9. Measurement with the Dataset of 2011 95
10.3. Results at Particle Level
least three jets in the final state passing the WBF preselection (mjj >350 GeV and|∆yjj|>3.0) in data and simulation. Multi-jets and tt¯backgrounds have been estimated from data. The hatched band incorporates the total statistical and systematic uncertainty on the predictions.
The yellow band reflects the total systematic uncertainty.
10.3. Results at Particle Level
This section presents the results of the Z/γ∗(→ee) + jets cross-section measurement at particle level with the full dataset of 2011 after WBF preselection. In order to provide results which are independent of the detector setup, the results are presented on particle level. Therefore, the measured multiplicity distributions and the kinematic distributions of the 3rd jet depicted in Sec. 10.2 are unfolded to particle level, taking into account the systematic uncertainties as discussed in Sec. 9.3. Predictions from NLO fixed-order pQCD predictions, are corrected for non-perturbative effects and QED radiation effects, as described in Sec. 9.4. Finally, both the predictions from NLO fixed-order pQCD cal-culations and from ALPGEN+HERWIG and SHERPA using the ATLAS configurations, as detailed in Sec. 7.2, are compared to the measured cross sections.
The figures in this section are organised such that they show the absolute or normalised cross sections in the upper part, together with the ratios BlackHat+SHERPA/data, ALPGEN/data and SHERPA/data in the lower three parts. The predictions from ALP-GEN+HERWIG and SHERPA have been normalised to the inclusive NNLO cross section with global K-factors. Theoretical uncertainties are shown separately from the total combined statistical and systematic uncertainty on the measurement.
A typical WBF preselection, requiring a large rapidity distance between the two tagging jets and a large dijet mass, is expected to have a similar effect on the jet multiplicity scaling as a hard cut on the transverse momentum of the leading jet [81]. Figure 10.8 shows the measured cross section as a function of the exclusive jet multiplicity and the ratio of cross
10. Higgs Boson Production via Weak Boson Fusion
sections for successive exclusive jet multiplicities for events with at least two jets in the final state passing the WBF preselection (mjj >350 GeV and |∆yjj|>3.0).
) [pb]jet)+ N-e+ e→*(γ(Z/σ
(a) Exclusive jet multiplicity
)jet)+ N-e+ e→*(γ(Z/σ+1) / jet)+ N-e+ e→*(γ(Z/σ 0.1
(b) Exclusive jet multiplicity ratio
Figure 10.8.: (a) Measured cross section as a function of the exclusive jet multiplicity and (b) ratio of cross sections for successive exclusive jet multiplicities for events with at least two jets in the final state passing the WBF preselection (mjj >350 GeV and |∆yjj|>3.0). The cross sections are normalised to the inclusive Z/γ∗(→ ee) cross section. The other details are as in Fig. 9.22.
The hypothesis of Poisson scaling is found to be consistent with the measured cross sections, at least in the first two ratios, but a larger cut on the dijet mass is expected to strengthen the effect of Poisson scaling. The predictions from BlackHat+SHERPA are consistent with the data, while the precision of the measurement exceeds the theory precision. In addition, the measurements are well described by the predictions from SHERPA, whereas ALPGEN+HERWIG predicts a too low number of events passing the WBF preselection, which is in line with the tendencies observed for large values of the absolute rapidity difference between the leading jets described in Sec. 9.5.6. In addition, the predictions from ALPGEN+HERWIG overestimates R3/2.
Figure 10.9 shows the measured cross section as a function of the transverse momentum and the absolute rapidity distribution of the 3rd jet after WBF preselection. The NLO fixed order predictions fromBlackHat+SHERPA, as well as the predictions from ALP-GEN+HERWIG and SHERPA agree well with the data, except for the high pjetT regime above 70 GeV, where a lack of data is observed.
Detailed values of the measured cross sections, as well as NLO pQCD predictions from BlackHat+SHERPA with respect to the fiducial region are listed in Appendix C.1.
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10.4. Conclusions
(3rd leading jet) [GeV]
jet
| (3rd leading jet)
|yjet
Figure 10.9.: Differential cross section as a function of (a) the transverse momentumpjetT and (b) the absolute rapidity |yjet| of the 3rd leading jet for events with at least three jets in the final state passing the WBF preselection (mjj >350 GeV and|∆yjj|>3.0). The cross sections are normalised to the inclusive Z/γ∗(→ee) cross section. The other details are as in Fig. 9.21.
