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Search for top-squark pair production in the single-lepton final state in pp collisions at \(\sqrt{s}=8\ \mathrm{TeV}\)

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Abstract

This paper presents a search for the pair production of top squarks in events with a single isolated electron or muon, jets, large missing transverse momentum, and large transverse mass. The data sample corresponds to an integrated luminosity of 19.5 fb−1 of pp collisions collected in 2012 by the CMS experiment at the LHC at a center-of-mass energy of \(\sqrt{s}=8~\mathrm{TeV}\). No significant excess in data is observed above the expectation from standard model processes. The results are interpreted in the context of supersymmetric models with pair production of top squarks that decay either to a top quark and a neutralino or to a bottom quark and a chargino. For small mass values of the lightest supersymmetric particle, top-squark mass values up to around 650 GeV are excluded.

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Acknowledgements

We thank Ian Low for assistance with polarization issues in top squark decays and Jiayin Gu for help in implementing the code for the variables of Ref. [55].

We congratulate our colleagues in the CERN accelerator departments for the excellent performance of the LHC and thank the technical and administrative staffs at CERN and at other CMS institutes for their contributions to the success of the CMS effort. In addition, we gratefully acknowledge the computing centres and personnel of the Worldwide LHC Computing Grid for delivering so effectively the computing infrastructure essential to our analyses. Finally, we acknowledge the enduring support for the construction and operation of the LHC and the CMS detector provided by the following funding agencies: BMWF and FWF (Austria); FNRS and FWO (Belgium); CNPq, CAPES, FAPERJ, and FAPESP (Brazil); MEYS (Bulgaria); CERN; CAS, MoST, and NSFC (China); COLCIENCIAS (Colombia); MSES (Croatia); RPF (Cyprus); MoER, SF0690030s09 and ERDF (Estonia); Academy of Finland, MEC, and HIP (Finland); CEA and CNRS/IN2P3 (France); BMBF, DFG, and HGF (Germany); GSRT (Greece); OTKA and NKTH (Hungary); DAE and DST (India); IPM (Iran); SFI (Ireland); INFN (Italy); NRF and WCU (Republic of Korea); LAS (Lithuania); CINVESTAV, CONACYT, SEP, and UASLP-FAI (Mexico); MSI (New Zealand); PAEC (Pakistan); MSHE and NSC (Poland); FCT (Portugal); JINR (Armenia, Belarus, Georgia, Ukraine, Uzbekistan); MON, RosAtom, RAS and RFBR (Russia); MSTD (Serbia); SEIDI and CPAN (Spain); Swiss Funding Agencies (Switzerland); NSC (Taipei); ThEPCenter, IPST and NSTDA (Thailand); TUBITAK and TAEK (Turkey); NASU (Ukraine); STFC (United Kingdom); DOE and NSF (USA).

Individuals have received support from the University of California Institute for Mexico and the United States; the Marie-Curie programme and the European Research Council and EPLANET (European Union); the Leventis Foundation; the A. P. Sloan Foundation; the Alexander von Humboldt Foundation; the Belgian Federal Science Policy Office; the Fonds pour la Formation à la Recherche dans l’Industrie et dans l’Agriculture (FRIA-Belgium); the Agentschap voor Innovatie door Wetenschap en Technologie (IWT-Belgium); the Ministry of Education, Youth and Sports (MEYS) of Czech Republic; the Agence Nationale de la Recherche ANR-12-JS05-002-01 (France); the Council of Science and Industrial Research, India; the Compagnia di San Paolo (Torino); the HOMING PLUS programme of Foundation for Polish Science, cofinanced by EU, Regional Development Fund; the Thalis and Aristeia programmes cofinanced by EU-ESF and the Greek NSRF.

