with masses as chosen here will also be produced at the LHC, but it will be difficult to distinguish direct topsquark production from its production in the decay of the gluino (\(\widetilde{\mathrm{g}}\)). The masses of the heavier coloured sparticles, the gluino and the squarks of the first and second generation (\(\widetilde{\mathrm{q}}\)), are chosen such that they will also be produced at reasonably rates at the LHC, and dedicated analyses will be able to detect them with the full luminosity delivered by the LHC.
The by far largest cross section in electroweakino production, above \(1\;\)pb, is obtained for \(\widetilde{\chi }^0_2 \widetilde{\chi }^{\pm }_1 \) production. This channel will therefore certainly be discovered at the LHC, by a multilepton search. The cross sections for other electroweak processes is lower, the largest cross section for neutralino–neutralino production appears for \(\widetilde{\chi }^0_3 \widetilde{\chi }^0_4 \) production with almost \(14\;\)fb. While the lighter electroweakinos could be well discovered at the ILC, the LHC searches would profit from the exact mass and crosssection information of these in order to specifically search for the heavier electroweakinos that would not be accessible at the ILC at a centreofmass energy of 500\(\,\text {GeV}\). One example is the production of \(\widetilde{\chi }^{\pm }_2\), which will be discussed later.
2.3 Production cross sections at the ILC
The key feature of the STCx models for the ILC is the mass spectrum of the sleptons and the lighter electroweakinos, and thus at treelevel STC8 and STC10 are identical from the ILC pointofview. Figure 2 shows the polarised cross sections^{1} for various STC processes in \(e^+e^\) collisions as a function of the centreofmass energy. In the part kinematically accessible at the ILC, they do not differ among the two models. While a few processes open up already below \(E_{\mathrm {cms}}=250\,\text {GeV} \) and thus would be accessible even when running near the Higgsstrahlung threshold, a plethora of thresholds of slepton, sneutrino and electroweakino production appears between \(E_{\mathrm {cms}}=250\) and 500\(\,\text {GeV}\). In most cases, these can be observed and even distinguished from each other in the clean ILC environment. The ability to operate at any desired centreofmass energy between 200 and 500\(\,\text {GeV}\) (or even 1\(\,\text {TeV}\)) and to switch the sign of the beam polarisations are unique tools to identify each of these processes. The low SM background levels allow in many cases a full and unique kinematic reconstruction of cascade decays.
In particular at the ILC running at \(E_{\mathrm {cms}}= 500\,\text {GeV} \), all sleptons and the lighter set of electroweakinos of the STCx scenarios can be produced. \( \widetilde{\chi }^0_3\) and \( \widetilde{\chi }^0_4\) become accessible in associated production around \(E_{\mathrm {cms}}= 600\,\text {GeV} \). Pair production of \( \widetilde{\chi }^{\pm }_2\) appears at around \(E_{\mathrm {cms}}= 850\,\text {GeV} \). At this energy, also pairproduction of \( \widetilde{\chi }^0_3\) and \( \widetilde{\chi }^0_4\) is possible; however because these two states are mainly Higgsino, the rate is very low. At \(E_{\mathrm {cms}}= 500\,\text {GeV} \), the cross sections are sizeable, as can be seen in Table 7. Only one of the kinematically allowed processes, \( {\, e}^+ {e}^ \rightarrow \widetilde{\tau }_1 \widetilde{\tau }_2 \), would have a production cross section below \(10\,\)fb for both beampolarisation configurations. The total SUSY cross section is well over \(1\,\)pb in both cases.
3 LHC projections
The searches for new physics beyond the Standard Model at the LHC are either kept as inclusive as possible, or tailored to search for a specific scenario of new physics. We follow here a representative selection of typical studies, starting with search for an excess of large hadronic activity caused by the heavy new particles, in connection with large missing transverse energy due to the escaping lightest SUSY particles (LSPs). Such searches have been performed by both the ATLAS and the CMS Collaborations based on data taken at 7 and 8\(\,\text {TeV}\) with and without btagging requirements [36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49] in the fullhadronic final state. Exclusive searches for top and bottom squarks rely on the use of special variables, as the production cross section for thirdgeneration sparticles is about an order of magnitude lower than the one for first or secondgeneration squarks of similar mass and the signal is hidden below a large background by SM topquark production. We discuss here a fullhadronic search for direct bottomsquark production, similar to searches performed by both the ATLAS and the CMS Collaborations based on data taken at 7 and 8\(\,\text {TeV}\) [28, 29, 50], where it is assumed that the pairproduced bottomsquark decays directly to a bottom quark and the lightest neutralino which is the LSP. Furthermore, we present the results of a search for direct top squark production in the singlelepton channel, also similar to previously published analyses by CMS and ATLAS [51, 52, 53]. Multilepton searches are sensitive to decays of the electroweakproduced sparticles, e.g. in the case of neutralinochargino production, as discussed for 7 and 8 \(\,\text {TeV}\) by the ATLAS and CMS collaborations [31, 54, 55]. The recent results are interpreted in the SMS approach which reflects a best case scenario, assuming a branching ratio of 100 % for one specific decay. In nature the 100 % are not realised, as also shown for our benchmark models in Table 2. For such cases the bounds for the chargino and neutralinos are weaker. We also present the results of a multilepton search and the possible interpretation in the case of a signal by the discussed model. We note that a large variety of search modes for 3rd generation squarks has also been discussed in phenomenological papers, including for instance [56, 57, 58, 59, 60]. However, these are not directly applicable to the scenario under study in this paper.
LHC allhadronic inclusive search: background and signal event yields corresponding to 300\(\,\text {fb}^\text {1}\). The notation “V” refers to W, Z and \(\gamma \). Four signal regions (SR) are shown here
Signal regions  \(\mathrm{t}\overline{\mathrm{t}}\) + jets  V + jets  VV + jets  Top + jets  Total SM  STC8  STC10 

SR A:  
\(H_{\mathrm {T}}\) \(>\) 2000 GeV; MHT \(>\)1500 GeV  0.29  43  2.1  0.01  45  45  35 
SR B:  
\(H_{\mathrm {T}}\) \(>\) 2000 GeV; MHT \(>\) 1000 GeV; n(Bjets) \(\ge \) 2  4.4  14  0.92  0.15  20  51  35 
SR C:  
\(H_{\mathrm {T}}\) \(>\) 3500 GeV; MHT \(>\) 1000 GeV  0.49  9.5  0.54  0.01  10  8.4  7.6 
SR D:  
\(H_{\mathrm {T}}\) \(>\) 3000 GeV; MHT \(>\)1500 GeV  0.1  6.3  0.41  0.002  6.8  8.2  7.2 
About 10–100 million events per background process that were produced for the Snowmass effort [64] with Madgraph5 [65], including up to four extra partons from initial and final state radiation, matched to Pythia6 for fragmentation and hadronisation, are used in this paper. The background cross section is normalised to nexttoleading order (NLO) in the background production process, which is based on the work in preparation for the Snowmass summer study 2013 and discussed in more detail in Refs. [64, 66, 67]. While we studied all the major sources of background events, background processes with low cross sections that might become relevant at 3000\(\,\text {fb}^\text {1}\) are not included. The signal samples are generated with Pythia6 and passed through the Delphes simulation. For Pythia6 the tune \(\mathrm {Z2}^{*}\) [68] is used. The signal cross sections are calculated at NLO with Prospino2 [32, 33].
Assuming systematic uncertainties of the same order as in the existing 8\(\,\text {TeV}\) analyses, we determine for each search the discovery sensitivity, using the Binomial significance \(Z_{\mathrm {Bi}}\) [69, 70, 71] in Roostats [72]. Here, the sensitivity is calculated in a frequentist way in onesided Gaussian standard deviations, performing a hypothesis test between backgroundonly and signalplusbackground, where the uncertainty on the background estimate is taken as Poisson distributed.
3.1 Fullhadronic search
Heavy squark and gluino production in Rparity conserving SUSY scenarios can lead to long decay chains with multiple jets and therefore a large amount of hadronic energy, and large missing transverse momentum. A typical search for such a scenario is based on the variable \(H_{\mathrm {T}}\), the scalar sum of the momenta of all jets with \(p_{\mathrm {T}} > 50\,\text {GeV} \) and \(\eta  < 2.5\), and missing hadronic transverse energy (MHT), which is defined as absolute value of the negative vectorial sum of all jets with \(p_{\mathrm {T}} > 30\,\text {GeV} \) and \(\eta  <5\). The SM background to this SUSY search arises mainly from the following processes: Z(\(\nu \nu \)) + jets events, and W(\(l\nu \)) + jets events from W, or \(\mathrm{t}\overline{\mathrm{t}}\) + jets, where at least one W boson decays leptonically. The W(\(l\nu \)) + jets events pass the search selection when the e/\(\mu \) escapes detection or when a top decays hadronically. QCD multijet events also contribute to the background when jetenergy mismeasurements or leptonic decays of heavyflavour hadrons inside jets produce large MHT. However, the QCD background generally becomes negligible at very high MHT as required here.
The recent searches by the CMS Collaboration split the events from the baseline selection into several exclusive search regions according to their \(H_{\mathrm {T}}\), MHT and btag multiplicity, while for this study we keep only four wellmotivated signal regions listed in Table 8. The most promising signal region targeting the inclusive production of heavy gluinos and squarks of all generations is SR A, where we require \(H_{\mathrm {T}} > 2000\,\text {GeV} \) and MHT \(>\)1500 GeV. Figure 3a, b shows the \(H_{\mathrm {T}}\) and MHT distribution for this selection. Two other signal regions, SR C and SR D, are characterised by higher \(H_{\mathrm {T}}\) requirements and reject too much signal, which could be taken as a hint on the (not too high) squark or gluino mass. In SR A we find 45 (35) signal events for STC8 (STC10) over 45 background events for an integrated luminosity of 300\(\,\text {fb}^\text {1}\). About 80 % of these signal events are first and secondgeneration squarks. Assuming a systematic uncertainty of 20 %, we determine a discovery sensitivity of about 3\(\,\sigma \).
Another signal region, SR B, defined by \(H_{\mathrm {T}} > 2000\,\text {GeV} \), MHT \(>\) 1000\(\,\text {GeV}\) and \(N_\text {btags} \ge 2\), is tailored to SUSY signals with a light third generation, being sensitive to either gluinos decaying through (virtual) top or bottom squarks or to directly produced thirdgeneration squarks. The results for this signal region are shown in Fig. 3c, d. We find 51 (35) signal events in STC8 (STC10), expecting 20 background events for 300\(\,\text {fb}^\text {1}\). A discovery sensitivity of 5\(\,\sigma \) will be reached with 200\(\,\text {fb}^\text {1}\), assuming a systematic uncertainty of 20 %. The signal consists mainly of gluinoassociated (\(\widetilde{\mathrm{g}}\) \(\widetilde{\mathrm{g}}\) and \(\widetilde{\mathrm{g}}\) \(\widetilde{\mathrm{q}}\)) and direct heavysquark production (about \(65\,\%\) of the final events).
Further studies of the kinematic variables may shed more light on the nature of the new physics seen in this scenario and are discussed in the following sections.
3.2 Search for direct bottomsquark production in the final states with two bquark and missing energy
In this section, we investigate the discovery potential for thirdgeneration squarks in the final state with two bjets and missing energy in the LHC. Of particular interest for this search is the decay \(\widetilde{\mathrm{b}} _1 \rightarrow \) b\(\widetilde{\chi }^0_1\), which is the dominant decay mode of bottom squark in the investigated models, with branching fractions of more than 50 %. Assuming that the bottom squarks are pairproduced, a final state containing exactly two bquarks and two neutralinos is expected for about 25 % of the signal events. As the masses of the \(\widetilde{\chi }^{\pm }_1\) and the \(\widetilde{\chi }^0_1\) are not degenerate, the contribution of the top squark to this final state is small the STCx models.
