5.1 Event Selection
5.1.2 Particle multiplicities and kinematic properties
Having defined the object selection criteria, the particle multiplicities and kinematic properties of the BC 1 scenario are presented next. The comparison of the SUSY scenario with Monte Carlo predictions for the relevant Standard Model processes allows to derive event selection cuts. The following histograms are scaled to an integrated luminosity of R
Ldt = 1 fb−1 at a centre-of-mass energy of √
s = 7 TeV using the predicted cross sections and k-factors of the different Monte Carlo samples. They do not include any event selection cuts, despite the pre-selection to avoid electrons in the crack region as described before. The various Standard Model contributions are grouped in the categories W + jets, Z + jets, di-boson production, tt and QCD di-jets. They are stacked on top of each other, while the BC 1 signal is shown in front of the Standard Model distributions.
In Figure 5.1 the number of selected electrons, muons, hadronic tau decays and jets per event are shown. One can immediately see the large excess of isolated electrons in the BC 1 signal compared to the Standard Model events. The mean number of muons (Figure 5.1b) is also relatively large compared to some of the Standard Model processes.
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Figure 5.1: Number of reconstructed and identified objects in BC 1 signal and Standard Model background. The quality requirements for the electrons, muons and (hadronically decayed) taus considered here are described in the text. Additionally the mentioned over-lap removal procedure between reconstructed objects was performed. No event selection cuts, despite the pre-selection explained in Section 5.1.1, were applied. The different background contributions are stacked on top of each other in the following order: tt, Z + jets, W + jets, di-boson, QCD jet production. The BC 1 signal (red) is drawn in front of the background histograms.
The large number of electrons and muons in the final state provides the most striking signature of the BC1 scenario.
In the ratio between electrons and muons an interesting property of the benchmark scenario BC 1 is visible. One observes a mean number of two to three electrons per BC 1 event, whereas the muon distribution peaks at one. This is the expected behaviour from the parton-level signatures reviewed in Section 1.2.3, cf. especially the row for the λ121 coupling in Table 1.4. The decay of two τe-LSPs in a typical BC 1 event leads at parton level to two to four electrons and up to two muons. Therefore the ratio of the number of reconstructed electrons and muons carries information about the involved B3 coupling. λ121 couples two lepton superfields of the first generation to one of the second generation. In this case the eτ-LSP decays produce more electrons than muons. If one
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Figure 5.2: Transverse momentumpTof the leading and the second reconstructed and iden-tified leptons in each event for the BC 1 signal and Standard Model background. Color scheme and selection are as in Figure 5.1. The “spikes” in the QCD di-jet distribution are caused by large scale factors that apply for some QCD Monte Carlo samples due to limited statistics.
assumes λ122 6= 0 instead, the situation would be reversed and the average number of muons to electrons would be roughly three.
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leppT and HT0 in BC 1 signal and Standard Model background. No event selection cuts, despite the cleaning cuts explained in the text, were applied.
Not only the bare numbers of the selected leptons per event are of interest, but also their transverse momenta. Figure 5.2 presents the pT distributions of the two hardest electrons and the two hardest muons. The pT distribution of the background falls off more rapidly than the signal especially for electrons. For large momenta (pT&100 GeV) of the second electron (Figure 5.2b) one can see that the signal already gets competitive with the important tt background. The transverse momenta of the leading and second leading electrons and muons will be used in the selection of BC 1 events.
Due to their large multiplicity and large transverse momenta, also leptons beyond the sub-leading electron and muon can contribute significantly to the energy deposition of all leptons. The scalar pT sum, P
leppT, of all electrons and muons (Figure 5.3a) is therefore another variable to be used in the event selection and accounts for the fact that the momenta of the signal lepton are on average larger than the background. The lepton momenta in BC 1 can be large because they are produced at the end of the decay chain of heavy SUSY particles.
The number of jets per event (Figure 5.1d) does not show a strongly expressed maximum for BC 1 events. This can be explained by the different sparticles produced and their various decay modes that contribute in the upper parts of the SUSY decay chain and gluon radiation. In the prototype case of squark pair production and decay via the lightest neutralino into the stau-LSP one would expect two high-momentum jets:
qq/gg→qeqe→jjχe01χe01→jj(eτ τ)(eτ τ)→jj(τ τ `+`−ν)(τ τ `+`−ν). (5.1) Gluino (eg) pair production instead of squark pair production will usually give two addi-tional jets,e.g.via the decayeg →jeq. Additional jets to those from the decay chain can occur from parton showers or non-identified hadronic tau decays. Indeed one observes that most events include between two and five jets. The distribution of the number of jets looks very different in the semi-leptonic tt decays for example. Here one expects two b-jets and two light quark jets from one of the W bosons. This behaviour is also
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Figure 5.4: Transverse momentum pT of the four leading jets for the BC 1 signal and the Standard Model background. No event selection cuts, despite the cleaning cuts explained in the text, were applied.
visible in the background distribution. The fact that less entries with no jets than with one jet are observed in the W + jets and Z + jets samples is an artifact of the selection of Monte Carlo samples. Only W and Z Monte Carlo events with at least one additional parton in the hard process are taken into account here, because only those are relevant as background.