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Appendices

Appendix A: Additional tables and figures

1.1 A.1 Further information about systematic uncertainties

The systematic uncertainties for the \({\widetilde{\mathrm{t}}}\to{\mathrm{t}} {\widetilde{\chi}^{0}_{1}}\) cut-based, \({\widetilde{\mathrm{t}}}\to{\mathrm{b}} {\widetilde{\chi}^{+}}\) BDT, and \({\widetilde{\mathrm{t}}}\to {\mathrm{b}}{\widetilde{\chi}^{+}}\) cut-based analyses are shown in Tables 7, 8, and 9, respectively. The corresponding information for \({\widetilde{\mathrm{t}}}\to{\mathrm {t}}{\widetilde{\chi}^{0}_{1}}\) BDT analysis is given in the body of the paper (see Table 2).

Table 7 The bottom row of this table shows the relative uncertainty (in percent) of the total background predictions for the \({\widetilde{\mathrm {t}}}\to{\mathrm{t}}{\widetilde{\chi }^{0}_{1}}\) cut-based signal regions. The breakdown of this total uncertainty in terms of its individual components is also shown
Table 8 The bottom row of this table shows the relative uncertainty (in percent) of the total background predictions for the \({\widetilde{\mathrm {t}}}\to{\mathrm{b}}{\widetilde{\chi}^{+}}\) BDT signal regions. The breakdown of this total uncertainty in terms of its individual components is also shown
Table 9 The bottom row of this table shows the relative uncertainty (in percent) of the total background predictions for the \({\widetilde{\mathrm {t}}}\to{\mathrm{b}}{\widetilde{\chi}^{+}}\) cut-based signal regions. The breakdown of this total uncertainty in terms of its individual components is also shown

1.2 A.2 Additional M T and BDT output distributions

In this section, M T and BDT-output distributions in addition to those shown in Figs. 8 and 9 are presented for the \({\widetilde{\mathrm {t}}}\to{\mathrm{t}}{\widetilde{\chi }^{0}_{1}}\) (Figs. 13, 14) and \({\widetilde{\mathrm{t}}}\to {\mathrm{b}}{\widetilde{\chi}^{+}}\) (Figs. 1519) BDT signal regions.

Fig. 13
figure 13

Comparison of data and MC simulation for the distributions of BDT output and M T corresponding to the \({\widetilde{\mathrm{t}}}\to {\mathrm{t}}{\widetilde{\chi}^{0}_{1}}\) scenario in training regions 1 and 2. The M T distributions are shown after the requirement on the BDT output, and the BDT output distributions are shown after the M T>120 GeV requirement (these requirements are also indicated by vertical dashed lines on the respective distributions). (aM T after the tight cut on the BDT1 output; (bM T after the cut on the BDT2 output; (c) BDT1 output after the M T cut; (d) BDT2 output after the M T cut. In all distributions the last bin contains the overflow

Fig. 14
figure 14

Comparison of data and MC simulation for the distributions of BDT output and M T corresponding to the \({\widetilde{\mathrm{t}}}\to {\mathrm{t}}{\widetilde{\chi}^{0}_{1}}\) scenario in training regions 3 and 5. The M T distributions are shown after the requirement on the BDT output, and the BDT output distributions are shown after the M T>120 GeV requirement (these requirements are also indicated by vertical dashed lines on the respective distributions). (aM T after the cut on the BDT3 output; (bM T after the cut on the BDT5 output; (c) BDT3 output after the M T cut; (d) BDT5 output after the M T cut. In all distributions the last bin contains the overflow

Fig. 15
figure 15

Comparison of data and MC simulation for the distributions of BDT output and M T corresponding to the x=0.25 \({\widetilde{\mathrm{t}}}\to {\mathrm{b}}{\widetilde{\chi}^{+}}\) scenario in training regions 1 and 2. The M T distributions are shown after the requirement on the BDT output, and the BDT output distributions are shown after the M T>120 GeV requirement (these requirements are also indicated by vertical dashed lines on the respective distributions). (aM T after the cut on the BDT1 output; (bM T after the cut on the BDT2 output; (c) BDT1 output after the M T cut; (d) BDT2 output after the M T cut. In all distributions the last bin contains the overflow