By vetoing events with at least one lepton with \(p_{\mathrm {T}} > 10\,\text {GeV} \), we suppress the main standardmodel background processes such as \(\mathrm{t}\overline{\mathrm{t}}\) and \(\mathrm{W+jets}\). The distribution of the missing energy for the events passing the above requirement is shown in Fig. 4c. We require missing transverse energy to be \(E_{\mathrm {T}}^{\text {miss}} >450\,\text {GeV} \).
3.3 Search for direct topsquark production in the singlelepton channel
In this section, we discuss the search for direct topsquark pair production. Previously conducted searches by the CMS collaboration [53] focus on simplified SUSY models, where only the process of interest is considered while all other sparticles masses are assumed to be out of reach. In these simplified models two top squarks are produced, which decay into either t\(\widetilde{\chi }^0_1\) or b\(\widetilde{\chi }^{\pm }_1\), with varying branching ratios. The two STC models considered here, however, only a very small fraction of events where two top squarks are produced exhibit the soughtafter decay process. As an example, in the STC8 model only 1.6 % of \(\widetilde{\mathrm{t}} _1\widetilde{\mathrm{t}} _1^*\) events are expected to have a decay mode \(\widetilde{\mathrm{t}} _1\widetilde{\mathrm{t}} _1^*\rightarrow (\mathrm{t} \widetilde{\chi }^0_1)(\bar{\mathrm{t}}\widetilde{\chi }^0_1)\).
Additionally, bottomsquark pair production enters as a sizeable intrinsic SUSY background when one of the bottom squarks decays to b\(\widetilde{\chi }^0_1\) and the other one decays to t\(\widetilde{\chi }^{\pm }_1\). Gluino and squark production also enter as an intrinsic background with top quarks in the decay chain resulting in similar signatures as expected for the process of interest. Thus, we face two major challenges in this analysis, one being a large SM background and the other one being the background from other SUSY processes.
The analysis method follows the aforementioned search performed by the CMS collaboration at 8\(\,\text {TeV}\) [53], but with tighter selection requirements. We require a single isolated electron or muon with \(p_{\mathrm {T}} > 30\,\text {GeV} \) and \(\eta  < 2.4\). Events are vetoed if there are additional isolated leptons with \(p_{\mathrm {T}} > 20\,\text {GeV} \). In addition, we require at least five jets with \(p_{\mathrm {T}} > 40\,\text {GeV} \) and \(\eta  < 2.4\), which enhances the fraction of \(\widetilde{\mathrm{t}} _1\widetilde{\mathrm{t}} _1^*\) events with respect to \(\widetilde{\mathrm{b}} _1\widetilde{\mathrm{b}} _1^*\) events. One or two of these jets must satisfy at least a medium btag requirement. To further reduce the SM background, we require \(E_{\mathrm {T}}^{\text {miss}} > 400\) \(\,\text {GeV}\).
Additionally, we introduce an angular variable \(\min \Delta \phi \), the minimum azimuthal angle between the leading or subleading jet and the \(E_{\mathrm {T}}^{\text {miss}}\). For this variable we require events to have a value greater than 0.8 in order to reduce backgrounds from SM processes. Another variable that aids in reducing backgrounds is centrality, defined as the sum of the \(p_{\mathrm {T}}\) of the lepton and jets divided by their total momentum \(\frac{\sum _i{\mathrm{jet}_i(p_{\mathrm {T}})}+\mathrm{lepton}(p_{\mathrm {T}})}{\sum _i{\mathrm{jet}_i(p)}+\mathrm{lepton}(p)}\). For SUSY events we expect this variable to be shifted towards higher values, while SM backgrounds are less central. Events are selected that satisfy centrality \(>\)0.6.
After requiring the transverse mass, \(m_{\mathrm {T}} \), calculated with Eq. (1) for the system consisting of the lepton \(p_{\mathrm {T}}\) and the missing transverse momentum vector, to satisfy \(m_{\mathrm {T}} > 260\,\text {GeV} \), the background arises predominantly from two sources: \(\mathrm{t}\overline{\mathrm{t}}\) events in which both W bosons decay leptonically but one lepton is lost, and diboson events. In order to suppress the \(\mathrm{t}\overline{\mathrm{t}}\) background, we require \(m_{\mathrm {T2}}^\mathrm{{\mathrm{W}}} \), defined as the minimum “mother” particle mass compatible with all the transverse momenta and massshell constraints [73], to be above 260\(\,\text {GeV}\). By construction, for the dilepton \(\mathrm{t}\overline{\mathrm{t}}\) background without mismeasurement effects, \(m_{\mathrm {T2}}^\mathrm{{\mathrm{W}}} \) has an endpoint at the top quark mass, while for semileptonic \(\mathrm{t}\overline{\mathrm{t}}\) events and signal it has a large tail. Figure 5 shows the \(\Delta \phi \), centrality, \(m_{\mathrm {T}} \), and the \(m_{\mathrm {T2}}^\mathrm{{\mathrm{W}}} \) distributions after all previously mentioned selection criteria are applied, except on the variables themselves. A cutflow can be found in the Appendix, in Table 11.
After all selection requirements, we find for 300\(\,\text {fb}^\text {1}\) 155 (STC8) and 113 (STC10) signal events with a very low background of 28 events. Assuming a systematic uncertainty of 15 %, the STC8 model could be discovered with 5 \(\sigma \) with an integrated luminosity of 25\(\,\text {fb}^\text {1}\), and STC10 with 40\(\,\text {fb}^\text {1}\). While the search targets direct topsquark pair production, the final composition of the selected events contains only about 42 % of this type for STC8 and 23 % for STC10. The additional events originate from squarkgluino production and bottomsquark pair production.
3.4 Search in the multilepton channel
In the STCx models, the cross section for direct \(\widetilde{\chi }^0_2\) \(\widetilde{\chi }^{\pm }_1\) production in proton–proton collisions amounts to more than 1 pb. The golden channel for the discovery of this process is the multilepton channel, with final states containing three or more prompt leptons. The leptons for the signal are produced by slepton mediated decays or by leptonic decays of W or Z bosons which are produced in the decay chain. However, in the STC8 model the \(\widetilde{\tau } _1\) is the NLSP and almost mass degenerated with \(\widetilde{\chi }^0_1\), leading to soft leptons in the dominant decay modes of \(\widetilde{\chi }^0_2\) and \(\widetilde{\chi }^{\pm }_1\) decays via \(\widetilde{\tau } _1\) (cf. Table 4). Most of these leptons will not pass the selection criteria, and thus we expect only a small sensitivity to these decay modes.
In the following we define the lepton to be either an isolated muon or an isolated electron, which includes the leptonic decay modes of the \(\tau \) leptons. As hadronic decays of \(\tau \) leptons are not optimally modelled in the used Delphes version, we do not consider these here. All leptons must have a transverse momentum \(p_{\mathrm {T}} > 10\,\text {GeV} \). In order to comply with the trigger, the leading (subleading) lepton must satisfy \(p_{\mathrm {T}} > 25\,\text {GeV} \) (15\(\,\text {GeV}\)). We present here the analysis of the threelepton final state requiring exactly three leptons. The analysis of events with four or more leptons does not increase the sensitivity and is not discussed further.
The WZ and ZZ production are summarised as VV background. Nonprompt backgrounds cover all events which include leptons from misidentified objects (also known as ‘fake’ sources), or leptons which are not produced by the hard scattering. For example, dileptonic decays of \(\mathrm{t}\overline{\mathrm{t}}\), where one of the bjets produces an isolated lepton, leads to final states with three leptons. All other processes which contribute to the three or fourlepton final states, e.g. SM Higgsboson production or tripleboson production, are summarised as rare backgrounds. The signal is subdivided into four production mechanisms, the direct charginoneutralino production of the secondlowest mass electroweakinos \(\widetilde{\chi }^0_2\) \(\widetilde{\chi }^{\pm }_1\), and the production of at least one highermass chargino, \(\widetilde{\chi }^{\pm }_2\), summarised as \(\widetilde{\chi }^{\pm }_2\) \( \widetilde{\chi }^n_{m}\). Other direct production modes of charginos and/or neutralinos are comprised in ‘other EWK’, while we label all events from other sources than electroweakino production, such as sleptonpair production or production of coloured SUSY particles, as ‘noEWK’.
Overall we define 45 independent search regions, which are listed in the Appendix in Table 12 and which all contribute to the final sensitivity. The applied uncertainties include lepton uncertainties (3 % per lepton), uncertainties on the \(E_{\mathrm {T}}^{\text {miss}}\) shape (15–25 %) and uncertainties of the MC statistics (0–30 %). When combining all search regions, we can discover STC8 with less than 200\(\,\text {fb}^\text {1}\). The most sensitive individual regions are at medium \(m_{\mathrm {T}}\) (200–400\(\,\text {GeV}\)) and medium \(E_{\mathrm {T}}^{\text {miss}}\) (200–400\(\,\text {GeV}\)), either requiring m\(_{\, \ell ^+ \ell ^}\) to be around the Zboson mass, which is mainly driven by direct \(\widetilde{\chi }^0_2\widetilde{\chi }^{\pm }_1\) production followed by \(\widetilde{\chi }^0_2 \rightarrow Z \widetilde{\chi }^0_1\), or for m\(_{\, \ell ^+ \ell ^}\) higher than the Zboson mass. In the latter signal region longchain decays of the highermass neutralinos and charginos give important contributions, whereas the role of decays of the \(\widetilde{\chi }^0_2\) via smuon or selectron is reduced due to their kinematic edge at m\(_{\, \ell ^+ \ell ^}< 110\,\text {GeV} \).
4 ILC projections
Due to the clean conditions at an \(e^+e^\) collider, the searches for SUSY at the ILC are exclusive, with separate analyses adapted to each specific channel searched for.
Beyond sleptonpair production, we summarise the results from previous studies performed on similar benchmark models and discuss them in the context of STCx. Most of these studies have been performed in full Geant4based simulation of the ILD detector concept, using samples simulated for the ILD LoI [77].
4.1 Analysis of direct electroweakino production
At the ILC, direct electroweakino production occurs at rates in the order of 100 pb, cf. Fig. 2. At a centreofmass energy of \(500\,\text {GeV} \), \( \widetilde{\chi }^0_1\) \( \widetilde{\chi }^0_1\), \( \widetilde{\chi }^0_1\) \( \widetilde{\chi }^0_2\), \( \widetilde{\chi }^0_2\) \( \widetilde{\chi }^0_2\) and \( \widetilde{\chi }^{\pm }_1\) \( \widetilde{\chi }^{\pm }_1\) are kinematically accessible in the STCx scenarios. By measuring their polarised production cross sections and the masses of the involved sparticles, the parameters of the electroweakino sector (\(M_1\), \(M_2\), \(\mu \), \(\tan {\beta }\)) can be determined [78], given sufficient precision of the experimental observations.
As a particular challenge of the STCx models, the \( \widetilde{\chi }^0_2\) and \( \widetilde{\chi }^{\pm }_1\) decay dominantly via the \( \widetilde{\tau }_1\) NLSP. Nevertheless, almost all electroweakinos have branching fractions at the few percent level to other final states than the notoriously difficult \(\tau \) lepton. The use of beam polarisation and tunable \(E_{\mathrm {cms}}\) will further enhance the power of the observations and allow to disentangle production modes with very similar final states.
4.1.1 \( \widetilde{\chi }^0_1\) \( \widetilde{\chi }^0_2\) production
The dominating decay \( \widetilde{\chi }^0_2\rightarrow \widetilde{\tau }_1\tau \), with a branching ratio of about 70 %, leads to the same final state content (\(\tau ^+\tau ^ \widetilde{\chi }^0_1 \widetilde{\chi }^0_1\)) as for \( \widetilde{\tau }_1\) pair production. However, they can be disentangled by their different beam polarisation dependency and kinematic properties. The di\(\tau \) invariant mass can be employed to measure the mass of the \( \widetilde{\chi }^0_2\). This channel has been studied based on fourvector smearing, indicating that precisions of 12\(\,\text {GeV}\) could be achievable [79]. In our scenario, the di\(\tau \) final state also receives background from \( \widetilde{\chi }^{\pm }_1 \widetilde{\chi }^{\pm }_1 \rightarrow \widetilde{\tau }_1\nu _{\tau } \widetilde{\tau }_1\nu _{\tau }\), which features a similar cross section \(\times \) BR at \(E_{\mathrm {cms}}=500\,\text {GeV} \). The two processes can in principle be disentangled by the different kinematic features, but the achievable resolutions would need to be studied. However, thanks to the tunable centreofmass energy of the ILC, this problem can be avoided altogether by collecting data below the threshold for charginopair production, in our case e.g. between \(E_{\mathrm {cms}}=350\) and 400 GeV, or by scanning the \( \widetilde{\chi }^0_1\) \( \widetilde{\chi }^0_2\) production threshold.
