s = 13 TeV
Based on the extensive comparison of grooming and substructure techniques at √
s = 8 TeV, presented in Section 6.1, the performance of the best few configurations and substructure vari-ables to identify boosted vector bosons was re-evaluated in MC simulation at√
s= 13 TeV. The best-performing algorithm, in terms of pile-up removal and background rejection was then deter-mind, for jets over a broadpT range (200< pT<2000 GeV). Two working points corresponding to a signal efficiency of 50% (medium) and 25% (tight) were defined for the most promising algorithm. As opposed to the 8 TeV studies, both the identification of W and Z bosons are optimised in this section. Therefore, signal samples, simulating the processW0 →W Z→qqqq, are generated with Pythia8 using the NNPDF2.3LO PDF set and the AU2 underlying event and parton shower tune. To allow for the extension of the jetpT range, signal samples are pro-duced with W0 masses ranging from 400 to 5000 GeV. The QCD dijet background is generated with exactly the same setup as the signal samples.
Optimisation
The optimisation of the boosted vector boson identification at √
s= 13 TeV closely follows the strategy in Section 6.1.1. Events are categorised based on the leading ungroomed C/AR= 1.2 truth jet with |ηTruth|< 2.0 in five different pTruthT ranges: [200, 350), [350, 500), [500, 1000), [1000, 1500) and [1500,2000) GeV. In the studies presented here, four grooming configurations and three substructure variables (C2β=1,D2β=1,τ21wta), that were deemed promising based on the 8 TeV studies, are selected:
• anti-ktR= 1.0 trimmed jets with fcut= 5%,Rsub= 0.2,
• C/A R= 1.0 pruned jets withZcut= 0.15,Rcut= 0.5,
• C/A R= 1.2 split-filtered jets withycut= 0.15,Rsub= 0.3,
• C/A R= 1.2 split-filtered jets withycut= 0.04,Rsub= 0.3,
where the last jet collection corresponds to the one widely used in diboson resonance searches at √
s = 8 TeV. For each grooming configuration, requirements on the groomed jet mass are imposed, yielding a signal efficiency ofεGW,Z = 68%. The pairwise combination of the mass win-dows with each of the three considered substructure variables is then studied to define a medium (εG&TW,Z = 50%) and tight (εG&TW,Z = 25%) signal efficiency working point. The selection criteria to obtain these signal efficiency working points are then applied to the QCD dijet background
6.2 Performance of Boosted Boson Identification at √
s= 13TeV to determine the background efficiencies εG&TQCD and to compare them. The combination of the grooming algorithm and the substructure variable yielding the smallest background rejection over a broad range ofpT is then further optimised.
The leading jet mass distributions for the four grooming configurations are depicted in Fig. 6.9 for the ranges 200 < pTruthT < 350 GeV and 1500 < pTruthT < 2000 GeV. No jet energy or mass calibrations are applied at this stage. Even though the distributions are truncated at 200 GeV, the background mass distributions exhibit high mass tails beyond 1 TeV for jets with 1500 < pTruthT < 2000 GeV. By studying the average jet mass dependence on the number of reconstructed vertices, it can be shown that these high-mass tails are not caused by the con-tamination of energy deposits from pile-up vertices but are instead from initial-state radiation captured in the large-R jet. On the other hand, the jet mass distribution for the pruned and split-filtered collection with ycut= 0.04 still exhibits a strong pile-up dependence in the lowest pTruthT range considered. For both the trimmed and pruned jet collection, the shape of the back-ground mass distribution strongly depends on the jet pT. For the split-filtered jet collections, the background mass distributions are more stable with pT, but the grooming configuration withycut= 0.04 has a maximum close to the signal mass distribution which can be removed by increasing the ycut criteria.
The smallest mass window that contains 68% of the signal events is then calculated for W and Z bosons for the different grooming configurations. Signal efficiency versus background rejec-tion curves are determined for the pairwise combinarejec-tions of the groomed mass window with the three considered substructure variables for each of the grooming algorithms. To compare their performance, two figures of merit are defined: a 50% and 25% signal efficiency working point.