10.4. Conclusions
TheZ/γ∗+ jets modelling has been tested in typical phase space regions expected for the decay of the Higgs boson, produced via WBF, in pp-collisions at a centre of mass energy of √
s = 7 TeV with the full dataset of 2011. In Higgs boson events produced via WBF two well separated high energetic jets and reduced central activity are expected. A veto on a 3rd jet can be used to distinguish signal from background.
Different observables which can be used for a central jet veto and 3rd jet veto efficiencies have been studied on detector level. In addition, total exclusive cross sections as a function of the jet multiplicity and their ratios, as well as the differential cross section as a function of the 3rd jet pT and |y| have been measured.
Systematic and statistical uncertainties have been evaluated and the systematic uncer-tainty has been reduced by normalising the cross sections to the inclusive Z/γ∗(→ ee) cross section.
The predictions from SHERPA and NLO fixed order pQCD calculations are consistent with the data, whereas ALPGEN+HERWIG predicts a too low number of events passing the WBF preselection. In addition, ALPGEN+HERWIG underestimates the jet veto efficiency.
This measurement can be used to tune MC generators, but for the mean time different reweighting procedures need to be studied. For the analysis with the full dataset of 2011 [169] a reweighting in bins of peeT has been used as a cross check.
11. Overall Conclusion
The inclusive and differential Z/γ∗(→ee) + jets cross section has been measured in pp-collisions at a centre-of-mass energy of √
s = 7 TeV with integrated luminosities of R L dt = 36 pb−1 (full dataset of 2010) and 4.6 fb−1 (full dataset of 2011). The full dataset of 2010 has the advantage of a relatively low collision rate and a low rate of multiple proton-proton interactions which allow for cross-section measurements at low jet transverse momentum, while the analysis with the full dataset of 2011 provides the most accurate results. In addition, the Z/γ∗+ jets modelling has been tested in typical phase space regions expected for the decay of the Higgs boson, produced via WBF, in pp-collisions at a centre of mass energy of √
s= 7 TeV with the full dataset of 2011.
The measurements have been corrected for detector effects back to particle level and compared to predictions from the matrix element plus parton shower generators ALP-GEN+HERWIG and SHERPA, Z/γ∗+≥1 jet production generated with PYTHIA and the inclusive Drell-Yan process modelled at NLO with MC@NLO using the ATLAS config-urations. In addition, predictions from NLO fixed-order pQCD calculations are compared to the measured cross sections. Electron kinematics on particle level in the MC event samples have been defined to include the contributions from photons within a cone of 0.1 around the electron direction. Jets have been clustered around all final state particles except for the dressed decay products of the Z boson and have been identified with the anti-kt algorithm with a cone of R= 0.4 in the region pT >30 GeV and |y|<4.4.
Total inclusive and exclusive cross sections have been measured as a function of jet multiplicity. Additionally, the inclusive and exclusive jet multiplicity ratios have been extracted for different values of the transverse momentum of the leading jet in order to test the jet multiplicity scaling. Furthermore, inclusive differential cross sections have been measured as a function of the jet transverse momentum, the jet rapidity, the transverse momentum of theZ boson,peeT , the invariant mass of the two leading jets and the angular separation between the two leading jets. Finally, inclusive differential cross sections as a function of HT, the scalar pT sum of all final state objects, and ST, the scalar pT sum of all hadronic jets in the final state, have been measured.
Systematic and statistical uncertainties have been evaluated and the systematic uncer-tainty has been reduced by normalising the cross sections to the inclusive Z/γ∗(→ ee) cross section.
In general, the data is well described by the predictions from NLO fixed order pQCD cal-culations and from ALPGEN+HERWIG and SHERPA, whereas PYTHIA and MC@NLO fail to describe the data in large phase space regions. PYTHIA only includes the tree-level matrix element forZ/γ∗+≥1 jet, additional jet emission are done by parton shower. For MC@NLO the associated first jet corresponds to the real emission term of the NLO calcu-lation and events with more than one jet in the final state are modelled by parton shower.
Therefore, the mismodelling can be attributed to the parton shower.
For exclusive jet multiplicities, the transition from staircase scaling to Poisson scaling for large scale differences between the leading jet and the additional radiated jets is
11. Overall Conclusion
confirmed by the measurement.