More recently, it has been shown in full Geant4based simulation of the ILD detector that the contribution from \( \widetilde{\chi }^0_1 \widetilde{\chi }^0_2\rightarrow \mu \mu \widetilde{\chi }^0_1 \widetilde{\chi }^0_1\), which is about a factor of 10 smaller, leads to competitive mass and crosssection measurements. Figure 7 shows for instance the invariant mass spectrum of the two muons before [(a), signal is scaled by a factor of 100] and after event selection (b). From this channel alone, the mass of the \( \widetilde{\chi }^0_2\) can be determined to a precision of about \(1\,\text {GeV} \) for an integrated luminosity of 500\(\,\text {fb}^\text {1}\) collected with \(\mathcal {P}_{80,+60}\), depending on the assumed precision for the mass of \(\widetilde{\mu }_\mathrm{R} \) and \( \widetilde{\chi }^0_1\) [80].
Within the same study, the corresponding uncertainty on \(\sigma ( {\, e}^+ {e}^ \rightarrow \widetilde{\chi }^0_1 \widetilde{\chi }^0_2)\times BR( \widetilde{\chi }^0_2\rightarrow \mu \mu \widetilde{\chi }^0_1)\) has been determined to about \(20\,\%\), while the precision on \(\sigma ( {\, e}^+ {e}^ \rightarrow \widetilde{\chi }^0_1 \widetilde{\chi }^0_2)\times BR( \widetilde{\chi }^0_2\rightarrow \tau \tau \widetilde{\chi }^0_1)\) has been estimated to \(2\,\%\) [79]. We thus conclude that the corresponding studies of the di\(\tau \) channel should be repeated with uptodate simulation of the expected detector and accelerator performance.
4.1.2 \( \widetilde{\chi }^{\pm }_1\) \( \widetilde{\chi }^{\pm }_1\) production
As discussed above, the final states of \( \widetilde{\chi }^{\pm }_1\) pair production will be dominated by di\(\tau \) plus missing fourmomentum final states from \( \widetilde{\chi }^{\pm }_1 \rightarrow \widetilde{\tau }_1 \nu _{\tau }\) or \( \widetilde{\chi }^{\pm }_1 \rightarrow \widetilde{\nu } _{\tau } \tau \) followed by an invisible decay of \(\widetilde{\nu } _{\tau }\), thus be similar to those from \( \widetilde{\chi }^0_1 \widetilde{\chi }^0_2\). While at \(E_{\mathrm {cms}}=500\) \(\,\text {GeV}\) the cross section \(\times \) BR should be clearly measurable above the \( \widetilde{\chi }^0_1 \widetilde{\chi }^0_2\) background, especially once the latter is known from running below the \( \widetilde{\chi }^{\pm }_1\) \( \widetilde{\chi }^{\pm }_1\) threshold, kinematic mass reconstruction in this channel needs further study, like in the case of \( \widetilde{\chi }^0_1 \widetilde{\chi }^0_2\). However, there are several alternatives to measure the mass:
On one hand, the \( \widetilde{\chi }^{\pm }_1\) features a branching ratio of about \(7\%\) to \( \widetilde{\chi }^0_1W^{\pm }\). Events where this decay, followed by \(W \rightarrow q \bar{q}'\), occurs for one of the \( \widetilde{\chi }^{\pm }_1\), while the other could e.g. decay to \( \widetilde{\tau }_1 \nu _{\tau }\), give a very unique signature. The edges in the energy spectrum of the W bosons can then be used to determine the mass of the \( \widetilde{\chi }^{\pm }_1\) if the \( \widetilde{\chi }^0_1\) mass is known (see Sect. 4.2). This reconstruction method has been studied in full detector simulation by ILD [77, 81] and SiD [82] for a SUSY scenario where the sleptons are heavier than the electroweakinos and thus both \( \widetilde{\chi }^{\pm }_1 \rightarrow \widetilde{\chi }^0_1 W\) and \( \widetilde{\chi }^0_2 \rightarrow \widetilde{\chi }^0_1 Z\) have branching ratios close to unity. These studies achieved mass resolutions of about \(1.5~\%\) for the \( \widetilde{\chi }^{\pm }_1\) based on \(125 \times 10^3\) \( \widetilde{\chi }^{\pm }_1 \rightarrow \widetilde{\chi }^0_1 W\) decays, assuming the \( \widetilde{\chi }^0_1\) mass is known from another source. In STCx, with an integrated luminosity of 500\(\,\text {fb}^\text {1}\), only \(11 \times 10^3 \) decays would be available and the \( \widetilde{\chi }^0_1\) mass would be known to permille level precision from sleptonpair production, cf. Sect. 4.2.1. However, backgrounds would also be lower, since (a) the branching ratio for \( \widetilde{\chi }^0_2 \rightarrow \widetilde{\chi }^0_1 Z\) is 100 times lower than in the original scenario of these studies and (b) the dominating SM background does not originate from fully hadronic W pairs anymore, but from semileptonic ones, where the charge of the lepton in conjunction with the forward–backward asymmetry provides an additional, very effective suppression mechanism [83]. But even neglecting these expected benefits, the pure scaling according to the number of decays yields a projected uncertainty of \(5~\%\) on the \( \widetilde{\chi }^{\pm }_1\) mass. With the full running program of the ILC [27], this would shrink to about \(2.5~\%\).
In addition, the decays \( \widetilde{\chi }^{\pm }_1 \rightarrow \widetilde{\nu } _e e\) and \( \widetilde{\chi }^{\pm }_1 \rightarrow \widetilde{\nu } _{\mu } \mu \) give important information not only on the \( \widetilde{\chi }^{\pm }_1\) mass, but also on the mass of the mostly invisible \(\widetilde{\nu } \). Since the mass difference between \( \widetilde{\chi }^{\pm }_1\) and \(\widetilde{\nu } \) is only 10\(\,\text {GeV}\), lower as well as the upper edge of the lepton energy spectrum are significantly below the lower edge from pair production of the lefthanded sleptons (cf. 4.2.1), at 8 and 16\(\,\text {GeV}\), respectively. Pair production of the righthanded selectrons is heavily suppressed by the appropriate choice of beam polarisation. Selectron and smuon backgrounds can be reduced further by selecting chargino decays to different lepton flavours in the two decay chains of an event. While \( \widetilde{\tau }_1\)pair production leads to different flavour leptons in the final state, the decay leptons of the \(\tau \) decays will be distributed over a wide range of energies (cf. Fig 12), whereas the signal leptons lead to a sharpedged, narrow box with the above edge positions. With the branching ratios of STCx, about \(20 \times 10^3 \) decays to \(\widetilde{\nu } _{\ell } \ell \) will be available from 500\(\,\text {fb}^\text {1}\) of data. Since this is similar in size to the available statistics for e.g. the \(\widetilde{\mu }_\mathrm{L} \) (cf. Sect. 4.2.1), with steeper edges due to the smaller range of lepton energies, a precision of \(1~\%\) or better should be achievable for both the \( \widetilde{\chi }^{\pm }_1\) and the \(\widetilde{\nu } \) mass.
4.1.3 Radiative \( \widetilde{\chi }^0_1\) \( \widetilde{\chi }^0_1\) production
As can be seen in Fig. 8, the statistical precision, here from a template fit to the energy spectrum of the ISR photons, is much lower already with this rather modest luminosity assumed in the study. A more detailed analysis of the impact of the beam energy spectrum should be performed in the future.
4.2 Analysis of direct slepton production

only two leptons in the final state

large missing energy and momentum

large acollinearity, with little correlation to the energy of the lepton

central production

no forward–backward asymmetry
These considerations lead to the following selection criteria, valid for all slepton studies: The events should contain less than 10 charged particles, and two lepton candidates. The total charge should vanish, while each of the leptoncandidates should have opposite charge. The mass of each of the candidates should be less than \(M_\tau \). The total visible energy in the event, \(E_{\mathrm {vis}}\), should not exceed 300\(\,\text {GeV}\), and the missing mass, \(M_\mathrm {miss}\), should be larger than 200\(\,\text {GeV}\). No particle in the event should have momentum above 180\(\,\text {GeV}\). Leptoncandidates are found using the DELPHI \(\tau \)finder [17], which is designed to identify both isolated electrons or muons, and decays of \(\tau \) leptons. It is also robust against extra activity in the detector coming from beambeam effects and overlaid low\(p_{\mathrm {T}}\) \(\gamma \gamma \) events.
4.2.1 Selectrons and smuons
Figure 9 shows the spectra of electron energies in selected dielectron events after collecting 500\(\,\text {fb}^\text {1}\) of data for each of the beampolarisations \(\mathcal {P}_{80,+30}\) and \(\mathcal {P}_{+80,30}\). The \(\widetilde{\mathrm{e}}_{\mathrm{R}} \) signal stands out above quite small SM and SUSY background for beampolarisation \(\mathcal {P}_{+80,30}\). The \(\widetilde{\mathrm{e}}_{\mathrm{L}} \) signal is less clean both due to smaller signal cross section (cf. Fig. 2), larger background and lower efficiency, but is nevertheless quite prominent. In particular, both edges are detectable. This will still be the case even for substantially smaller branching ratios for the direct decay to lepton and LSP, compatible with LHC limits.
The position of the edges is determined by subdividing the full data sample in subsets, and finding the most and least energetic lepton in each subset, after excluding a certain fraction of the extreme cases. The size of the subsamples, and the fraction to be excluded is optimised to yield the lowest possible uncertainty on the endpoints. The resulting endpoints averaged over the subsamples show a bias. This bias has been corrected for by means of a toy Monte Carlo procedure; the uncertainty on the SUSY masses is determined with this procedure as well. In this way, we obtain \(M_{\widetilde{\chi }^0_1} = 95.47 \pm 0.16\,\text {GeV} \) and \( M_{ \widetilde{e}_r} = 126.20 \pm 0.21\,\text {GeV} \) from the \(\widetilde{\mathrm{e}}_{\mathrm{R}} \) spectrum. The true masses in STCx are \(M_{\widetilde{\chi }^0_1} =95.59\,\text {GeV} \) and \(M_{\widetilde{\mathrm{e}}_{\mathrm{R}}} = 126.24\,\text {GeV} \).
In addition to the mass determination from the spectrum edges, the mass of both \(\widetilde{\mathrm{e}}_{\mathrm{R}}\) and \(\widetilde{\mu }_\mathrm{R}\) can be determined by scanning the production threshold near \(250\,\text {GeV} \), as illustrated by Fig. 11. Close to threshold, the cross section is obviously small, but on the other hand, the signal is very clean: since the sleptons are produced almost at rest, and they undergo twobody decays, the decay products are almost monoenergetic. In addition, in STCx the massdifference between the LSP and \(\widetilde{\mathrm{e}}_{\mathrm{R}}\) and \(\widetilde{\mu }_\mathrm{R}\) is rather large, so that even in a decay at rest the produced leptons have momentum \(\sim \)25\(\,\text {GeV}\). Hence, by selecting events with two oppositesign, sameflavour leptons with large acoplanarity, and with momentum in a narrow window, a large efficiency, low background sample can be obtained, and an significant excess of events can be obtained quite close to the threshold. For STCx, it was demanded that the two leptons should have momentum between 20 and 37\(\,\text {GeV}\), and both the acoplanarity and the acollinearity angles should be below 3.1 radians. With these cuts, the efficiency for the signal is between 85 and 95 %, and the signaltobackground ratio is above 1 for almost all points, the exception being the lowest \(E_{\mathrm {cms}}\) for the \(\widetilde{\mu }_\mathrm{R}\).