Fig. 16
figure 16

Comparison of data and MC simulation for the distributions of BDT output and M T corresponding to the \({\widetilde{\mathrm{t}}}\to {\mathrm{b}}{\widetilde{\chi}^{+}}\) scenario in training regions 3 (for x=0.25) and 2 (for x=0.5). The M T distributions are shown after the requirement on the BDT output, and the BDT output distributions are shown after the M T>120 GeV requirement (these requirements are also indicated by vertical dashed lines on the respective distributions). (aM T after the cut on the BDT3 (x=0.25) output; (bM T after the loose cut on the BDT2 (x=0.5) output; (c) BDT3 (x=0.25) output after the M T cut; (d) BDT2 (x=0.5) output after the M T cut. In all distributions the last bin contains the overflow

Fig. 17
figure 17

Comparison of data and MC simulation for the distributions of BDT output and M T corresponding to the x=0.5 \({\widetilde{\mathrm{t}}}\to {\mathrm{b}}{\widetilde{\chi}^{+}}\) scenario in training regions 2 and 4. The M T distributions are shown after the requirement on the BDT output, and the BDT output distributions are shown after the M T>120 GeV requirement (these requirements are also indicated by vertical dashed lines on the respective distributions). (aM T after the tight cut on the BDT2 output; (bM T after the cut on the BDT4 output; (c) BDT2 output after the M T cut; (d) BDT4 output after the M T cut. In all distributions the last bin contains the overflow

Fig. 18
figure 18

Comparison of data and MC simulation for the distributions of BDT output and M T corresponding to the x=0.75 \({\widetilde{\mathrm{t}}}\to {\mathrm{b}}{\widetilde{\chi}^{+}}\) scenario in training regions 1 and 2. The M T distributions are shown after the requirement on the BDT output, and the BDT output distributions are shown after the M T>120 GeV requirement (these requirements are also indicated by vertical dashed lines on the respective distributions). (aM T after the cut on the BDT1 output; (b) M T after the cut on the BDT2 output; (c) BDT1 output after the M T cut; (d) BDT2 output after the M T cut. In all distributions the last bin contains the overflow

Fig. 19
figure 19

Comparison of data and MC simulation for the distributions of BDT output and M T corresponding to the x=0.75 \({\widetilde{\mathrm{t}}}\to {\mathrm{b}}{\widetilde{\chi}^{+}}\) scenario in training regions 3 and 4. The M T distributions are shown after the requirement on the BDT output, and the BDT output distributions are shown after the M T>120 GeV requirement (these requirements are also indicated by vertical dashed lines on the respective distributions). (a) M T after the cut on the BDT3 output; (b) M T after the cut on the BDT4 output; (c) BDT3 output after the M T cut; (d) BDT4 output after the M T cut. In all distributions the last bin contains the overflow

1.3 A.3 Further information about model interpretations

The interpretations for the \({\widetilde {\mathrm{t}}}\to{\mathrm{t}}{\widetilde {\chi}^{0}_{1}}\) and \({\widetilde{\mathrm {t}}}\to{\mathrm{b}}{\widetilde{\chi}^{+}}\) scenarios, using the cut-based analysis, are presented in Fig. 20. Maps of the most sensitive signal regions for the cut-based and BDT searches are shown in Figs. 21 and 22. The variations in the \({\widetilde{\mathrm {t}}}\to{\mathrm{b}}{\widetilde{\chi}^{+}}\) x=0.25 and 0.75 limits due to assumptions about particle polarizations are presented in Fig. 23.

Fig. 20
figure 20

Interpretations based on the results of the cut-based analysis. (a\({\widetilde{\mathrm{t}}}\to {\mathrm{t}}{\widetilde{\chi}^{0}_{1}}\) model; (b) \({\widetilde{\mathrm{t}}}\to {\mathrm{b}}{\widetilde{\chi}^{+}}\) model with x=0.25; (c) \({\widetilde{\mathrm{t}}}\to {\mathrm{b}}{\widetilde{\chi}^{+}}\) model with x=0.50; (d) \({\widetilde{\mathrm{t}}}\to {\mathrm{b}}{\widetilde{\chi}^{+}}\) model with x=0.75; The color scale indicates the observed cross section upper limit. The observed (solid black), median expected (solid red), and ±1σ expected (dotted red) 95 % CL exclusion contours are indicated. The variations in the excluded region due to ±1σ uncertainty of the theoretical prediction of the cross section for top-squark pair production are also indicated

