Nuclear Physics B Proceedings Supplement 00 (2014) 1–7
Supplement
Discovering Supersymmetry and Dark Matter at the International Linear Collider
Mikael Berggren, on behalf of the ILC Physics and Detector Study
DESY, Notkestrasse 85, D-22607 Hamburg, Germany
Abstract
Although the LHC experiments have put strong limits on coloured supersymmetric states, it is still possible that electroweakly interacting supersymmetric particles have masses in the range 100-200 GeV. Even outside of super- symmetry, candidates for the particle of dark matter may have masses in this range unconstrained by LHC data. In e+e−annihilation, the low backgrounds, precise knowledge of the initial-state beams, and sensitivity to small energy depositions would allow the discovery and precision measurement of such particles. This contribution will report the current status of studies for the prospects of measurements of light electroweak states at the International Linear Collider, with results from full-simulation studies of their production in the detectors proposed for the ILC.
Keywords: Linear Collider, Supersymmetry, Dark Matter
1. The ILC
The International Linear Collider (ILC) [1] is a proposed e+e− collider, colliding electrons and positrons separately accelerated by two linear acceler- ators equipped by superconducting radio-frequency ac- celerating structures. The total length of the two linacs and the beam-delivery systems is 31 km. The centre-of- mass energy (EC MS) is to be tunable between 200 and 500 GeV, with an upgrade path to 1 TeV defined. Both beams are polarised, with an expected polarisation of the electron beam of 80%, and of the positron beam of at least 30%. The sign of the polarisation can be rapidly switched to be able to control the systematic uncertainty on the instantaneous polarisation. Once it is tuned up, the machine is designed to deliver an integrated lumi- nosity (R
Ldt) of 250 fb−1 per year. The luminosity will be disrtibuted to two experiments sharing one in- teraction region. The current time-scale of the project is such that it would be running concurrently with the high luminosity run of the LHC.
WhileEC MS of the ILC is certainly lower than that of the LHC, several features make it promising to be not only a precision machine, but also a discovery one. First of all, as it is a lepton-collider, i.e. a collider of elemen-
tary particles, the initial state is known. This is in con- trast to proton colliders, where composite particles are collided, and the initial state of the system of coliding partons is a priori unknown. Furthermore, the produc- tion processes are electroweak, which implies that the- oretical uncertainties are small, and that there is no “un- derlying event” accompanying the hard interaction. It also implies low cross-sections, compared to the strong interaction production at LHC. This is so not only for the interesting signal processes, but also for the back- ground ones. The resulting low rates have several ben- eficial consequences for the experiments: the detectors will not be required to be radiation-hard, meaning that they can be made thin, with only a few percent of a radiation-length (X0) in front of the calorimeters, and that they can be quite close to the interaction point, with the first layer of the vertex detector as close as 1 to 2 cm. The detectors can also have very close to 4π coverage: the only blind spot would be the holes for the beam-pipes in the forward calorimetry, correspond- ing to around 0.2 msr. Such excellent hermeticity is required to reject background processes with high en- ergy particles at low angles. Finally, the low rates al- low trigger-less operation, particularly important for the
search for new phenomena. Further details of the pro- posed detectors for the ILC can be found in [2].
Taken together, on one hand these features enable the high precision (sub-%) measurements needed to extend our knowledge from precision measurements beyond that gained at LEP, at the Tevatron, and at LHC, and on the other hand to be sensitive to Beyond the Stan- dard Model (BSM) signals, even if they are quite hard to detect, due to low visible energy deposits.
2. SUSY with no loop-holes
The corner-stone of SUSY is thatsparticles couple as particles[3]. This is independent of the mechanism responsible for SUSY breaking. In particular, the cou- plings to the photon and the Z-boson are known, which implies that the cross-section for any e+e−→ sparti- cle – anti-sparticle pair process that proceeds only via the s-channel is determined by the kinematics alone, i.e. byEC MS and the mass of the sparticle. Contribu- tions from sparticle exchange in the t-channel are possi- ble in ˜νe,˜e,χ˜0i or ˜χ±i pair-production, by exchange of a χ˜±i,χ˜0i,˜e or ˜νe, respectively. Also with such diagrams contributing, all couplings are known, and the cross- section will still be determined by the kinematic rela- tions, at the cost that one must consider both the mass of the produced and of the exchanged sparticle.