Sleptons are scalars – if not the new physics the observations have revealed is not supersymmetry. Therefore, it is certain that sleptonpairs are produced in a Pwave, and hence that the rise of the cross section with increasing \(E_{\mathrm {cms}}\) is proportional to \(\beta ^3 = \left[ 1  4 \left( { M_{\widetilde{\ell }} / E_{\mathrm {cms}}} \right) ^2 \right] ^{3/2} \). Investing a few months of ILC beamtime,^{4} the mass of \(\widetilde{\mathrm{e}}_{\mathrm{R}}\) can be determined to \(\sim \) \(190\,\text {MeV} \), and at the same time that of \(\widetilde{\mu }_\mathrm{R}\) to \(\sim \) \(220\,\text {MeV} \), by fitting the observed backgroundsubtracted cross section to \(\beta ^3( E_{\mathrm {cms}})\).
In addition, one can test the hypothesis that the observed states are spin1/2 particles, rather than scalars. If the particles indeed have spin1/2, the pairs are produced in an Swave, and the rise of the cross section with increasing \(E_{\mathrm {cms}}\) would be proportional to \(\beta \) rather than \(\beta ^3\). The dashed curve in Fig. 11 is the best fit of \(\beta ( E_{\mathrm {cms}})\) to the data. For the \(\widetilde{\mathrm{e}}_{\mathrm{R}}\) case the fitprobability is \( <\) \( 10^{9}\), while it is \(7\times 10^{5}\) in the \(\widetilde{\mu }_\mathrm{R}\) case. The spin1/2 hypothesis would therefore be excluded by the data.
4.2.2 The \(\widetilde{\tau }\)sector
Especially in \(\widetilde{\tau }\)coannihilation scenarios, a precise determination of the \(\widetilde{\tau }\) sector is essential in order to be able to predict the expected relic density with sufficient precision to test whether the \( \widetilde{\chi }^0_1\) is indeed the dominant Dark Matter constituent. The \( \widetilde{\tau }_1\)pair production is different from \(\widetilde{\mathrm{e}}_{\mathrm{R}}\) or \(\widetilde{\mu }_\mathrm{R} \)pair production in several aspects: The mass difference to the LSP is much smaller, meaning that the \(\tau \) spectrum is softer than the spectrum of the leptons in \(\widetilde{\mathrm{e}}_{\mathrm{R}}\) or \(\widetilde{\mu }_\mathrm{R}\) decays. In addition, \(\tau \) leptons decay, further softening the spectrum of observed particles, and making the particle identification requirements less effective in background suppression. This leads to a signal that much more resembles that of \(\gamma \gamma \) events, but also more resembles diboson events decaying to \(\tau \nu \tau \nu \). The generic slepton selection therefore needs to be supplemented by several further criteria to reduce these sources of background: The requirements on \(E_{\mathrm {vis}}\) and \(M_\mathrm {miss}\) are strengthened to \(<\)120 and \(>\)250 GeV, respectively, and the visible mass, \(M_\mathrm {vis}\), should be below \(M_{Z}5\), which reduces the diboson background. The cosine of the direction of the missing momentum is required to be between \(0.8\) and 0.8, \(M_\mathrm {vis}\) should be above 20\(\,\text {GeV}\), and the total energy observed below 30 degrees to the beamaxis should not exceed 2\(\,\text {GeV}\). This selection reduces the \(\gamma \gamma \) background, which is then further decreased by a cut on the likelihood that the event is a \(\gamma \gamma \) event. Finally, to reduce the SUSY background from \(\widetilde{\mathrm{e}}_{\mathrm{R}}\) or \(\widetilde{\mu }_\mathrm{R}\)pair production, as well as from diboson events, it is required that the event is not identified as a dielectron or dimuon event. With these cuts, the selection efficiency for \( \widetilde{\tau }_1\)pair production is 17 %.
Only the upper endpoint can be measured in \( \widetilde{\tau }_1\) production: due to the decay of the \(\tau \), the lower endpoint is only visible as a knee in the spectrum of the decayproducts of the \(\tau \). Because of the small massdifference between the \( \widetilde{\tau }_1\) and \(\widetilde{\chi }^0_1\), this knee is in a region where the spectrum is strongly distorted by the cuts removing the \(\gamma \gamma \) background. Contrary to the case for \(\widetilde{e}\) or \(\widetilde{\mu }\), the upper kinematic limit is not an edge, but the endpoint of the spectrum of \(\tau \) decayproducts. This endpoint is determined by fitting the background in the region well above the endpoint and then fitting a signal contribution in the data above the extrapolated background fit.
Figure 12 shows the energyspectrum at \(E_{\mathrm {cms}}= 500\,\text {GeV} \) of selected \(\tau \)jets for an integrated luminosity of 500\(\,\text {fb}^\text {1}\), and polarisation \(\mathcal {P}_{+80,30}\). In the case of \( \widetilde{\tau }_1\) production, the endpoint could be determined to be E\(_\mathrm {endpoint}=44.49^{+0.11}_{0.09}\) \(\,\text {GeV}\), corresponding to an uncertainty of \(M_{ \widetilde{\tau }_1}\) of 200\(\,\text {MeV}\), if an uncertainty on the LSP mass of \(\sim \)100\(\,\text {MeV}\) is assumed. Similarly, the \( \widetilde{\tau }_2\) mass could be determined with an uncertainty of 5\(\,\text {GeV}\).
In [83], where a model quite similar to STCx has been studied, it is found that, in addition to \(M_{ \widetilde{\tau }_1}\), the production cross section for both these modes can be determined at the level of 4 %, and the polarisation of \(\tau \)leptons from the \( \widetilde{\tau }_1\) decay, which gives access to the \(\widetilde{\tau }\) and \( \widetilde{\chi }^0_1\) mixing,^{5} could be measured with an accuracy better than 10 % from shape of the \(\pi \) spectrum in the \(\tau \rightarrow \pi ^+\nu _{\tau }\) mode or to better than 5 % by a template fit of \(R=E_{\pi }/E_{jet}\) in the \(\tau ^\rightarrow \rho ^\nu _{\tau } \rightarrow \pi ^ \pi ^0\nu _{\tau }\) (and c.c.) mode.
4.2.3 The sneutrinos
While the vast majority of sneutrino decays proceeds to a completely invisible final state, the \(\widetilde{\nu } _{\tau }\) has a branching fraction of about \(5~\%\) to \( \widetilde{\tau }_1 W\). In this situation there are two possible strategies: (a) search for the completely invisible final state via its recoil against a hard photon from initial state radiation in analogy to Sect. 4.1.3 and (b) select \(\widetilde{\nu } _{\tau }\) pair events where at least one visible decay occurs. Neither case has yet been studied in detailed simulations, but we will sketch the strategies here.
In the case of the ISR recoil, the situation is more difficult than for \( \widetilde{\chi }^0_1\)pair production since the cross section for the lowbackground polarisation \(\mathcal {P}_{+80,30}\) is about one order of magnitude smaller than for the \( \widetilde{\chi }^0_1\) case. At the same time, due to the larger mass of the sneutrinos, the energies of the photons are smaller, thus buried in the steep shoulder of the \( \widetilde{\chi }^0_1\) spectrum [87]. Therefore, the \(\mathcal {P}_{80,+30}\) combination seems more promising. In this case, the sneutrinopair production cross section is an order of magnitude larger than the cross section of \( \widetilde{\chi }^0_1\) pair production, and of roughly the same size as the \( \widetilde{\chi }^0_1\) cross section in the other polarisation, cf. Table 7. The price to pay is a background from SM neutrinopair production which is about a factor of 5 larger than in the \(\mathcal {P}_{+80,30}\) case [84]. This means that the control of systematic uncertainties becomes even more important than in the classic \( \widetilde{\chi }^0_1\) case. However, due to the lower photon energy endpoint, a large part of the photon energy spectrum will be signal free, which should give an excellent possibility to constrain absolute normalisation uncertainties as well as shape uncertainties, arising e.g. due to the finite knowledge of the beam energy spectrum. Therefore, based on the experience from radiative neutralino production, we expect that both crosssection and mass measurements are possible, but would need a quantitative study.
The visible decays of the \(\widetilde{\nu } _{\tau }\) lead to a rather unique final state with a \(\tau \), a (hadronic) W and large missing fourmomentum. SM background from \(WW \rightarrow \tau \nu _{\tau } q \bar{q}'\) as well as the main SUSY background from \( \widetilde{\chi }^{\pm }_1 \widetilde{\chi }^{\pm }_1 \rightarrow \widetilde{\tau }_1 \nu _{\tau } \widetilde{\chi }^0_1 W\) can be reduced very effectively by choosing \(\mathcal {P}_{+80,30}\), since the polarisation dependence for the pure schannel \(\widetilde{\nu } _{\tau }\) is much weaker. Furthermore, both backgrounds feature different kinematics from the signal, since the \(\tau \) and the W stem from different hemispheres, and not from the same as in the signal case, which can be exploited efficiently once the masses of the \( \widetilde{\tau }_1\) and \( \widetilde{\chi }^{\pm }_1\) have been measured. The SM WW background can be further suppressed by exploiting the forward–backward asymmetry [83]. Once a sufficiently clean signal has been selected, the \(\widetilde{\nu } _{\tau }\) mass can be determined from the endpoints of the W energy spectrum (cf. Sect. 4.1.2), based on the \( \widetilde{\tau }_1\) mass measured in direct \( \widetilde{\tau }_1\)pair production as described above. Similar to the ISR recoil case, this analysis seems feasible, but it awaits a detailed simulation study for quantitative conclusions.
Thus, the currently most obvious way to access the \(\widetilde{\nu } \) mass are the \( \widetilde{\chi }^{\pm }_1\) cascade decays discussed in Sect. 4.1.2.
4.3 Analysis of sleptons in cascade decays
A particularly interesting channel for the determination of slepton properties is \( {\, e}^+ {e}^ \rightarrow \widetilde{\chi }^0_2 \widetilde{\chi }^0_2\) and the \( \widetilde{\chi }^0_2\) decay to \(\widetilde{\mu }_\mathrm{R}\) \(\mu \) (or equivalently to \(\widetilde{\mathrm{e}}_{\mathrm{R}} \)e), even if the branching ratio is at the level of a few percent as in STCx. These cascade decays can be fully kinematically constrained at the ILC, and would promise to yield even lower uncertainties on the \(\widetilde{\mu }_\mathrm{R}\) and \(\widetilde{\mathrm{e}}_{\mathrm{R}}\) masses than the threshold scans, of the order of 25\(\,\text {MeV}\). This is estimated on an earlier study in a scenario with about twice as large branching ratios for the considered decay mode, where a precision of \(10\,\text {MeV} \) [88] was found. The corresponding distribution of the reconstructed \(\widetilde{\mu }_\mathrm{R}\) mass is shown in Fig. 13a, including all SM and SUSY backgrounds.
5 LHCILC interplay
In this section, we employ the simulation studies based on the STCx scenarios to illustrate how discoveries and measurements at the LHC and a future linear collider like the ILC could work together to gain as precise knowledge as possible about the origin of the BeyondtheStandardModel (BSM) observations.
5.1 Discoveries at the LHC
By construction, several sectors of the STCx spectra offer discovery opportunities at the LHC. For instance the lefthanded selectron and smuon could be seen early if their branching ratio for the direct decay \(\widetilde{\ell }_{\mathrm L}\rightarrow l \widetilde{\chi }^0_1\) is large, cf. Sect. 2.1. The righthanded sleptons, on the other hand, are much harder to detect at the LHC, due to the – for the same mass values – lower production rates, and in particular in the STCx points due to their smaller mass difference, which leads to softer leptons in the visible final state. The \(\widetilde{\tau } _1\) and \(\widetilde{\tau } _2\) will be very hard to observe.