Fig. 21
figure 21

The most sensitive signal region in the \(m_{ \widetilde{\chi}^{0}_{1} }\) vs. \(m_{ \widetilde{\mathrm {t}} }\) parameter space in the BDT analysis, for the (a) \({\widetilde{\mathrm{t}}}\to {\mathrm{t}}{\widetilde{\chi}^{0}_{1}}\) model, and the \({\widetilde{\mathrm{t}}}\to {\mathrm{b}}{\widetilde{\chi}^{+}}\) model with chargino mass parameter (b) x=0.25, (c) 0.5, and (d) 0.75. The number indicates the BDT training region

Fig. 22
figure 22

The most sensitive signal region in the \(m_{ \widetilde{\chi}^{0}_{1} }\) vs. \(m_{ \widetilde{\mathrm {t}} }\) parameter space in the cut-based analysis, for the (a) \({\widetilde{\mathrm{t}}}\to {\mathrm{t}}{\widetilde{\chi}^{0}_{1}}\) model, and the \({\widetilde{\mathrm{t}}}\to {\mathrm{b}}{\widetilde{\chi}^{+}}\) model with chargino mass parameter (b) x=0.25, (c) 0.5, and (d) 0.75. LM and HM refer to low ΔM and high ΔM, respectively, and the number indicates the \(E_{\mathrm {T}}^{\text{miss}}\) requirement

Fig. 23
figure 23

The observed 95 % CL excluded regions for the \({\widetilde{\mathrm{t}}}\to{\mathrm {b}}{\widetilde{\chi}^{+}}\) model with (a) x=0.25 and (b) 0.75 for the nominal scenario, right- vs. left-handed charginos (\(\tilde{\chi}_{R}^{\pm}\) and \(\tilde{\chi}_{R}^{\pm}\), respectively), and right- vs. left-handed W\(\widetilde{\chi}^{0}_{1}\) \({\widetilde{\chi }^{\pm}}_{1}\) couplings

Appendix B: Monte Carlo modeling of initial-state radiation

The experimental acceptance for signal events depends on initial-state radiation (ISR). As the simulation is not necessarily expected to model ISR well, we validate the simulation by comparing MadGraph MC predictions with data. The predicted p T spectrum of the system recoiling against the ISR jets is compared with data in Z+jets, \(\mathrm{t}\bar {\mathrm{t}}\), and WZ final states. These processes can be measured with good statistical precision in data and cover a variety of masses and initial states.

Z+jets events are selected by requiring exactly two opposite-sign, same-flavor leptons (ee or μμ) with an invariant mass between 81 and 101 GeV. These events, as well as the \(\mathrm{t}\bar{\mathrm{t}}\) and WZ samples discussed below, are collected with dilepton triggers. Events with at least one b-tagged jet or with additional lepton candidates are vetoed to remove contributions from \(\mathrm{t}\bar{\mathrm {t}}\) and diboson (WZ/ZZ) production, respectively. In Z+jets events, the Z boson is expected to be balanced in transverse momentum with the ISR jet system. The p T of the Z boson is thus computed in two ways: as the p T of the dilepton system, and, for events with at least one reconstructed jet, as the p T of the vector sum of the reconstructed jets, termed the “jet system” p T. The predicted MC spectrum for each quantity is compared with data, as shown in Fig. 24. The MC prediction is normalized to the total data yield so that the shapes can be readily compared. This procedure changes the normalization of the simulation by 4 %, consistent with the luminosty uncertainty. Agreement is observed at lower p T, while at higher p T the MC predictions lie above the data. The predictions from simulation exceed the data by about 10 % for p T=150 GeV and 20 % for p T=250 GeV. Both quantities show the same trend, validating the jet recoil method of measuring this quantity. The dilepton p T and jet system p T are also checked for events with exactly one, two, or three jets, as well as at least four jets, and in each case the results are consistent with the inclusive results shown in Fig. 24. The impact of the jet energy scale uncertainty, which only affects the jet system p T, is found to be much smaller than the observed discrepancies.