Furthermore, by definition there is one Lightest SUSY Particle (LSP), and one Next-to-Lightest SUSY Particle (NLSP). If it is stable, it is un-avoidable that the LSP must be neutral and weakly interacting, due to cosmological constraints. The NLSP, on the other hand, could be any sparticle - a slepton, a bosino, or a squark.
However, there is only a limited number of sparticles.
While an arbitrary sparticle in the spectrum of any spe- cific SUSY model typically would decay through cas- cades of other, lighter sparticles, the NLSP only has one decay-mode, namely to its SM partner and to the LSP, which is the topology defining asimplified model.
At the LHC, simplified models have become a widely used and important tool to cover the more diverse phe- nomenology beyond constrained SUSY models. How- ever they come with a substantial number of caveats themselves, and great care needs to be taken when draw- ing conclusions from limits based on the simplified ap- proach. The LHC is particularly powerful in searching for coloured sparticles, either gluinos or first and second generation squarks. Exactly these sparticles are those that are expected to be the the heaviest ones in most SUSY models. Therefore it is rather unlikely that their decays directly to the LSP and the SM partner would have a large branching ratio, and that the “simplified
model” approach would un-ambiguously cover a large parameter-space in a general MSSM model.
0 50 100 150 200 250
0 50 100 150 200 250 Exclusion
Discovery
Excludable at 95% CL NLSP : µ˜R
MNLSP [GeV]
MLSP [GeV]
0 50 100 150 200 250
240 242 244 246 248 250 Exclusion
Discovery NLSP : µ˜R
MNLSP [GeV]
MLSP [GeV]
0 50 100 150 200 250
0 50 100 150 200 250 Exclusion
Discovery
Excludable at 95% CL NLSP : τ˜1
MNLSP [GeV]
MLSP [GeV]
0 50 100 150 200 250
200 210 220 230 240 250 Exclusion
Discovery NLSP : τ˜1
MNLSP [GeV]
MLSP [GeV]
Figure 1: Discovery-reach for a ˜µR(top) or ˜τ1(bottom) NLSP for RLdt=500 fb−1at√
s=500 GeV. In the ˜τ1case, the mixing angle was chosen to give the lowest possible production cross-section. Left:
full scale, Right: zoom to last few GeV before the kinematic limit [4].
As was pointed out above and in [4], at the ILC the situation is different - quite on the contrary simplified models are model independent, since any SUSY model must contain one processes - NLSP pair production - with such a signature. The size of it only depends on MLS P, MNLS P and the SUSY principle. At the ILC, this process would in the vast majority of cases be de- tectable, if it is at all kinematically allowed.
Figure 1 shows the expected exclusion and discovery reach for two different hypotheses on the nature of the NLSP: the easy case of a ˜µRNLSP, and the more dif- ficult case of a ˜τ1 NLSP at the ˜τmixing angle giving the lowest possible production cross-section. As can be seen from these figures, at the ILC, one would expect to either discover or exclude NLSPs up to some GeV below the kinematic limit.
This can be compared with present and projected lim- its at the LHC. In figure 2, the current limits in theMχ˜0 - MNLSP plane from the di- and tri-lepton searches of1
ATLAS [5] are shown, together with the projected de- scovery reach at 14 TeV withR
Ldt=300 or 3000 fb−1 [6]. Here it is assumed that Mχ˜0
2 = Mχ˜±1, and that in- deed Br(χ → W(∗)/Z(∗)χ˜01)=1. On the same figure, the corresonding limit from LEP [7, 8, 9] is also shown (shaded). For the latter, only ˜χ±1 pair production is as-
Figure 2: Discovery or exclusion regions in theMNLS P−MLS Pplane for a ˜χ±1or ˜χ02NLSP. Solid brown area: LEP exclusion; Solid red and dashed grey lines: ATLAS exclusion (observed and expected); Solid blue (green) lines: ATLAS 14 TeV discovery projections forR
Ldt
=300 (3000) fb−1; Dashed green (magenta) lines: ILC discovery ex- pectation forEC MS =500 (1000) GeV; Solid black line: below line, no GUT scale gaugino mass unification.