In the case of STC8, the dedicated search for bottom squarks decaying directly into a bquark jet and the LSP would report a \(5\,\sigma \) deviation from the SM with about 90 \(\,\text {fb}^\text {1}\) (assuming a systematic uncertainty of 15 %). With the higher bottomsquark mass of STC10, however, a substantially larger amount of integrated luminosity, 300\(\,\text {fb}^\text {1}\), would be required. This is due to the fact that the bottomsquark selection has a much higher purity, in particular it is less sensitive to gluinosquark production than the topsquark search. Thus the difference in integrated luminosity required to observe a signal in these channels does not necessarily correlate with the masses of the targeted squarks.
After an integrated luminosity of 150 \(\,\text {fb}^\text {1}\), the multilepton channel would report a \(5\,\sigma \) deviation from the SM in either STC8 or STC10. Since btagging does not play a role in this analysis, it will be highly likely that this deviation is not caused by thirdgeneration partners, but by lighter sparticles, i.e. electroweakinos and/or sleptons. The variation of the excess over the numerous signal regions gives a hint that several different sparticles with sizeable mass differences contribute to the overall signal. For the expected significance shown in Fig. 14 we combine the results of all search regions [89, 90, 91]. The prediction for the nonprompt background is the most controversial part of this analysis, since the fake rate has to be assumed. With the fake rate increased by a factor of 2, the discovery would require an integrated luminosity of 200 \(\,\text {fb}^\text {1}\) instead of 150 \(\,\text {fb}^\text {1}\).
All search channels show strong dependency on systematical uncertainties at different pileup and higher luminosity scenarios, as shown in Fig. 14b, d. In particular the singlelepton stop (Sect. 3.3) and the hadronic searches would profit significantly from an improved understanding of the background level beyond the 15–20 % assumed as default here. The hadronic search requiring two btagged jets (Sect. 3.2) and the hadronic bottomsquark search (Sect. 3.1) are most susceptible to systematic uncertainties. For STC8like masses, they would miss the \(5\,\sigma \)level with 300\(\,\text {fb}^\text {1}\) if the systematic uncertainty on the background was larger than 25 and 30 %, respectively, while in the case of STC10 a \(5\,\sigma \) discovery is only possible if the backgrounds are controlled to better than 15 %. The singlelepton search is, not surprisingly, more robust and would still reach \(5\,\sigma \) with uncertainties of 50 % in the case of STC8 and 40 % in the case of STC10. The sensitivity of the multilepton search depends on the significance in the 45 different search bins. With decreasing systematic uncertainty, the contribution of the low \(m_{\mathrm {T}}\) signal regions gains significance, leading to a steeper rise in the sensitivity for very small systematic uncertainties, as shown in Fig. 14c. However, we expect systematic uncertainties of the order of 20 % for this analysis.
5.2 Signal characterisation at the LHC
Once a clear deviation from the SM has been discovered, the immediate question will be the origin of this deviation. Given the fact that at this stage neither the masses of the produced sparticles, nor their decay chains and branching ratios are known, it seems highly unlikely that the contributing production modes could be identified at that stage.
The most promising candidates for isolation of a sufficiently pure sample of an individual decay chain are the direct slepton decays \(\widetilde{\ell }_{\mathrm L}\rightarrow l \widetilde{\chi }^0_1\) and the direct bottomsquark decay \(\widetilde{\mathrm{b}} _1 \rightarrow b \widetilde{\chi }^0_1 \). These could then be used to obtain information on the masses of the produced sparticles via kinematic edges.
The expected distributions are shown in Fig. 15 for an integrated luminosity of 300 \(\,\text {fb}^\text {1}\) after the selection presented in Sect. 3.2. With this amount of integrated luminosity, the edge position in model STC8 could be determined, while for STC10 this would be possible only with the luminosity that can be reached at the HLLHC, 3000\(\,\text {fb}^\text {1}\).
The edge is smeared out by the jet energy resolution, which has still to be determined for the \(14\,\text {TeV} \) data with the corresponding jet reconstruction at higher pileup. Assuming a resolution of 10 % for \(p_{\mathrm {T}} (j)=300500\,\text {GeV} \) jets (which is a typical transverse momentum for jets from bottomsquark decays, as shown in Fig. 4), motivated by a corresponding 7\(\,\text {TeV}\) measurement [92], we can deduce a resolution of about 15 % for the \(m_{\mathrm {CT}}\) variable, corresponding to about \(120\,\text {GeV} \) in STC8 and \(150\,\text {GeV} \) in STC10. The edge position gets further diluted or even biased by the SM background as well as by the SUSY background, in combination with fluctuations due to low statistics. While the situation could be partly improved by removing the SM background based on prediction from simulation, which is expected to be well understood with 300\(\,\text {fb}^\text {1}\) of data, the SUSY background remains a priori unknown and can distort the determined endpoint as shown in the following.
In order to determine the mass edge, one could e.g. exploit a typical edgefinder like the socalled edgetobump method [93]. To test the capability of this method for the model STC8, we generate 1000 times pseudodata from the distribution shown in Fig. 15a, and determine the edge position with the edgetobump method. The mean of the fitted value is at 832\(\,\text {GeV}\) with an RMS of 114\(\,\text {GeV}\), which is compatible with the expected value of 780\(\,\text {GeV}\). This RMS is expected from the resolution of the \(m_{\mathrm {CT}}\) variable. With ten times more statistics from the HLLHC, this uncertainty could be reduced roughly by a factor of 3. Without further knowledge about the \(\widetilde{\chi }^0_1\), the determined endpoint can be interpreted as lower limit on the bottomsquark mass using Eq. (4), assuming a massless neutralino, of \(832 \pm 114\,\text {GeV} \). Higher masses of the neutralino would lead to higher bottomsquark masses.
Analogously, an edge in the contransverse mass spectrum would be expected from the decays of \(\widetilde{\mathrm {e}}_{\mathrm {L}}\) and \(\widetilde{\mu }_{\mathrm {L}}\) near \(m_{\mathrm {CT}} ^{\mathrm {edge}}(l_1,l_2) = 175\,\text {GeV} \). Without any information from ILC, this would yield a lower limit on the slepton mass.
5.3 Discoveries at the ILC
In the recently published running scenario [27], the ILC starts up in its TDR baseline configuration at \(E_{\mathrm {cms}}=500\,\text {GeV} \). In this case, the picture changes drastically with already a modest amount of data, since very first evidence for BSM at the ILC would be observed after a few days of running from selectron pair production. Figure 16 shows the selectron signal expected with only 5\(\,\text {fb}^\text {1}\), allowing already a first determination of both the selectron and the LSP masses according to the technique described in Sect. 4. Since the lighter set of sleptons must have a 100 % branching ratio to lepton and LSP, their production cross sections can be measured unambiguously. In particular for the selectron and smuon case, where the mixing is typically small, the coupling can be extracted once the mass is known, thus enabling the first verification that the couplings of the exotic states equal those of their SM partners – a fundamental property of supersymmetry!
Beyond the specific case of STCx, any sparticle lighter than half the centreofmass energy of an \(e^+e^\) collider will be observable. If furthermore, like in the STCx models, Rparity is conserved so that the LSP is stable, the NLSP will have a 100 % BR to the LSP and the corresponding SM particle. This means that the search for NLSP pair production at the ILC can be seen as a loophole free search for SUSY [94]. The case of a general STClike model, where the NLSP is the \( \widetilde{\tau }_1\), is illustrated in Fig. 17, showing the exclusion and discovery reach for the NLSP at the ILC is shown in the plane of the only free parameters, i.e. \(M_{\widetilde{\chi }^0_0}\) and \(M_{\mathrm {NLSP}}\). It should be pointed out that the case with the NLSP being the \( \widetilde{\tau }_1\) is one of the most experimentally difficult ones, due to the need to detect \(\tau \)leptons in the final state.
5.4 Signal characterisation at the ILC
According to the currently favoured running scenario for the ILC [27], 500 \(\,\text {fb}^\text {1}\) would be collected at \(E_{\mathrm {cms}}=500\,\text {GeV} \) within the first 4 years of operation. For these data, a sharing between the four possible configurations with different polarisation signs is foreseen: 40 % of the data would be collected at each of the configurations \(\mathcal {P}_{80,+30}\) and \(\mathcal {P}_{+80,30}\), while 10 % would be collected at each of the \(\mathcal {P}_{80,30}\) and \(\mathcal {P}_{+80,+30}\) ones. This would allow a first assessment of all SUSY particles with masses below \(250\,\text {GeV} \), including their masses and mixings, with a precision typically a factor 1.6 worse than the values quoted in Sect. 4.
After the initial run at \(E_{\mathrm {cms}}=500\,\text {GeV} \), it is foreseen the lower the centreofmass energy to scan the toppair production threshold and to run near the Zh threshold for a highprecision determination of the Higgsboson mass and its coupling to the Z boson. These runs would also be of high interest for SUSY spectroscopy:
Running near the Zh threshold could include a scan of the threshold for pair production of the lighter sleptons as shown in Fig. 11, which provides mass measurements of the \( \widetilde{e}_R\) and \( \widetilde{\mu }_R\) with precisions of 190\(\,\text {MeV}\) and 220\(\,\text {MeV}\), respectively. The shape of the threshold as well as angular distributions identify the produced partners of electrons and muon as scalar particles [95].
At or slightly above the \(\mathrm{t}\overline{\mathrm{t}}\) threshold, the cross section for \(\widetilde{\tau } _1 \widetilde{\tau } _2\) mixed production could be measured with high precision due to the absence of the \(\widetilde{\tau } _2\)pair production background which limits the purity of this measurement at \(E_{\mathrm {cms}}=500\,\text {GeV} \). This provides an interesting possibility to determine the \(\widetilde{\tau } \) mixing and \(\tan {\beta }\). Together with the masses of the \( \widetilde{\tau }_1\) and the \( \widetilde{\chi }^0_1\) and the \( \widetilde{\chi }^0_1\) mixing determined at \(E_{\mathrm {cms}}=500\,\text {GeV} \) (cf. Sects. 4.2.2 and 4.2.1), these are important inputs for the prediction of the dark matter relic density within the MSSM, since in the STCx scenarios LSP pair annihilation and \( \widetilde{\tau }_1\)coannihilation contribute about equally to the cosmic dark matter annihilation. By comparing the predicted value for the relic density to the cosmologically observed one, the \( \widetilde{\chi }^0_1\) can be either identified as the sole constituent of dark matter, or as being responsible for only a fraction of the observed relic density. This has been explicitly demonstrated in a SUSY scenario with an electroweak sector very similar to the STCx cases [96].
After a luminosity upgrade, the integrated luminosity at 500\(\,\text {GeV}\) is then foreseen to be increased to 4\(\,\text {ab}^\text {1}\), with the same polarisation sharing as before, enabling a full BSM precision program, which reaches the permillelevel for many observables. While the currently assumed running scenario is based on guaranteed measurements only, it will be adjusted to future discoveries by scheduling further threshold scans as well as runs at dedicated energies not far above important thresholds. Such special runs give e.g. important information for parameter determination in the neutralino sector, which in turn enables predictions of the masses of the kinematically not accessible states [97]. The results of the initial run at \(E_{\mathrm {cms}}=500\,\text {GeV} \) will give decisive input to determining the detailed running strategy.
5.5 Combining ILC and LHC
With ILC information on the lower part of the spectrum, the situation at the LHC changes drastically. While the clear advantage of the LHC is the larger kinematic reach for the production of the more heavy sparticles, disentangling their signals is challenging due to the multitude of decay modes, most of them with small branching ratios. Thus the information from the ILC might provide the key to access all the information contained in the LHC data, on one hand by exploiting the knowledge of the lower parts of the decay chain in the data analysis, on the other by combining LHC and ILC results in global pMSSM fits. This has been pointed out in several previous studies [96, 98, 99]. Most of them, however, are based on scenarios with a light, subTeV, coloured sector, which is by now excluded by LHC measurements. Thus we highlight here the specific possibilities arising in the more challenging STCx benchmark points.