Fig. 24
figure 24

Comparison of data to MC predictions for the (a) dilepton p T and (b) jet recoil system p T in Z+jets events. The MC prediction is normalized to the total data yield. The data/MC ratio is also shown. The shaded band is centered on the weight values. The width of the band indicates the associated systematic uncertainty. In both distributions the last bin contains the overflow

Dilepton \(\mathrm{t}\bar{\mathrm{t}}\) events are selected by requiring an opposite-sign eμ pair and exactly two b-tagged jets. Events containing a third lepton candidate are vetoed. These requirements select dilepton \(\mathrm{t}\bar{\mathrm{t}}\) events with high purity (about 97 % in simulation) and unambiguously identify all the visible \(\mathrm{t}\bar {\mathrm{t}}\) decay products. Because of the presence of neutrinos in the \(\mathrm{t}\bar {\mathrm{t}}\) decays, the p T of the \(\mathrm{t}\bar{\mathrm{t}}\) cannot be directly measured but can be inferred from the ISR jet recoil system. Additional jets beyond the two b-tagged jets in these events are thus considered to be ISR jets for the purposes of this study, and the “jet system” is formed by the vector sum of ISR jets. The p T of the jet system defined this way is found in simulation to accurately reproduce the p T of the generated \(\mathrm{t}\bar{\mathrm{t}}\) system. The predicted jet system p T spectrum is compared with data in Fig. 25. Agreement is found at lower p T. At higher p T, the simulation is consistent with the data to within the uncertainties, but it also exhibits a trend to overpredict the data, as in the case of Z+jets events. The jet system p T is also checked for events with exactly one, two, or three jets, as well as at least four jets, and in each case the results are consistent with the inclusive results shown in Fig. 25. Again, the effect of the jet energy scale uncertainty is examined and found to be small.

Fig. 25
figure 25

Comparison of data to MC prediction for the jet recoil system p T in \(\mathrm{t}\bar{\mathrm {t}}\) events. The MC prediction is normalized to the total data yield. The ratio of data/MC is also shown. The shaded band shows the weights derived for MC simulation and the variation to assess systematic uncertainties. The last bin contains the overflow

Finally, WZ→ℓνℓℓ events are selected by requiring exactly three leptons, with two opposite-sign same-flavor leptons (ee or μμ) consistent with the Z boson mass and a third lepton (e or μ) with M T>50 GeV. Events with at least one b-tagged jet are vetoed. The expected purity of this selection from simulation is about 83 %, with about 7 % of events coming from ZZ production. As with \(\mathrm{t}\bar{\mathrm{t}}\) events, the neutrino in the final state prevents a direct measurement of the WZ system p T, but the jet recoil system can be used and is defined in the same way as for the Z+jets sample. In data, this selection yields on the order of 1000 events, so the statistical uncertainty at high values of jet system p T is large. As for the \(\mathrm{t}\bar{\mathrm{t}}\) MC simulated events, the WZ simulation is found to be consistent with the data to within the uncertainties, but also shows a trend to overpredict the data at large p T that is consistent with the level observed for the Z+jets events.

Given the MC overprediction observed in the high-statistics Z+jets events, and the consistency of the other final states with this result, weights are derived to correct the MC prediction as a function of the p T of the system recoiling against ISR jets. These weights are applied to the MadGraph signal samples used in this analysis, and the full values of the corrections are taken as a systematic uncertainty. The values of the weights range from 0–20 % depending on the p T of the system recoiling against ISR jets. The shaded bands shown on the ratio plots in Figs. 2425 are centered on the weighted MC prediction, with the width of the band showing the associated uncertainty.

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The CMS Collaboration., Chatrchyan, S., Khachatryan, V. et al. Search for top-squark pair production in the single-lepton final state in pp collisions at \(\sqrt{s}=8\ \mathrm{TeV}\) . Eur. Phys. J. C 73, 2677 (2013). https://doi.org/10.1140/epjc/s10052-013-2677-2

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