The main backgrounds to this measurement are QCD multi-jet production and W → µν + jets where a jet is misidentified as τhad-vis (j → τhad-vis). In a small fraction of events, the selected probe is a light lepton (` → τhad-vis). A combina-tion of data-driven and simulacombina-tion-based approaches exploiting the strong charge-correlation between the tag muon and the τhad-vis probe is used to model these backgrounds. The background estimation separates events where the muon and theτhad-vis candidate have the same charge (“same-sign”, SS) and those where they are of opposite charge (“opposite-sign”, OS). As the signal process is expected to be mainly present in OS events, the signal region (SR) where the τ-trigger efficiency is measured contains only OS events.
6.3 Background Estimation and (d)ETmissafter the preselection cuts of theZ →τ τ trigger efficiency measurement. The grey band indicates the statistical uncertainty on the yield prediction.
The full estimate of the background in the SR can be written as NOSfake =ROS/SSNDataSS +NZ→µµOS−SS+NWOS−SS→µν +NtopOS−SS,
where each term is detailed in the following. The “OS−SS” superscript indicates
Table 6.3: Selection cuts applied after the preselection step to define the signal and control regions of the Z →τ τ trigger efficiency measurement. A dash means that no cut is placed.
Variable SR SS CR QCD CR W+jets CR
Muon isolation Yes Yes Inverted Yes
q(µ)·q(τhad-vis) −1 +1 −1 −1
mT(µ, ETmiss) [GeV] <50 <50 <50 >60 mvis(µ, τhad-vis) [GeV] ∈[45,80] ∈[45,80] ∈[45,80]
-Pcos (∆φ) >−0.5 >−0.5 >−0.5
-ETmiss [GeV] - - - >20
the subtraction that is used to determine the charge-asymmetric contribution of the various background processes.
The term ROS/SSNDataSS accounts for the multi-jet background and the charge-symmetric components of the other background processes, such as W+jets, Z → µµ + jets and processes involving t quarks, mainly t¯t production. It is modelled using data in the SS control region where the charge-product between the tag and the probe is positive and a negligibleZ →τ τ →µτhad-vis3νcontamination is found, which is subtracted from the data to construct the final template of the charge-symmetric background estimate. As the expected number of background events depends on the charge-product between the tag and the probe, the normalization of the SS data is corrected by theROS/SS factor. This factor is measured in a multi-jet enriched control region defined by inverting the isolation requirement around the tag muon. The ROS/SS factor is the ratio of the number of events in OS and SS data, and is parametrized using the track multiplicity of the τhad-vis candidate and the ID criterion applied to it, as well as the muonpT, and it is independently measured with and without applyingτ triggers. Example distributions in the QCD CR are shown in Fig.6.4, showing the pT(µ) distributions needed to calculate the ROS/SS factors for 1-prong τhad-vis candidate events without an applied τ-lepton trigger. The corresponding pT(τhad-vis) 1-prong template distribution from the SS CR is shown in Fig.6.5, along with the 3-prong template distribution.
The “OS−SS” terms account for the charge-asymmetric component of the back-grounds, which are added to the charge-symmetric component included in the ROS/SSNDataSS term. They are estimated as
NOS−SS =kOSW Nj→τOShad-vis−kWSSROS/SSNj→τSS had-vis+N`→τOShad-vis−ROS/SSN`→τSS had-vis , where NOS−SS ∈ {NZ→µµOS−SS, NWOS−SS→µν, NtopOS−SS} . The kW corrections account for
6.3 Background Estimation
QCD CR OS 1-prong
) [GeV]
QCD CR SS 1-prong
(a) (b)
Figure 6.4: Distribution of pT(µ) in the (a) OS and (b) SS QCD CRs for 1-prong τhad-vis candidates. The ratio of these distributions is used to extract the factor ROS/SS which scales the charge-symmetric background tem-plate from the SS CR to obtain the SR prediction.