First of all, the determined edge position from bottomsquark pair production could be turned into a measurement of the bottomsquark mass by adding the information from ILC about the \(\widetilde{\chi }^0_1\) mass, which can be determined at the ILC with a negligible uncertainty. Using Eq. (4), we find a bottomsquark mass of \(843 \pm 115\,\text {GeV} \), which is compatible with the true value of 795\(\,\text {GeV}\), as well as with the value obtained for a massless LSP. Even with HLLHC precision of 30–40 \(\,\text {GeV}\), the hypothesis of a massless LSP would yield a bottomsquark mass compatible with the model value. However, already for an LSP mass of 200\(\,\text {GeV}\) which could still be accessed at the ILC with \(E_{\mathrm {cms}}=500\,\text {GeV} \) from radiative neutralino production (cf. Sect. 4.1.3), the bias due to the zeromass hypothesis rises to 50\(\,\text {GeV}\) and thus surpasses the statistical uncertainty on \(m_{\mathrm {CT}} ^{\mathrm {edge}}\).
In addition, we could use the measured bottomsquark mass to calculate the cross section for this process and compare it with the cross section times branching fraction determined above from counting the events in the signal region. While the mass determination is independent of the spin of the newly discovered particle, the measured event rate that can be related to the cross section (times branching fraction) depends on the spin of the new particle and therefore help identify whether the newly discovered particle is actually a SUSY particle or not. Final conclusions could only be drawn if the branching fraction can be determined in addition. For the latter, input from the ILC on the lowermass sparticle spectrum might be exploited as well.
Figure 18 shows the \(M_{\widetilde{\chi }^{\pm }_2}\) by using the MC level information as well as reconstructed objects. The resolution gets smeared by two different effects: first, the \(E'_\mathrm{lep}\) is not fixed because of the natural widths of the \(\widetilde{\chi }^{\pm }_1 \) and the \(\widetilde{\nu } \). Second, the boost vector \(\vec {\beta }\) is not perfectly parallel to the lepton. Therefore, we expect to measure the \(M_{\widetilde{\chi }^{\pm }_2}\) to be \(412 \pm 43\,\text {GeV} \). In order to suppress the SM background we require exactly three leptons (\(p_{\mathrm {T}} = 25/15/10\,\text {GeV} \)), one oppositesign sameflavour lepton pair with an invariant mass between 84\(\,\text {GeV}\) and 96\(\,\text {GeV}\), at least one btagged jet (\(p_{\mathrm {T}} > 100\,\text {GeV} \) and \(\eta < 2.4\)), more than three jets (\(p_{\mathrm {T}} > 40\,\text {GeV} \) and \(\eta < 2.4\)) where the leading jet has \(p_{\mathrm {T}} > 120\,\text {GeV} \) and \(E_{\mathrm {T}}^{\text {miss}} > 200\,\text {GeV} \). With this selection our signal consists dominantly of \(\widetilde{\chi }^{\pm }_2\) produced by stop decays, which has the best signal to background ratio. With a slightly softer selection we would also have sensitivity to direct \(\widetilde{\chi }^{\pm }_2\) \( \widetilde{\chi }^n_{m}\) production, which also can be accessible at HLLHC. Per construction the \(M_{\widetilde{\chi }^{\pm }_2}\) must be larger than \(\sqrt{(M_{\widetilde{\chi }^{\pm }_1})^2+(M_{Z})^2} > 200\,\text {GeV} \). As first observation we see much more SUSY events than we would expect from our targeted decay chain. Most of these events include heavy electroweakinos (\(\widetilde{\chi }^{\pm }_2\), \(\widetilde{\chi }^0_3\), \(\widetilde{\chi }^0_4\)) decaying via Z bosons. The third lepton stems from the other decay products, which in most cases are \(\tau \) leptons. This signature carry mass information about the heavy charginos and would be worth to be studied with the hadronic \(\tau \) lepton final states. The other SUSY events passing this selection contains slepton decays, which has a kinematic edge signature close to the Z mass. This kind of background could be studied further if one requires the invariant mass of the oppositesing sameflavour lepton pair exactly at the position of the edge. Overall the peak from our targeted decay chain around \(420\,\text {GeV} \) is visible.
The obtained knowledge of the \( \widetilde{\chi }^{\pm }_2\) and \( \widetilde{\chi }^0_{3,4}\) masses in turn would add significantly to the physics case of a 1TeVupgrade of the ILC, or of an even higher energy \(e^+e^\) collider like CLIC. Furthermore, the full knowledge of the electroweakino masses, mixings and decay modes could provide the decisive information to isolate a signal from topsquark production, e.g. in its largest decay mode \(\widetilde{\mathrm{t}} _1 \rightarrow b \widetilde{\chi }^{\pm }_2\), enabling a determination of the \(\widetilde{\mathrm{t}} _1\) mass.
6 Conclusions
In this paper we discussed the complementarity and interplay of a proton–proton collider, the LHC, and an electron–positron collider, the ILC, in discovering new particles and in determining their properties. As example we used an Rparity and CP conserving supersymmetric model where the \( \widetilde{\tau }_1\) is the nexttolightest supersymmetric particle and has a small mass difference of about \(10\,\text {GeV} \) to the lightest supersymmetric particle, the LSP, which is the lightest neutralino \(\widetilde{\chi }^0_1\). In such a scenario, \( \widetilde{\tau }_1\)coannihilation allows for a sufficiently small dark matter relic density. All sleptons and electroweakinos have masses below \(500\,\text {GeV} \), while the lightest coloured sparticles, the lighter top and bottom squarks, have masses around 800 or \(1000\,\text {GeV} \). All other coloured sparticles are much heavier, up to \(2\,\text {TeV} \).
We showed that such a scenario can easily be discovered at the LHC running at \(13/14\,\text {TeV} \). In particular, this is true for the heavier selectrons and smuons, the heavier electroweakinos, as well as the lighter top and bottom squarks, if their masses are not much higher than a \(\,\text {TeV}\). Depending on the search channel, on the exact masses and on the achieved control of systematic uncertainties, the integrated luminosities to discover deviations from the SM expectation due to production of these sparticles range from 50 to 1000\(\,\text {fb}^\text {1}\). The earliest discovery would come from the singlelepton stop search, followed by hadronic searches including \(\mathrm{b}\)tags. Inclusive hadronic searches would require systematic uncertainties to be controlled better than \(10~\%\) in order to achieve a \(5\,\sigma \) discovery.
However, in most cases the observed deviations from the SM expectation cannot be attributed to a single process, but result from a mixture of e.g. diverse electroweakino processes or, in the case of the coloured sector, of stop, sbottom and gluino production. The best chances are to identify a single process with sufficiently high purity, in order to learn something about the properties of the produced sparticles originating from direct decays of the produced sparticle to its standardmodel partner and the LSP. For the investigated scenarios, the direct decay has a sizeable branching fraction in the case of the heavier sleptons and the lighter bottom squark. Here, a kinematic edge can be isolated e.g. in the contransverse mass distribution. Without further knowledge of the mass of the LSP, the position of this edge can be converted into a lower limit on the sparticle mass.
As example, we analysed the case of \(\widetilde{\mathrm{b}}_1 \rightarrow \mathrm{b} \widetilde{\chi }^0_1 \), and found that the edge in the contransverse mass distribution for the model with bottomsquark mass could be determined with an uncertainty of about \(115\,\text {GeV} \) with an integrated luminosity of 300\(\,\text {fb}^\text {1}\) at \(14\,\text {TeV} \). Assuming that systematic uncertainties play only a minor role, this could be improved to about \(30\,\text {GeV} \) at the HighLuminosity LHC. For higher bottomsquark masses of about 1\(\,\text {TeV}\), the discovery is still possible, however, the uncertainties on the mass determination will be significantly larger due to strongly reduced number of signal events.
The ILC on the other hand would complement these spectacular discoveries at the LHC with a systematic precision analysis of the lower part of the spectrum, actually discovering some of the lighter states. In this paper, we especially present uptodate detector simulation studies of the slepton sector at the ILC, both in the continuum and in threshold scans. In particular a sufficiently light selectron will lead to a striking signal within a few weeks of ILC operation. Already after the 500\(\,\text {fb}^\text {1}\) collected in the first 4 years of ILC operation, this would allow a permillelevel determination of the LSP mass, and the masses of the righthanded sleptons, improving further with the \(4\,\text {ab}^\text {1} \) foreseen for the full ILC program. In conjunction with threshold scans and operation with different beam polarisations, all sleptons and the lighter half of the electroweakino spectrum can be characterised with at least percentlevel precision, including masses and mixing angles. This would demonstrate that the observed new particles are indeed of a supersymmetric nature, and at least some of the parameters of the underlying SUSY model can be determined.
This information from the ILC then creates new opportunities to analyse the LHC data. Obviously, a precise determination of the LSP mass from the ILC can be employed to turn edge determinations into mass measurements. Even better, the detailed information from the ILC can be used in the analysis of the data themselves to disentangle the contributions of different production modes and to reconstruct quantities which are sensitive to masses of the heavier sparticles with more complex decay chains. As an example, we illustrated this in the case of the \(\widetilde{\chi }^{\pm }_2\). With the knowledge of the masses of the \(\widetilde{\chi }^{\pm }_1\) and the \(\widetilde{\nu }\) from the ILC, the signal can be isolated from the electroweakino mix and its mass can be reconstructed on an eventbyevent basis with a resolution of about \(50\,\text {GeV} \) with an integrated luminosity of 300\(\,\text {fb}^\text {1}\) at \(14\,\text {TeV} \), with corresponding improvements at the HighLuminosity LHC.
Although we studied the capabilities and the interplay of LHC and ILC based on a specific example, many aspects are transferable to other scenarios which comprise new particles in the kinematic reach both colliders. In this context, it should be noted that the LHC in many cases the sensitivity to the lightest new physics states is significantly smaller than to some of the heavier states, and that some of the lighter states might even await explicit discovery at a lepton collider. We finally conclude that the combination of LHC and ILC data could reveal significantly more information as regards the properties and the origin of new particles than the results from either collider alone.
Footnotes
 1.
Here, and in the following, \(\mathcal {P}_{p^,p^+}\) denotes the beampolarisation configuration \(\mathcal {P}(e^,e^+)=(p^,p^+)\), with \(p^\) and \(p^+\) given in percent [for brevity fully left (right) handed beams are denoted by L(R)].
 2.
Usually, X and Y are particle and antiparticle.
 3.
Equation (2) shows that the lighter state receives a lower fraction of the total initial energy than the heavier state in \(\widetilde{\mathrm{e}}_{\mathrm{R}} \widetilde{\mathrm{e}}_{\mathrm{L}} \) production, so that the upper edge from the \(\widetilde{\mathrm{e}}_{\mathrm{R}} \) decay is lower than what it is in the symmetric case in \(\widetilde{\mathrm{e}}_{\mathrm{R}} \widetilde{\mathrm{e}}_{\mathrm{R}} \) production seen in Fig. 9a.
 4.
Note that this centreofmass energy range is also optimal for studying the properties of the Higgs boson with the modelindependent recoilmass method.
 5.
Interaction of sfermions and gauginos conserve chirality, while the Yukawa interaction of the Higgsinos flips chirality.
Notes
Acknowledgments
We would like to thank the Whizard authors, the LC Generator Group as well as the ILD MC production team for their help in producing the large samples of events used in this work. The results presented could not be achieved without the National Analysis Facility and we thank the NAF team for their continuous support. We thankfully acknowledge the support by the DFG through the SFB 676 “Particles, Strings and the Early Universe”.