The pT spectra of the four hardest jets are visualised in Figure 5.4. It is clear that the jet spectra are fully dominated by QCD jet events. Anyhow, jets provide important information to suppress Standard Model background from W+jets and Z+jets events. The jet spectra for the BC 1 signal are relatively flat over a wide range of transverse momenta, whereas they are much more steeply falling for the background. In the spectrum of the leading jet (Figure 5.4a) one can see a maximum in the region of pT = 350 GeV to 400 GeV. This wide peak is mainly caused by the decay of squarks into the lightest neutralino χe01. The mass difference between most of the squarks and the χe01 is about 400 to 500 GeV in BC 1 [43, 59].
Additional softer jets may arise from the decay of gluinos into squarks. Here the mass differences are usually only around 100 GeV, so those jets appear in the sub-leading pT
distributions Figure 5.4c and 5.4d. From Figure 5.4 one can see that the signal-to-background ratio will improve by demanding very hard jets. This leads to the definition of the so-called visible hadronic massHT0 =P
jet 1–4pT as the scalar sum of the transverse momenta of the four leading jets. Summing over more jets would reduce the separation to tt events, where more jets are expected than in BC 1 (cf.Figure 5.1d). The distribution of HT0 in Figure 5.3b reflects the above considerations.
It may be surprising at first sight that the number of selected hadronic tau decays per BC 1 event in Figure 5.1c does only rarely exceed two. In most BC 1 events no hadronic tau lepton is selected at all. Naively one would expect four tau leptons in the basic process (5.1) from which about 65 % each should decay hadronically. It turns out that only a small fraction of the hadronic tau decays can be identified as such in the BC 1 events. One reason is the low energy of the τ±, which often causes the visible part of the tau decay to have transverse momenta below 10 GeV. The η-pT distribution of hadronically decaying taus in BC 1 is depicted in Figure 5.5. It is clearly visible that a significant fraction of the τ leptons is outside the acceptance region (dashed line) of the τ identification.
Figure 5.5: Distribution in the ηvis-pvisT plane of hadronically decaying taus in BC 1. All true hadronic decays are in-cluded here,i.e.no detector simulation or acceptance cuts were applied. Only the visible component of the tau de-cay products is considered. The dashed line illustrates the acceptance region for
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Another important reason, why much less τ are found than naively expected, is the event topology of the BC 1 signal. Many tau leptons are “hidden” by electrons, muons or other jets in the events, because of the relatively large abundance of those objects.
This effect can be seen in Figure 5.6 where the efficiency for the reconstruction and identification of hadronic tau decays is shown as a function of the Monte Carlo truth momentum. Even at the same visible tau momentum the efficiency in BC 1 events (open symbols) is reduced by more than a factor of two compared to Z→τ−τ+ events (solid symbols), the “standard candle” for the tau identification. In the Figure only the efficiency for the reconstruction and identification is included to visualise the effect on the τ ID itself. Additional losses in the efficiency occur due to the overlap removal applied in the analysis.
For completeness the momentum distributions of the leading and sub-leading selected tau lepton are shown in Figure 5.2e and 5.2f. From the discussion above it is clear that the tau leptons cannot be used reasonably well to distinguish BC 1 signal from Standard
Figure 5.6: Reconstruction and identifi-cation efficiency of hadronically decay-ing taus in BC 1 (open symbols) and Z→τ−τ+ events (solid symbols). The τ candidates are selected as given in Ta-ble 5.1, but no overlap removal was
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Model background. Still their identification will be important for the reconstruction of the mass of the eτ-LSP as we will see in Section 5.3.
The missing transverse energyETmissis an important observable in the case ofR-parity conserving SUSY models, where the LSP is stable and leaves the experiment undetected, cf. the discussion in Section 1.2.2. In R-parity violating models this argument does not hold and the missing transverse energy is expected to be much smaller than in RPC models. However, the observed ETmiss in Figure 5.7 can be significant compared to Standard Model processes with ETmiss, like di- and semi-leptonic tt events. The reason for this are the neutrinos from the eτ-LSP decays
χe01 →eτ1+τ
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and the neutrinos from the successive τ decays. However, no explicit cut on ETmiss will be applied in the event selection in order to keep the analysis complementary to searches for R-parity conserving SUSY in ATLAS.
It should be kept in mind, that the discovery of an ETmiss signal does not necessarily contradict R/p models. ETmiss alone is not sufficient to distinguishR-parity violating from
Figure 5.7: Distribution of the missing transverse energy ETmiss in BC 1 and Standard Model background. No event selection cuts, despite the cleaning cuts
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R-parity conserving SUSY. Finally, a lepton (linear) collider may be needed to clarify the nature of the LSP and the source of the missing energy [35]. Further observables, like kinematic edges, allow to gain insights in the SUSY mass spectrum to constrain the SUSY models [141].