) [GeV] 3-prong candidates. These distributions are used as templates for the estimation of charge-symmetric background contributions in the SR.
possible mismodellings of the fraction of jets that are mislabelled as τhad-vis ob-jects (“fake-rate”) in simulation, and are measured in the W+jets CR defined in Tab. 6.3. This correction is the ratio between the observed data and the W → µν+jets and top-quark production events expected from simulation. As an approximation, all W → µν+jets and top-quark production events without
truth-matched τhad-vis object are treated as j → τhad-vis backgrounds, while all Z →µµ events are treated as` →τhad-vis backgrounds. For the simulated charge-asymmetric component of the` →τhad-vis background, no data-driven correction is applied as this contribution is found to be small. ThekW factors are parametrized using the track multiplicity of theτhad-vis candidate, the ID criterion applied to it and pT(τ) as well as q(µ)·q(τ), and is independently measured with and without applying τ triggers. The calculation is illustrated in Fig. 6.6, which shows the pT(τhad-vis) distributions used to calculate the kW factors for OS and SS 3-prong τhad-vis candidate events. The obtained kW and ROS/SS factors together with their statistical uncertainties are given in Tab. 6.4.
) [GeV]
W+jets CR OS 3-prong
) [GeV]
W+jets CR SS 3-prong
(a) (b)
Figure 6.6: Distributions of pT(τhad-vis) in the (a) OS and (b) SS QCD CRs for 3-prong τhad-vis candidates. The factor needed to scale the sum of the W+jets and fake t-quark contribution such that the normalizations of data and MC processes coincide is named kW.
The contribution from top-quark production events with true τhad-vis objects is estimated from simulation, and is also excluded from the top-quark production background contributions and is subtracted from data in all the control regions.
The contribution ofZ →τ τ →µτhad-vis3νevents where the selectedτhad-visprobe is a misidentified jet is found to be negligible, and is added to theZ →``contribution in plots of the SR. The resulting modelling is displayed in Fig. 6.7, which shows the pT(τhad-vis) distribution in the SR, separated in 1-prong and 3-prong τhad-vis
candidates.
A discrepancy is found at values of pT(τhad-vis) above 50 GeV. This was found to be caused by events with ∆φ(µ, τhad-vis) < 2.4, as evidenced by the distributions shown in Fig.6.8.
The low values of |∆φ(τhad-vis, µ)| contain a disagreement between data and
6.3 Background Estimation
Table 6.4: Overview of the kW and ROS/SS factors derived for the SR background estimation. The separating pT values are pT(τhad-vis) = 35 GeV for kW
and pT(µ) = 50 GeV for ROS/SS. The number in parentheses is the statistical uncertainty on the last given digit.
without τ-lepton trigger with τ-lepton trigger
Factor 1-prong 3-prong 1-prong 3-prong
low-pT high-pT low-pT high-pT low-pT high-pT low-pT high-pT
ROS/SS 1.23(3) 1.28(5) 1.40(5) 1.37(8) 1.25(4) 1.27(7) 1.43(9) 1.3(1) kWOS 1.14(1) 1.12(1) 1.26(1) 1.26(2) 1.15(1) 1.15(1) 1.25(3) 1.32(2)
kSSW 1.23(1) 1.36(2) 1.29(2) 1.49(4) 1.31(2) 1.43(3) 1.29(5) 1.62(6)
(a) (b)
Figure 6.7: Distribution of the pT of theτhad-vis candidate in the SR applying the loose RNN-based ID working point, for (a) 1-prong and (b) 3-prong candidates. The red band indicates statistical as well as systematic uncertainties on the predicted distributions.
prediction in Fig. 6.8a, and removing these events leads to a better agreement between data and prediction at high pT(τhad-vis) values. Despite this observation, the cut ∆φ(µ, τhad-vis) > 2.4 was not applied for the final measurement because the obtained efficiencies were found not to be biased by these events. Therefore,
Events
Figure 6.8: Comparison of P
cos(∆φ) and pT(τhad-vis) distributions in the SR for 1-prongτhad-viscandidate events for (a & c) the default selection and (b
& d) when adding the cuts P
cos(∆φ)>−0.15 and |∆φ(µ, τhad-vis)|>
2.4 to the selection, requiring medium RNN-based ID for the τhad-vis
candidate. The grey band indicates the statistical uncertainty on the prediction.
in order to keep the available dataset as large as possible, the baseline selection was kept.