References
 1.S.P. Martin, A supersymmetry primer. Adv.Ser. Direct. High Energy Phys. 18, 1 (1997). arXiv:hepph/9709356v6
 2.J. Wess, B. Zumino, Supergauge transformations in four dimensions. Nucl. Phys. B 70, 39 (1974)ADSCrossRefMathSciNetGoogle Scholar
 3.H.P. Nilles, Supersymmetry, supergravity and particle physics. Phys. Rep 110, 1 (1984)ADSCrossRefGoogle Scholar
 4.H.E. Haber, G.L. Kane, The search for supersymmetry: probing physics beyond the standard model. Phys. Rep. 117, 75 (1987)ADSCrossRefGoogle Scholar
 5.R. Barbieri, S. Ferrara, C.A. Savoy, Gauge models with spontaneously broken local supersymmetry. Phys. Lett. B 119, 343 (1982)ADSCrossRefGoogle Scholar
 6.S. Dawson, E. Eichten, C. Quigg, Search for supersymmetric particles in hadronhadron collisions. Phys. Rev. D 31, 1581 (1985)ADSCrossRefGoogle Scholar
 7.G.L. Kane, C. Kolda, L. Roszkowski, J.D. Wells, Study of constrained minimal supersymmetry. Phys. Rev. D 49, 6173–6210 (1994). doi: 10.1103/PhysRevD.49.6173 ADSCrossRefGoogle Scholar
 8.A.H. Chamseddine, R. Arnowitt, P. Nath, Locally supersymmetric grand unification. Phys. Rev. Lett. 49, 970–974 (1982). doi: 10.1103/PhysRevLett.49.970 ADSCrossRefGoogle Scholar
 9.N. ArkaniHamed, P. Schuster, N. Toro, J. Thaler, L.T. Wang et al., MARMOSET: the path from LHC data to the new standard model via onshell effective theories. Report no.: FERMILABFN0800CD. arXiv:hepph/0703088
 10.J. Alwall, P. Schuster, N. Toro, Simplified models for a first characterization of new physics at the LHC. Phys. Rev. D 79, 075020 (2009). arXiv:0810.3921 ADSCrossRefGoogle Scholar
 11.D. Alves et al., Simplified models for LHC new physics searches. J. Phys. G 39, 105005 (2012). arXiv:1105.2838 ADSCrossRefGoogle Scholar
 12.G.R. Farrar, P. Fayet, Phenomenology of the production, decay, and detection of new hadronic states associated with supersymmetry. Phys. Lett. B 76, 575 (1978)ADSCrossRefGoogle Scholar
 13.O. Buchmueller, R. Cavanaugh, A. De Roeck, J. Ellis, H. Flacher et al., Likelihood functions for supersymmetric observables in frequentist analyses of the CMSSM and NUHM1. Eur. Phys. J. C 64, 391–415 (2009). arXiv:0907.5568 [hepph]ADSCrossRefGoogle Scholar
 14.O. Buchmueller, R. Cavanaugh, A. De Roeck, J. Ellis, H. Flacher et al., The NUHM2 after LHC Run 1. Eur. Phys. J. C 74, 3212 (2014). arXiv:1408.4060 [hepph]CrossRefGoogle Scholar
 15.ATLAS Collaboration, G. Aad et al., Search for the electroweak production of supersymmetric particles in \(\sqrt{s}\) collisions with the ATLAS detector. Report no.: CERNPHEP2015218. arXiv:1509.07152 [hepex]
 16.ATLAS Collaboration, G. Aad et al., Search for the direct production of charginos, neutralinos and staus in final states with at least two hadronically decaying taus and missing transverse momentum in \(pp\) = 8 TeV with the ATLAS detector. JHEP 1410, 96 (2014). arXiv:1407.0350 [hepex]
 17.DELPHI Collaboration, J. Abdallah et al., Searches for supersymmetric particles in e+ e collisions up to 208GeV and interpretation of the results within the MSSM. Eur. Phys. J. C 31, 421–479 (2003). arXiv:hepex/0311019
 18.Particle Data Group Collaboration, K. Olive et al., Review of particle physics. Chin. Phys. C 38, 090001 (2014)CrossRefGoogle Scholar
 19.H. Baer, J. List, Post LHC8 SUSY benchmark points for ILC physics. Phys. Rev. D 88, 055004 (2013). arXiv:1307.0782 [hepph]
 20.S. Dimopoulos, G.F. Giudice, Naturalness constraints in supersymmetric theories with nonuniversal soft terms. Phys. Lett. B 357, 573–578 (1995). arXiv:hepph/9507282 ADSCrossRefGoogle Scholar
 21.G. Ross, SUSY: Quo Vadis? Eur. Phys. J. C 74, 2699 (2014)ADSCrossRefGoogle Scholar
 22.R.L. Arnowitt, B. Dutta, T. Kamon, N. Kolev, D.A. Toback, Detection of SUSY in the stauneutralino coannihilation region at the LHC. Phys. Lett. B 639, 46–53 (2006). arXiv:hepph/0603128 ADSCrossRefGoogle Scholar
 23.R.L. Arnowitt, A. Aurisano, B. Dutta, T. Kamon, N. Kolev, P. Simeon, D.A. Toback, P. Wagner, Indirect measurements of the stauneutralino 1(0) mass difference and mSUGRA in the coannihilation region of mSUGRA models at the LHC. Phys. Lett. B 649, 73–82 (2007)ADSCrossRefGoogle Scholar
 24.R.M. Godbole, M. Guchait, D.P. Roy, Using Tau polarization to probe the stau coannihilation region of mSUGRA Model at LHC. Phys. Rev. D 79, 095015 (2009). arXiv:0807.2390 [hepph]ADSCrossRefGoogle Scholar
 25.Z.H. Yu, X.J. Bi, Q.S. Yan, P.F. Yin, Detecting light stop pairs in coannihilation scenarios at the LHC. Phys. Rev. D 87(5), 055007 (2013). arXiv:1211.2997 [hepph]ADSCrossRefGoogle Scholar
 26.C. Adolphsen, M. Barone, B. Barish, K. Buesser, P. Burrows et al., The international linear collider technical design report–volume 3.II: accelerator baseline design. ISBN 9783935702775. arXiv:1306.6328 [physics.accph]
 27.ILC Parameters Joint Working Group Collaboration, T. Barklow, J. Brau, K. Fujii, J. Gao, J. List, N. Walker, K. Yokoya, ILC operating scenarios. Report nos.: ILCNOTE2015068, DESY 15–102, IHEPAC2015002, KEK Preprint 2015–17, SLACPUB16309. arXiv:1506.07830 [physics.hepex]
 28.ATLAS Collaboration, G. Aad et al., Search for direct thirdgeneration squark pair production in final states with missing transverse momentum and two \(b\) collisions with the ATLAS detector. JHEP 1310, 189 (2013). arXiv:1308.2631 [hepex]
 29.CMS Collaboration, Search for direct production of bottom squark pairs. Technical Report CMSPASSUS13018 (CERN, Geneva 2014)Google Scholar
 30.ATLAS Collaboration, G. Aad et al., Search for direct production of charginos, neutralinos and sleptons in final states with two leptons and missing transverse momentum in \(pp\) 8 TeV with the ATLAS detector. JHEP 1405, 071 (2014). arXiv:1403.5294 [hepex]
 31.CMS Collaboration, V. Khachatryan et al., Searches for electroweak production of charginos, neutralinos, and sleptons decaying to leptons and W, Z, and Higgs bosons in pp collisions at 8 TeV. Eur. Phys. J. C 74(9), 3036 (2014). arXiv:1405.7570 [hepex]
 32.W. Beenakker, R. Hopker, M. Spira, P. Zerwas, Squark and gluino production at hadron colliders. Nucl. Phys. B 492, 51–103 (1997). arXiv:hepph/9610490 ADSCrossRefGoogle Scholar
 33.W. Beenakker, M. Klasen, M. Kramer, T. Plehn, M. Spira et al., The Production of charginos/neutralinos and sleptons at hadron colliders. Phys. Rev. Lett. 83, 3780 (1999). arXiv:hepph/9906298 ADSCrossRefGoogle Scholar
 34.D. Tovey, On measuring the masses of pairproduced semiinvisibly decaying particles at hadron colliders. JHEP 0804, 034 (2008). arXiv:0802.2879 ADSCrossRefGoogle Scholar
 35.G. Polesello, D.R. Tovey, Supersymmetric particle mass measurement with the boostcorrected contransverse mass. JHEP 1003, 030 (2010). arXiv:0910.0174 [hepph]ADSCrossRefzbMATHGoogle Scholar
 36.ATLAS Collaboration, G. Aad et al., Search for new phenomena in final states with large jet multiplicities and missing transverse momentum using \(\sqrt{s}=7\) collisions with the ATLAS detector. JHEP 1111, 099 (2011). arXiv:1110.2299 [hepex]
 37.ATLAS Collaboration, G. Aad et al., Search for squarks and gluinos using final states with jets and missing transverse momentum with the ATLAS detector in \(\sqrt{s}=7\) TeV protonproton collisions. Phys. Lett. B 710, 67–85 (2012). arXiv:1109.6572 [hepex]
 38.ATLAS Collaboration, G. Aad et al., Search for squarks and gluinos with the ATLAS detector in final states with jets and missing transverse momentum using 4.7 fb\(^{1}\) TeV protonproton collision data. Phys. Rev. D 87, 012008 (2013). arXiv:1208.0949 [hepex]
 39.ATLAS Collaboration, G. Aad et al., Hunt for new phenomena using large jet multiplicities and missing transverse momentum with ATLAS in 4.7 fb\(^{1}\) TeV protonproton collisions. JHEP 1207, 167 (2012). arXiv:1206.1760 [hepex]
 40.ATLAS Collaboration, G. Aad et al., Search for top and bottom squarks from gluino pair production in final states with missing transverse energy and at least three bjets with the ATLAS detector. Eur. Phys. J. C 72, 2174 (2012). arXiv:1207.4686 [hepex]
 41.ATLAS Collaboration, G. Aad et al., Search for squarks and gluinos with the ATLAS detector in final states with jets and missing transverse momentum using \(\sqrt{s}=8\) TeV protonproton collision data. JHEP 1409, 176 (2014). arXiv:1405.7875 [hepex]
 42.ATLAS Collaboration, G. Aad et al., Search for new phenomena in final states with large jet multiplicities and missing transverse momentum at \(\sqrt{s}\)=8 TeV protonproton collisions using the ATLAS experiment. JHEP 1310, 130 (2013). arXiv:1308.1841 [hepex]
 43.ATLAS Collaboration, G. Aad et al., Search for strong production of supersymmetric particles in final states with missing transverse momentum and at least three \(b\)= 8 TeV protonproton collisions with the ATLAS detector. JHEP 1410, 24 (2014). arXiv:1407.0600 [hepex]
 44.CMS Collaboration, S. Chatrchyan et al., Search for new physics with jets and missing transverse momentum in pp collisions at \(\sqrt{s} = 7\) TeV. JHEP 08, 155 (2011). arXiv:1106.4503 [hepex]
 45.CMS Collaboration, S. Chatrchyan et al., Search for New Physics in the Multijet and Missing Transverse Momentum Final State in ProtonProton Collisions at \(\sqrt{s}=7\) TeV. Phys. Rev. Lett. 109, 171803 (2012). arXiv:1207.1898 [hepex]
 46.CMS Collaboration, S. Chatrchyan et al., Search for new physics in the multijet and missing transverse momentum final state in protonproton collisions at \(\sqrt{s}= 8\) TeV. JHEP 1406, 055 (2014). arXiv:1402.4770 [hepex]
 47.CMS Collaboration, S. Chatrchyan et al., Search for supersymmetry in events with b jets and missing transverse momentum at the LHC. JHEP 1107, 113 (2011). arXiv:1106.3272 [hepex]
 48.CMS Collaboration, S. Chatrchyan et al., Search for supersymmetry in events with bquark jets and missing transverse energy in pp collisions at 7 TeV. Phys. Rev. D 86, 072010 (2012). arXiv:1208.4859 [hepex]
 49.CMS Collaboration, S. Chatrchyan et al., Search for gluino mediated bottom and topsquark production in multijet final states in pp collisions at 8 TeV. Phys. Lett. B 725, 243 (2013). arXiv:1305.2390 [hepex]