sumed, with no assumption on the decay mode. The expected limits for the ILC atEC MS =500 or 1000 GeV are also shown with the same assumptions as for the LEP plot. The thick diagonal line indicates whereMχ˜0
(orMχ˜±1) is twiceMχ˜0 2
1. Below this line, GUT scale uni- fication of the gaugino mass-parametersM1andM2 is not possible, hence no model where such unification is assumed would be allowed in that region. As can be seen from the region not covered by the LHC, there is a large discovery potential for the ILC, even after the high luminosity LHC data has been fully exploited.
3. Example: Natural SUSY with light, degenerate higgsinos
In supersymmetric extensions of the Standard Model, higgsino-like charginos and neutralinos are preferred to have masses of the order of the electroweak scale by nat- uralness arguments. The mass of the Z boson is related to the SUSY parameters according to [10, 11]:
m2Z = 2m2H
utan2β−m2H
d
1−tan2β −2|µ|2 wherem2H
u,Hd are the Higgs soft masses. The require- ment to have a low amount of fine-tuning between the terms leads to the conclusion thatµ=O(weak scale).
If, in addition to the low value of µ, the gaugino masses are high (multi-TeV), then ˜χ01, ˜χ02 and ˜χ±1 are pure higgsinos. The rest of the SUSY spectrum will
be in the multi-TeV range. In addition,Mχ˜0
1,2,Mχ˜±1 ≈µ, and are near degenerate, with a mass-gap between the LSP and the NLSP (∆M) of 1 GeV or less [12]. Such light, degenerate, bosinos will be difficult to observe at any collider.
At the ILC, the main problem to overcome to observe such events with only a few low momentum tracks pro- duced together with the invisible LSP is the abundant background from γγ-events. The method to mitigate this problem was pioneered at LEP [7, 8, 9], and con- sists of tagging the events by demanding the presence of a detected ISR photon, then study the rest of the event, and is illustrated in figure 3. The top two schematic
Figure 3: Sketches of aγγevent (left) and low∆(M) SUSY event (right). The top figures show the situation without a detected ISR-γ, while the bottom ones show it when an ISR-γis detected.
drawings shows aγγ-event and a signal event. One can see that the detected system is identical in the two cases, since the beam-remnant electron and positron in theγγ- event escape un-detected through the out-going beam- pipe (largely exaggerated in size in the sketch). The lower two plots shows the situation when the require- ment that a well reconstructed ISR photon should be present in the event. In this case, the detected system is no longer the same for background and signal, since the electron or positron emitting the ISR will be deflected into the detector acceptance. This illustrates the impor- tance of hermeticity and good detection capabilities at the smallest possible angles to the beam-axis.
In [12], two such models - denoted by dM1600 and dM770 - were studied. The key-properties were:
• dM1600: ∆(M)=1.6 GeV, mh=124 GeV, Mχ˜0
1=164.2 GeV.
• dM770: ∆(M)=0.77 GeV, mh=127 GeV, Mχ˜0
1=166.6 GeV.
/GeV s’
200 250 300 350 400 450 500
Events
0 200 400 600 800 1000
1200 γ
2
χ0
∼
1
χ0
∼
1γ χ -
∼
1
χ+
∼
SM simul. data
0.8 GeV
± = 166.3
fit 2 χ0
M∼
dM770
/GeV s’
200 250 300 350 400 450 500
Events/10 GeV
0 200 400 600
800 χ∼1+χ∼1 -γ
2γ χ∼0 1
χ∼0
SM simul. data
1.4 GeV
± = 168.0
fit 1 χ∼±
M
dM1600
Figure 4: Distribution of the reduced centre-of-mass energy (√ s0) of the system recoiling against the hard ISR photon for all selected events forR
Ldt=500 fb−1,P(e−,e+)=(−80%,+30%). The NLSP mass is determined from a linear fit to the distribution near the endpoint.