The background rejection factors for the medium signal efficiency working point are shown in Fig. 6.10 and Fig. 6.11 separately forW and Z boson tagging with 200< pTruthT <350 GeV and 1500 < pTruthT < 2000 GeV, respectively. Furthermore, the background rejection factors are indicated for a narrower mass window size corresponding to εGW,Z = 50%. The rejection factors are however significantly smaller than for the combination of selection criteria on the jet mass and an additional substructure variable. In the case of the narrower mass window, the better separation of the Z-jet mass distribution from the background compared to W-jets, results in larger background rejection factors forZ-jets thanW-jets. The same behaviour can be observed for the pairwise combination of the jet mass and a substructure variable for high-pTruthT jets in Fig. 6.11. Conversely, for low-pTruthT jets in Fig. 6.10, the pairwise combinations result in higher background rejection power for W-jets than for Z-jets. As it can be seen in Fig. 6.9, the mass distribution of Z-jets is broader than that ofW-jets at lowpTruthT . Therefore, the mass window containing 68% of theZ boson signal has to be wider than that forW bosons and thus resulting in a smaller background rejection power compared to W-jets. At high pTruthT , the width of the W-jet andZ-jet mass distributions are about the same. The substructure selection criteria are expected to have approximately the same effect on W-jets andZ-jets.
Comparing the background rejection power corresponding to the medium and tight signal effi-ciency working point for all considered pTruthT ranges, both the trimmed jet collection in
Jet mass [GeV]
Figure 6.9: Leading uncalibrated jet mass distribution for W and Z signal samples and QCD dijet background in two different pT ranges: 200 < pTruthT < 350 GeV and 1500 < pTruthT <
2000 GeV [108]. The distributions are shown for (a) anti-ktR= 1.0 trimmed jets withfcut= 5%
and Rsub = 0.2, (b) C/A R = 1.0 pruned jets with Zcut = 0.15, Rcut = 0.5, (c) C/A R = 1.2 split-filtered jet with ycut = 0.15, Rsub = 0.3 and (d) C/A R = 1.2 split-filtered jet with ycut= 0.04,Rsub= 0.3.
6.2 Performance of Boosted Boson Identification at √
s= 13TeV
ATLAS Simulation Preliminary = 13 TeV
s = Optimal grooming + tagging combination
Reco Cut
Bkg. rejection @ 50% signal eff.
0
s = Optimal grooming + tagging combination
Reco Cut
Bkg. rejection @ 50% signal eff.
0
Figure 6.10: Background rejection corresponding to a W (top) and Z (bottom) boson signal efficiency of εG&TW,Z = 50% for different combinations of substructure variables and grooming algorithms for jets with 200< pTruthT <350 GeV. The uncertainties are stastical errors only.
ATLAS Simulation Preliminary = 13 TeV
s = Optimal grooming + tagging combination
Reco Cut
Bkg. rejection @ 50% signal eff.
0
s = Optimal grooming + tagging combination
Reco Cut
Bkg. rejection @ 50% signal eff.
0
Figure 6.11: Background rejection corresponding to a W (top) and Z (bottom) boson signal efficiency of εG&TW,Z = 50% for different combinations of substructure variables and grooming algorithms for jets with 1500< pTruthT <2000 GeV. The uncertainties are stastical errors only.
6.2 Performance of Boosted Boson Identification at √
s= 13TeV
[GeV]
Jet pT
500 1000 1500 2000
Fitted mean jet mass [GeV]
60 80 100 120 140
160 ATLAS Simulation Preliminary
R=1.0 jets anti-kt
= 0.2) = 5%, Rsub
Trimmed (fcut
| < 2.0, W-jets η
|
Fitted mean σ
± µ
σ
± 2 µ Linear fit
[GeV]
Jet pT
500 1000 1500 2000
Fitted mean jet mass [GeV]
60 80 100 120 140
160 ATLAS Simulation Preliminary
R=1.0 jets anti-kt
= 0.2) = 5%, Rsub
Trimmed (fcut
| < 2.0, W-jets η
|
Fitted mean σ
± µ
σ
± 2 µ Linear fit
Figure 6.12: Average W-jet signal mass of anti-kt R = 1.0 trimmed jets with fcut = 5% and Rsub = 0.2 as a function of the jetpT before (left) and after (right) the mass calibration [108].
nation withDβ=12 and the pruned jet collection in combination withC2β=1 seem to perform well in terms of W- and Z boson tagging. Taking into account that the pruned jet mass exhibit a non-negligible pile-up dependence at low-pT, anti-kt R = 1.0 trimmed jets with fcut = 5%, Rsub = 0.2 were chosen as baseline grooming algorithm for boosted vector boson identification in early Run-II.
