Precision Measurements of Supersymmetry at the International Linear Collider

While the 7 and 8 TeV results from the LHC exclude highly constrained SUSY models with a light sparticle spectrum, less constrained models are still viable. Certain such models promise both discovery of coloured sparticles during the 14 TeV run of the LHC, and a rich spectrum of non-coloured states, accessible at the ILC. The LHC might or might not give a hint of the existence of these electro-weak states, but only at the ILC can measurements with su ﬃ cient precision be done to elucidate the details of the model. This contribution reports on studies of such models at the ILC based on simulation of the current detector proposals.


Introduction
The first SUSY channel to manifest itself at the ILC depends on the SUSY scenario and on the inital centerof-mass energy of the machine. An example for a scenario consistent with all current constraints, which predicts an extremely rich spectrum in the kinematic reach of the ILC are the STC series [1]. The large number of different thresholds and the effect of different beam polarisation choices is illustrated in Fig. 1(left). If the ILC starts out as a Higgs factory at √ s = 250 GeV, e + e − →τ 1τ1 (brown) andχ 0 1χ 0 1 γ (blue) would be the first observable channels in this scenario.

Early Discovery
As soon as the center-of-mass energy is raised past the pair production threshold for right-handed selectrons (in STC4 when √ s > 270 GeV), the e + e − +missing 4-momentum signature would see the striking signal shown in Fig. 1(right) within a few days. With an integrated luminosity of 500 fb −1 , theẽ R and LSP masses can be measured with precisions of δMẽ R = 230 MeV and δMχ0 1 = 170 MeV, respectively.

Kinematic Edges vs Threshold Scan
The cross-section forμ R pair production is much lower than forẽ R 's due to the absence of a t-channel. Still theμ R mass can be determined from the kinematic endpoints of the decay muon energy spectrum shown in Fig. 2(left). With 500 fb −1 at √ s = 500 GeV and P(e − , e + ) = (+80%, −30%), precisions of δMμ R = 500 MeV and δMχ0 1 = 380 MeV can be achieved by this technique. These numbers can be improved by collecting more data, or by exploiting the tunable center-Available online at www.sciencedirect.com of-mass energy of the ILC for a scan of the production threshold near 270 GeV ( Fig. 2(right)). Collecting 90 fb −1 of data, again with P(e − , e + ) = (+80%, −30%), is sufficient to achieve a precision of 200 MeV for thẽ μ R and LSP masses.

Cascade decays: SUSY is a peak!
A particularly interesting channel for slepton reconstruction is e + e − →χ 0 2χ 0 2 followed byχ 0 2 →μ R μ or e R e, even if the branching ratio is at the level of a few percent like in our example point. These cascade decays can be fully kinematically constrained at the ILC, and promise to yield even lower uncertainties on theμ R andẽ R masses than the threshold scans, of the order of 25 MeV. This is estimated based on an earlier study [4] in a scenario with branching ratios about twice as large for the considered decay mode, where a precision of 10 MeV was found. The corresponding distribution of the reconstructedμ R mass is shown in Fig. 3(left) including all SM and SUSY backgrounds. Even the decays toτ 1 τ, which are more challenging due to the undetected neutrinos, can be reconstructed as shown in Fig. 3(right) and yield results comparable to a threshold scan.

The Cosmic Connection:τ Mass and Crosssection
Especially inτ-coannihilation scenarios like the STC series, a precise determination of theτ sector is essential in order to test whether theχ 0 1 is indeed the dominant Dark Matter constituent. With the ILC at √ s = 500 GeV, theτ 1 mass can be determined to 200 MeV (Fig. 4(left)), and theτ 2 mass to 5 GeV from the endpoint of the τ-jet energy spectrum. The production cross-sections for both these modes can be determined at the level of 4% [5]. By using all available collider observables to constrain the relevant SUSY parameters, one can predict the relic density based on the assumption that theχ 0 1 is the only contribution to Dark Matter. This was studied by the Fittino group in a similar model, in particular theτ 1 andχ 0 1 properties were identical to STC4. Figure 4(right) shows the result of determining Ω DM h 2 from a fit with 18 free SUSY parameters from LHC data alone and from both LHC and ILC data. The polarisation of τ-leptons originating from theτ 1 decay, which gives access to theτ 1 andχ 0 1 mixinggauginos conserve chirality, higgsinos flip it -can be measured with an accuracy better than 10%, eg. from τ → π ± ν τ decays or from decays to ρ-mesons (τ → ρ ± ντ → π ± π 0 ν τ ). In the latter case, the observable R = E π /E jet can be used to measure the τ-polarisation to ±5% by a fit of templates for the τ's being of negative, of opposite, or positive helicity (Fig. 5) to the data (Fig. 6 (left)). Theτ mixing itself can be extracted in several ways: Comparing the cross-section at different beam polarisations, determining the cross-section for τ 1τ2 production, or from comparing the masses of the (un-mixed)ẽ's andμ's to Mτ 1 and Mτ 2 [5].

SUSY at √ s = 250 GeV: NMSSM Higgs Bosons
In the NMSSM, the Higgs boson discovered at the LHC does not need to be the lightest Higgs boson. Current limits on invisible decays allow for a sizable branching fraction of h 1,2 → a 1 a 1 , where a 1 can be very light down to a few GeV and decays eg. to τ or μ pairs. Already at a 250 GeV ILC, these states can be discovered and their masses measured to δM a 1 = 5 MeV and δM h 1,2 = 200 MeV from 250 fb −1 of data, using kinematic reconstruction (a 1 , Fig. 7(left)) and recoil techniques (h 1,2 , Fig. 7(right)) [8].

Conclusions
Although Supersymmetry has not yet been discovered at the LHC, there are plenty of opportunities for electroweak states, sleptons and additional Higgs bosons to be observable at the ILC. This contribution illustrated the ILC's potential for precision measurements of SUSY particles with several examples, all based on realistic detector simulations. If new particles are discovered in future runs of the LHC or at the ILC itself, the ILC will be able to measure masses, polarised crosssections and other observables at the level of a few percent or better, which enables to test the connection of the new particles to the big open questions of particle physics, such as the nature of Dark Matter or the origin of neutrino masses.