Top: e+e−→˜χ01χ˜02in the dM770 scenario; Bottom: e+e−→˜χ±1χ˜±1 in the dM1600 scenario.
In both cases, all other SUSY particles had masses in the multi-TeV range. The stars in figure 2 show where the two models are in theMNLS P-MLS Pplane. Clearly, the existence of such models would be very hard to determine at the LHC. The production channels are e+e−→χ˜01χ˜02or ˜χ±1χ˜±1 in the s-channel. There is no pro- duction of ˜χ0iχ˜0i due to weak isospin, and no t-channel ˜e or ˜νexchange, because the bosinos are higgsinos.
The bosinos undergo few-body decays or, for ˜χ02, ra- diative decays. To determine model-parameters, one needs to be able to separate ˜χ±1 from ˜χ02, which can be done by requiring either semi-leptonic orγfinal states, since the former only occurs in ˜χ±1 decays, the latter only in ˜χ02 decays. The branching ratios for these de- cays, and all other possible ones, were calculated with Herwig [13, 14]. The requirement to observe an ISR
/GeV s’
250 300 350 400 450 500
/GeVπE*
0 2 4
6 χ∼1 -γ
1 +
χ∼
2γ
0
χ∼
1 0
χ∼ SM
dM770
π/GeV E*
0 0.5 1 1.5 2 2.5
Events/0.1 GeV
0 5 10 15
20 γ
1
χ -
∼
1
χ+
∼
2γ χ0
∼
1
χ0
∼
simul. data - <SM>
0.04 GeV
± = 0.81 Mfit
∆
dM770
Figure 5: Measurement of Mχ˜± 1 −Mχ˜0
1 for R
Ldt = 500 fb−1, P(e−,e+) =(−80%,+30%) in the dM770 scenario. The upper fig- ure showsE∗πvs. √
s0. The dashed line indicates the cut onE∗π, the solid one the cut on√
s0. The arrow indicates the true value of∆(M).
The lower plots showsEπ∗(background subtracted) after the√ s0cut.
photon in the event gives the possibility to determine the reduced √
s0froms0=s−2√
sEγ. Here, √ sis the nominalEC MS, which is known at the ILC, andEγis the energy of the ISR photon, measured by the low-angle calorimeters. The knowledge of √
s0gives the possibil- ity to “auto-scan” the available energy available for the production process, see figure 4. The end-point of the excess over the SM background enables to determine the bosino masses: at this point, where the value ofs0is denoted s0|thresh, the chargino pair is produced nearly at rest, and
Mχ˜±
1 =1
2
ps0|thresh= 1 2
q s−2√
sEγ.
Using this relation, the bosino masses could be deter- mined to∼1 GeV.
At the threshold, where the bosino pair is produced at rest, the energy of the decay-product in the bosino rest-frame,E∗π, is given by
E∗π= 1
1/∆(M)+1/Σ(M) + m2π 2Mχ˜±1
≈∆(M)
/ TeV M1
-10 -5 0 5 10
/ TeV2M
0 2 4 6 8 10
dM1600 ), 2 ab-1 1
χ0 2, χ0
∆ M(
≤ 50 β tan
= 10 β tan
/ TeV M1
-20 -10 0 10 20
/ TeV2M
0 5 10 15 20
dM770 ), 2 ab-1 1
χ0 2, χ0
∆ M(
≤ 50 β tan
Figure 6: The 1-σcontours for determination ofM1andM2 in the dM1600 (top) and dM770 (bottom) scenarios forR
Ldt=2 ab−1. The input values ofM1andM2are indicated by the stars ((tanβ)true = 44). ForM1>0, other values of tanβdo not further extend allowed regions. In dM1600, solutions exist forM1 <0, but only for 8 ≤ tanβ≤16 in a narrow strip nearM1∼ −500 GeV.
The last equality is because both the mass difference and mπare several orders of magnitude smaller than the hig- gsino masses, soE∗πis equal to the mass difference itself to a very good approximation. Using this relation, and studyingE∗π close to the end-point,∆(M) could be de- termined to∼100 MeV, see figure 5.