Working Point Derivation
The baseline vector boson identification algorithm is then further optimised to be used in physics analyses. Dedicated jet energy and mass calibrations are derived, using the procedure described in Section 5.1. To demonstrate the effect of the calibration on the jet mass, the W-jet mass distribution is fitted with a Gaussian distribution and the mean value is plotted as a function of the jet pT in Fig. 6.12 before and after the mass calibration was applied. The striking pT -dependence of the jet mass is removed by the jet mass calibration. Furthermore, the width of the mass distribution is indicated by the 1σ and 2σ ranges. The optimisation procedure that was previously used to identify the best-performing algorithm requires the definition of signal mass windows that contain 68% of the signal. As the width of the mass distribution increases withpT, also the width of the mass window would increase. For analyses that rely on a smoothly falling distribution of the invariant dijet mass spectrum, the changing mass window sizes in the different pT ranges could distort the spectrum and result in difficulties to parameterise the background.
Therefore, instead of defining the mass window size based on a fixed signal efficiency, a±15 GeV mass window around the mean of the W/Z-jet mass distribution is chosen across thepT range, resulting in εGW,Z = 55−80%. The 15 GeV mass window size provides a compromise between the good mass resolution at low pT and its degradation at highpT.
The medium and tight working point are then derived by imposing selection criteria on the Dβ=12 variable after requiring jets to fall within the 15 GeV mass window. The D2β=1 selection
[GeV]
Jet pT
500 1000 1500 2000
@ 50% signal eff.2D
1 1.5 2 2.5 3
Fit: fourth order polynomial
ATLAS Simulation Preliminary
R=1.0 jets anti-kt
= 0.2) = 5%, Rsub
Trimmed (fcut
| < 2.0, W-jets η
|
[GeV]
Jet pT
500 1000 1500 2000
@ 50% signal eff.2D
1 1.5 2 2.5 3
Fit: fourth order polynomial
ATLAS Simulation Preliminary
R=1.0 jets anti-kt
= 0.2) = 5%, Rsub
Trimmed (fcut
| < 2.0, Z-jets η
|
Figure 6.13: Requirement on the Dβ=12 variable as a function of the calibrated jet pT for the medium working point corresponding to a W (left) andZ (right) signal efficiency of 50% [108].
requirements are one-sided, with the lower boundary of zero and the upper boundary as shown in Fig. 6.13 for the medium working point as a function of the jetpTforW-jets andZ-jets. The maximum Dβ=12 selection criteria increases approximately linear with the jet pT. A change in the slope can be observed for jets with pT >1750 GeV where the jet mass resolution degrades significantly. Only a slightly larger fraction of signal events, compared to the medium working point, are thus selected and result in the loose criteria on D2β=1. To avoid bin-edge effects that may result from the use of discrete selection criteria, thepT dependence of the maximumD2β=1 selection criteria is fitted with a fourth-order (second-order) polynomial for the medium (tight) signal efficiency working point.
The resulting signal efficiencies and background rejection factors for W-tagged jets are shown in Fig. 6.14. The efficiencies for Z-tagged jets are not shown here as they are almost identical to those ofW-tagged jets. The uncertainty bands include uncertainties on the jetpT, mass and Dβ=12 scale, derived in Section 5.2.3 as well the corresponding resolution uncertainties. The scale uncertainties are treated as fully correlated whereas the resolution uncertainties are treated as uncorrelated. The large uncertainties on the background rejection for the tight working point are dominated by theDβ=12 scale uncertainties. The derived upper boundaries on theD2β=1variable, corresponding to the tight working point, are close to the maximum of theDβ=12 distribution in the background sample. Therefore, even small variations of theDβ=12 value have a large impact on the background efficiency.
6.2.1 Summary
In this section, an algorithm was developed for Run-II to identify boosted hadronically decaying vector bosons based on the optimisation studies performed in Run-I.
To mitigate the influence of pile-up effects on anti-kt jets with a radius parameter of R = 1.0, jets are trimmed with Rsub = 0.2 and fcut = 5%. Furthermore, selection criteria are imposed