For some phase space regions discrepancies between the predictions from the ME+PS generators and the measurements have been evaluated. The jet multiplicity is well de-scribed by ALPGEN+HERWIG and SHERPA up to five jets, but additional jet emissions are modelled by parton shower, which fail to describe the data. Furthermore, ALP-GEN+HERWIG overestimates the cross section for high energetic jets or highly boosted Z bosons, which is mainly due to higher-order QCD effects. SHERPA predicts a too wide rapidity distribution, which translates into the absolute rapidity difference, the angular separation in y - φ space and the invariant mass of the two leading jets. Finally, for events passing the WBF preselection, the predictions from ALPGEN+HERWIG overes-timate the measured cross sections for higher jet multiplicities, which leads to a small underestimation of the probability to survive a veto on a 3rd jet in the low pjetT regime.
The NLO fixed-order pQCD calculations fromBlackHat + SHERPA underestimate the cross section for large HT and ST by several standard deviations, which is attributed to missing higher parton multiplicities in the calculation. Similar deviations have been found for large values of peeT . Exclusive sums of the NLO fixed-order pQCD calculations for Z/γ∗+ 1 jet and Z/γ∗+≥2 jets show a much better description of the hard HT, ST
and peeT regime.
The analysis with the full dataset of 2011 provides the most precise measurements of this kind to date.
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12. Outlook
The analysis presented in this thesis covers a large spectrum of physics with jets in as-sociation with a Z boson, which provide a valuable input for the tuning of Monte Carlo (MC) event generators.
In addition, part of the measurements exceeds the precision of the theory predictions.
The largest contribution to the theoretical uncertainty comes from the impact of QCD higher-order effects. This could be reduced by either using nNLO calculations [9] or by optimising the method to evaluate this uncertainty.
The analysis also leaves the possibility for optimisations and extensions. For most phase-space regions the measurements are already limited by systematics, mainly due to the JES, especially in the forward region. The dominant component of the JES uncertainty in the forward region comes from the η-intercalibration. This can be reduced by using more sophisticated methods to estimate the uncertainties due to generator modelling.
For a reduced JES systematic uncertainty, the uncertainty coming from the unfolding process becomes dominant. It has been shown in this thesis that multi-dimensional un-folding is able to reduce this uncertainty, due to the fact that the model dependence for multi-dimensional unfolding is lower.
As shown in this thesis the event topology changes for extrem phase-space regimes, e.g. large transverse momentum of the Z boson, large jet transverse momentum and large HT, but measurements in this regions are limited by statistics. With more data, these kinematic regimes become accessible and allow to study the event shapes in more detail. Potential observables to characterise the event shapes are for example: the absolute azimuthal separation, the minimal azimuthal difference between aZ boson and a jet, the transverse momentum ratio of the two leading jets [8] or the central trust [170]. The probe of the Z/γ∗+ jets modelling in these regimes is of particular interest for searches of new physics and for further tests of NLO fixed order pQCD predictions.
The fraction of Z/γ∗ + jets events produced via double-parton interactions (DPI) is rather small, but for other analyses, such as the measurement of W + b jets produc-tion, the fraction of events originating from DPI is expected to be much larger, at the order of 30% [171]. Since the effective area parameter for DPI is expected to be approx-imately independent of the process and the phase space requirements, the measurement inZ/γ∗+ jets events can contribute to a better understanding of DPI.
A. Measurement with the Dataset of 2010
A.1. Further Uncorrected Distributions
(leading jet) [GeV]
jet
(2nd leading jet) [GeV]
jet
(c) Leading jety
(2nd leading jet) yjet
(d) 2nd leading jety
Figure A.1.: Transverse momentum distribution of (a) the leading jet and (b) the 2nd leading jet and rapidity distribution of (c) the leading jet and (d) the 2nd leading jet in data and simulation. Only statistical uncertainties are shown. Multi-jets background have been estimated from data.
A. Measurement with the Dataset of 2010
(leading jet, 2nd leading jet) [GeV]
mjj
(a) Invariant dijet mass
| (leading jet, 2nd leading jet) yjj
(b) Absolute rapidity difference
| (leading jet, 2nd leading jet) [rad]
φjj
|∆
0 0.5 1 1.5 2 2.5 3
Events / 0.39 rad
10-1
(c) Absolute azimuthal separation
(leading jet, 2nd leading jet) Rjj
(d) Angular separation in y-φspace
Figure A.2.: (a) Invariant mass mjj and the angular separations (b) |∆yjj|, (c) |∆φjj| and (d) ∆Rjj of the two leading jets in events with at least two jets in the final state in data and simulation. Only statistical uncertainties are shown. Multi-jets background have been estimated from data.
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