The precise measurements of the bosino masses, of
∆(M), and of the production cross-sections, enables to extract the model-parametersµ, M1and M2(There is lit- tle tanβdependence on the observables.). It was found that µ can be determined to ∼ 5 %. After collecting R Ldt=2 ab−1of data, the limits on M1and M2shown in figure 6 could be obtained. It can be noted that for both models, the relative sign of M1and M2can be de- termined. Lowerand upperlimits on M2 could be set in both models, as well as lower limits on M11. For the dM1600 model, also an upper limit for M1could be set. The fact that both upper and lower limits could be
1The narrow allowed strip atM1≈-500 GeV in dM1600 will most likely be excluded by combiningMχ˜0
1
≈165 GeV as measured at the ILC with limits from the LHC: It would predict a bino-like ˜χ03with mass∼500 GeV, decaying toW,Zorhand one of the higgsinos, which are all invisible at the LHC. At the LHC, the process would therefore be experimentally equivalent to NLSP→LSP+W,Zorh, and from the projections in figure 2 one sees that (MLS P,MNLS P)≈ (165,500) GeV would be excluded.
?
χ
χ
e+
e-
?
χ
χ e+
e-
Figure 7: WIMP annihilation (left) and production (right) diagrams.
determined for at least some of the model parameters il- lustrates how results from the ILC could point to what energy reach would be needed for a future facility to be able to directly study the mechanism of SUSY breaking.
4. Example: Only WIMPs
Cosmological observations indicate that about 85%
of the matter in the universe is some kind of completely unknown non-baryonic Dark Matter (DM) [15]. One interesting candidate for the nature of DM is that it con- sists of Weakly Interacting Massive Particles (WIMPs, denoted generically byχ)[16]. Many theories of BSM physics postulate the existence of such a particle, e.g.
the LSP of SUSY or the lightest KK state in extra- dimension theories. As the cosmological indications of existence of DM does not provide information on the detailed nature of DM, not even whether it is expected to be accompanied by other new particles, it is simplest to search for DM under the assumption that the WIMP is theonly accessible BSM particle.
Under the assumption that DM is a WIMP, cosmol- ogy indicates that WIMPs annihilated in the early uni- verse at a certain rate in order to arrive at the before- mentioned 85% abundance. If the annihilation took place by pairs of WIMPs annihilating to SM particles, the reverse of the process could take place at colliders, as illustrated in figure 7.
As the WIMP is weakly interacting, it will not be de- tectable, so to search for direct WIMP pair-production at a collider, one needs to make the invisible visible. As in the case of the light, degenerate Higgsino scenario discussed in the previous section, this is accomplished by requiring a detected initial state radiation. In the WIMP case, the ISR will recoil against “nothing”, i.e.
the undetectable WIMP-pair. At the LHC one would search forpp→χχgorχχγ, while at the ILC, the sig- nal process would be e+e−→χχγ, studied in [17] and [18].
There are two possible avenues to interpret the exper- imental observations:
• An effective operator approach [19], where one writes down all possible operators, and analyses the observations accordingly. This approach will yield exclusion regions in theMχ/Λplane, for each operator, whereΛis the mass-scale of the media- tor of the interaction (effectively the strength of a WIMP-fermion contact interaction). It should be kept in mind that this approach looses its validity ifΛis not much higher than √
s.
• A cosmological approach [20], where one assumes that the DM consists entirely of one single kind of WIMP. By assuming the cosmological value of the DM abundance (ΩDM), the experimental obser- vations can be cast into exclusion regions in the Mχ/coupling plane, for each WIMP spin and dom- inant partial wave.
In this note, we follow the effective operator approach.
4.1. Backgrounds and Signal extraction
There is one irreducible SM background to WIMP- pair production at the ILC, namely ee → ννγ. This background can be tackled two ways. Firstly, inee → ννγthe recoil-mass peaks atMZ, while the signal shows no such behaviour, see figure 8. Secondly, due to the nature of theZννandWνevertices, it can be “switched off” by choosing the polarisation of the electron beam to be right-handed (P(e−)=1). Another important, al- beit not irreducible, background is Bhabha-scattering accompanied by ISR. This will constitute a background if both the electron and the positron escape detection by leaving the detector through the outgoing beam-pipes.