 50.ATLAS Collaboration, G. Aad et al., Search for scalar bottom quark pair production with the ATLAS detector in \(pp\) TeV. Phys. Rev. Lett. 108, 181802 (2012). arXiv:1112.3832 [hepex]
 51.ATLAS Collaboration, G. Aad et al., Search for direct top squark pair production in final states with one isolated lepton, jets, and missing transverse momentum in \(\sqrt{s}=7\) of ATLAS data. Phys. Rev. Lett. 109, 211803 (2012), arXiv:1208.2590 [hepex]
 52.ATLAS Collaboration, G. Aad et al., Search for top squark pair production in final states with one isolated lepton, jets, and missing transverse momentum in \(\sqrt{s} =\) collisions with the ATLAS detector. JHEP 1411, 118 (2014). arXiv:1407.0583 [hepex]
 53.CMS Collaboration, S. Chatrchyan et al., Search for topsquark pair production in the singlelepton final state in pp collisions at \(\sqrt{s}\) = 8 TeV. Eur. Phys. J. C 73(12), 2677 (2013). arXiv:1308.1586 [hepex]
 54.ATLAS Collaboration, G. Aad et al., Search for supersymmetry in events with four or more leptons in \(\sqrt{s}\) = 8 TeV pp collisions with the ATLAS detector. Phys. Rev. D 90(5), 052001 (2014). arXiv:1405.5086 [hepex]
 55.ATLAS Collaboration, G. Aad et al., Search for direct production of charginos and neutralinos in events with three leptons and missing transverse momentum in \(\sqrt{s} =\) collisions with the ATLAS detector. JHEP 1404, 169 (2014). arXiv:1402.7029 [hepex]
 56.M. Graesser, J. Shelton, Probing supersymmetry with thirdgeneration cascade decays. JHEP 06, 039 (2009). arXiv:0811.4445 [hepph]ADSCrossRefGoogle Scholar
 57.N. Desai, B. Mukhopadhyaya, Signals of supersymmetry with inaccessible first two families at the large hadron collider. Phys. Rev. D 80, 055019 (2009). arXiv:0901.4883 [hepph]ADSCrossRefGoogle Scholar
 58.H. Baer, V. Barger, A. Lessa, X. Tata, Supersymmetry discovery potential of the LHC at s**(1/2) = 10TeV and 14TeV without and with missing E(T). JHEP 09, 063 (2009). arXiv:0907.1922 [hepph]ADSCrossRefGoogle Scholar
 59.H. Li, W. Parker, Z. Si, S. Su, Sbottom signature of the supersymmetric golden region. Eur. Phys. J. C 71, 1584 (2011). arXiv:1009.6042 [hepph]ADSCrossRefGoogle Scholar
 60.S. Bornhauser, M. Drees, S. Grab, J.S. Kim, Light stop searches at the LHC in events with two bjets and missing energy. Phys. Rev. D 83, 035008 (2011). arXiv:1011.5508 [hepph]ADSCrossRefGoogle Scholar
 61.J. de Favereau, C. Delaere, P. Demin, A. Giammanco, V. Lematre et al., DELPHES 3, A modular framework for fast simulation of a generic collider experiment. JHEP 1402, 057 (2014). arXiv:1307.6346 [hepex]
 62.T. Sjostrand, S. Mrenna, P.Z. Skands, PYTHIA 6.4 physics and manual. JHEP 0605, 026 (2006). arXiv:hepph/0603175 [hepph]
 63.M. Cacciari, G.P. Salam, Pileup subtraction using jet areas. Phys. Lett. B 659, 119–126 (2008). arXiv:0707.1378 [hepph]ADSCrossRefGoogle Scholar
 64.A. Avetisyan, J.M. Campbell, T. Cohen, N. Dhingra, J. Hirschauer et al., Methods and results for standard model event generation at \(\sqrt{s}\) = 14 TeV, 33 TeV and 100 TeV proton colliders (a snowmass whitepaper), in Community Summer Study 2013: Snowmass on the Mississippi (CSS2013) (Minneapolis, 2013). arXiv:1308.1636 [hepex]
 65.J. Alwall, M. Herquet, F. Maltoni, O. Mattelaer, T. Stelzer, MadGraph 5: going beyond. JHEP 1106, 128 (2011). arXiv:1106.0522 [hepph]ADSCrossRefzbMATHGoogle Scholar
 66.J. Anderson, A. Avetisyan, R. Brock, S. Chekanov, T. Cohen et al., Snowmass energy frontier simulations, in Community Summer Study 2013: Snowmass on the Mississippi (CSS2013) (Minneapolis, 2013). arXiv:1309.1057 [hepex]
 67.A. Avetisyan, S. Bhattacharya, M. Narain, S. Padhi, J. Hirschauer et al., Snowmass energy frontier simulations using the open science grid (a snowmass 2013 whitepaper), in Community Summer Study 2013: Snowmass on the Mississippi (CSS2013) (Minneapolis, 2013). arXiv:1308.0843 [hepex]
 68.R. Field, Early LHC underlying event data–findings and surprises, in Hadron Collider Physics. Proceedings, 22nd Conference, HCP2010 (Toronto, 2010). arXiv:1010.3558 [hepph]
 69.R.D. Cousins, J.T. Linnemann, J. Tucker, Evaluation of three methods for calculating statistical significance whe n incorporating a systematic uncertainty into a test of the backgroundonly hypothesis for a Poisson process. Nucl. Instrum. Methods Phys. Res. Sect. A 595, 480 (2008). arXiv:physics/0702156
 70.K. Cranmer, Statistical challenges for searches for new physics at the LHC, in Statistical Problems in Particle Physics, Astrophysics and Cosmology. Proceedings, Conference, PHYSTAT05 (Oxford 2005), pp. 112–123. arXiv:physics/0511028
 71.J. Linnemann, Measures of significance in HEP and astrophysics, in Statistical Problems in Particle Physics, Astrophysics, and Cosmology. Proceedings, Conference, PHYSTAT 2003, vol. C030908 (Stanford, 2003), p. MOBT001. arXiv:physics/0312059
 72.L. Moneta, K. Belasco, K.S. Cranmer, S. Kreiss, A. Lazzaro et al., The RooStats project. PoS ACAT2010, 057 (2010). arXiv:1009.1003 [physics.dataan]
 73.Y. Bai, H.C. Cheng, J. Gallicchio, J. Gu, Stop the top background of the stop search. JHEP 1207, 110 (2012). arXiv:1203.4813 [hepph]ADSCrossRefGoogle Scholar
 74.T. Behnke, J.E. Brau, P.N. Burrows, J. Fuster, M. Peskin et al., The international linear collider technical design report–volume 4: detectors. ISBN 9783935702782. arXiv:1306.6329 [physics.insdet]
 75.W. Kilian, T. Ohl, J. Reuter, WHIZARD: simulating multiparticle processes at LHC and ILC. Eur. Phys. J. C 71, 1742 (2011). arXiv:0708.4233 [hepph]ADSCrossRefGoogle Scholar
 76.M. Berggren, SGV 3.0–a fast detector simulation, in International Workshop on Future Linear Colliders (LCWS11) (Granada, 2011). arXiv:1203.0217 [physics.insdet]
 77.Linear Collider ILD Concept Group Collaboration, T. Abe et al., The international large detector: letter of intent. arXiv:1006.3396 [hepex]
 78.S. Choi, J. Kalinowski, G.A. MoortgatPick, P. Zerwas, Analysis of the neutralino system in supersymmetric theories: addendum. Report nos.: DESY02020, IFT0203. arXiv:hepph/0202039
 79.M. Ball, Rekonstruktion von Neutralinos mit TESLA. Diploma thesis, University of Hamburg (2003). https://bibpubdb1.desy.de/record/295174/. Accessed 22 Feb 2016
 80.N. D’Ascenzo, Study of the neutralino sector and analysis of the muon response of a highly granular hadron calorimeter at the international linear collider. Ph.D. thesis, University of Hamburg (2009). http://wwwlibrary.desy.de/cgibin/showprep.pl?desythesis09004. Accessed 17 Feb 2016
 81.T. Suehara, J. List, Chargino and neutralino separation with the ILD experiment. Report no.: DESY09099. arXiv:0906.5508 [hepex]
 82.H. Aihara, P. Burrows, M. Oreglia, E. Berger, V. Guarino et al., SiD letter of intent. Report nos.: SLACR989, FERMILABLOI200901, FERMILABPUB09681E. arXiv:0911.0006 [physics.insdet]
 83.P. Bechtle, M. Berggren, J. List, P. Schade, O. Stempel, Prospects for the study of the \(\tilde{\tau }\)system in SPS1a’ at the ILC. Phys. Rev. D 82, 055016 (2010). arXiv:0908.0876 [hepex]
 84.C. Bartels, M. Berggren, J. List, Characterising WIMPs at a future \(e^+e^\) linear collider. Eur. Phys. J. C 72, 2213 (2012). arXiv:1206.6639 [hepex]
 85.C. Bartels, WIMP search and a Cherenkov detector prototype for ILC polarimetry. Ph.D. thesis, University of Hamburg (2011). http://wwwlibrary.desy.de/preparch/desy/thesis/desythesis11034.pdf. Accessed 17 Feb 2016
 86.G. MoortgatPick, T. Abe, G. Alexander, B. Ananthanarayan, A. Babich et al., The role of polarized positrons and electrons in revealing fundamental interactions at the linear collider. Phys. Rep. 460, 131–243 (2008). arXiv:hepph/0507011 ADSCrossRefGoogle Scholar
 87.C. Bartels, O. Kittel, U. Langenfeld, J. List, Measurement of radiative neutralino production, in International Workshop on Future Linear Colliders (LCWS11) (Granada, 2011) arXiv:1202.6324 [hepph]
 88.M. Berggren, Reconstructing sleptons in cascadedecays at the linear collider, in Proceedings of LCWS04 (Paris, April 2004), pp. 907–910. arXiv:hepph/0508247
 89.A.L. Read, Presentation of search results: the cl s technique. J Phys G: Nucl Part Phys 28(10), 2693 (2002). http://stacks.iop.org/09543899/28/i=10/a=313
 90.T. Junk, Confidence level computation for combining searches with small statistics. Nucl. Instrum. Meth. A 434, 435–443 (1999). arXiv:hepex/9902006
 91.The ATLAS Collaboration, The CMS Collaboration, The LHC Higgs Combination Group, Procedure for the LHC Higgs boson search combination in Summer 2011. Technical report CMSNOTE2011005. ATLPHYSPUB201111, CERN, Geneva, Aug (2011). https://cds.cern.ch/record/1379837. Accessed 17 Feb 2016
 92.CMS Collaboration, Jet energy resolution in CMS at sqrt(s)=7 TeV. Technical report CMSPASJME10014 (2011)Google Scholar
 93.D. Curtin, Mixing it up with MT2: unbiased mass measurements at hadron colliders. Phys. Rev. D 85, 075004 (2012). arXiv:1112.1095 [hepph]ADSCrossRefGoogle Scholar
 94.M. Berggren, Simplified SUSY at the ILC, in Community Summer Study 2013: Snowmass on the Mississippi (CSS2013) (Minneapolis, 2013). arXiv:1308.1461 [hepph]
 95.A. Freitas, H.U. Martyn, U. Nauenberg, P. Zerwas, Sleptons: masses, mixings, couplings, in Linear Colliders. Proceedings, International Conference, LCWS 2004 (Paris, 2004), pp. 939–946. arXiv:hepph/0409129
 96.P. Bechtle, K. Desch, M. Uhlenbrock, P. Wienemann, Constraining SUSY models with Fittino using measurements before, with and beyond the LHC. Eur. Phys. J. C 66, 215–259 (2010). arXiv:0907.2589 [hepph]ADSCrossRefGoogle Scholar
 97.A. Bharucha, J. Kalinowski, G. MoortgatPick, K. Rolbiecki, G. Weiglein, Oneloop effects on MSSM parameter determination via chargino production at the LC. Eur. Phys. J. C 73(6), 2446 (2013). arXiv:1211.3745 [hepph]ADSCrossRefGoogle Scholar
 98.LHC/LC Study Group Collaboration, G. Weiglein et al., Physics interplay of the LHC and the ILC. Phys. Rep. 426, 47–358 (2006). arXiv:hepph/0410364 ADSCrossRefGoogle Scholar
 99.G. Blair, A. Freitas, H.U. Martyn, G. Polesello, W. Porod et al., Reconstructing supersymmetry at ILC/LHC. Acta Phys. Polon. B 36, 3445–3462 (2005). arXiv:hepph/0512084 ADSGoogle Scholar
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