Here, once again, the hermeticity and capabilities of the low-angle calorimetry become crucial to suppress back- ground. Even so, the radiative Bhabha process is the dominating background whenP(e−,e+)=(+80%,-60%) has been chosen.
The WIMP mass and its production cross-section can be obtained from the shape of theγspectrum, see fig- ure 8. In the most naive approach, this can be done by global event counting. However, this approach is quite sensitive to systematic errors, and a better method is fractional event counting [21], where binned data is weighted by the significance in each bin bySbin/√
Bbin. The ILC results shown here use the latter method, and include systematic uncertainties on luminosity, beam- spectrum, polarisation, γ detection efficiency and γ energy-scale.
In figure 9, we show the results, including a com- parison with current and projected LHC results. (LHC data: [22], projections: [23] ) We show two examples:
[GeV]
recoil
M
0 50 100 150 200 250 300 350 400 450 500 10
102
103
104
[GeV]
recoil
M
0 50 100 150 200 250 300 350 400 450 500 10
102
103
104
signal polarised beams
Figure 8: Recoil mass distribution for 150 GeV Spin-1 WIMP for EC MS=500 GeV. The signal contribution is shown in solid red.
Figure 9: Exclusion-reach in the WIMP searches. Top: Vec- tor operator; bottom Axial vector operator. Green (blue) dashed lines: ILC at R
Ldt = 500 (2000) fb−1, P(e−,e+) = [+80%,−30%]([+80%,−60%]),EC MS=500 GeV; Black dotted (red dashed): LHC atR
Ldt=300 (3000) fb−1,EC MS=14 TeV; Brown solid: CMS, current exclusion.
the vector operator (“spin independent”) case, with a fermion WIMP (Sχ = 1/2), and the axial-vector op- erator (“spin dependent”) case, also withSχ=1/2. As
expected, it can be seen that the LHC reaches higher masses, while the ILC probes larger Λ, i.e. smaller cross-sections. It is important to note that the LHC curves assume pure coupling tohadrons, while the ILC ones assume pure coupling toleptons. These two cases are not a priori comparable; they are rather complemen- tary. It is quite possible that the WIMP has widely dif- ferent couplings to leptons or quarks, e.g. if the medi- ator is similar to a slepton or a squark, or if the WIMP itself carries lepton- or baryon-number.
5. Conclusions
We have demonstrated that the ILC has a loop-hole free discovery potential for SUSY, up to the kinematic limit. It includes a vast region of moderate-to-small LSP-NLSP mass-differences, not explorable by the high luminosity LHC.
Futhermore, even in natural SUSY scenarios where the only sparticles below the multi TeV range are almost mass-degenerate higgsinos, it was shown that the ILC can both discover them, and do precise measurements allowing to determine model-parameters, including pa- rameters of the high-mass sector. In most cases, the ILC measurements would allow to constrain the high-mass sector both from below and above, thereby pointing in which direction to go in future facilities to be able to explore the SUSY breaking mechanisim in detail.
In searches for dark matter, the ILC yields orthog- onal information to the LHC and direct searches. By probing WIMP-lepton interaction bottom-up, it would test contact interactions at scales up to 3-4 TeV. In addi- tion, if WIMPs are discovered at the ILC, precise prop- erty determination would be possible: the WIMP mass would be known to 1-2%, as would its helicity structure, and the spin of the mediator. With such information, it would be possible to discriminate among different mod- els.
6. Acknowledgements
This talk was presented on the behalf of the ILC Physics and Detector Study, and the speaker thankfully acknowledges the contributions of the members of the group. We thank H. Sert, J. List, K. Rolbiecki, G.
Moortgat-Pick, T. Robens, F. Br¨ummer, H. Baer, M.
Perelstein and A. Chaus for useful discusions, and the ILC Generator and MC production Groups for provid- ing the SM background samples. The speaker acknowl- edges the support by the DFG through the SFB 676
“Particles, Strings and the Early Universe”.
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