4. Measurement of the Photon Identification Efficiency 83
4.5. Event Selection
4.5.2. Electron Selection with a Tag-and-Probe Method
In order to obtain a sample of pseudo-photons, i.e. of transformed electrons, that can be used to measure the photon identification efficiency, it is necessary to have a pure and unbiased electron sample to which the shower-shape transformations can be applied. Such a sample can be obtained by selecting electrons fromZ-boson decays using a tag-and-probe method. In this method, events are selected which fire at least one of the single-electron triggers mentioned in Section 4.4 and which contain at least one electron and one positron candidate. For the sake of simplicity, both electrons and positrons will be called electrons henceforth.
For all possible combinations of two electron candidates with opposite charge in a given event, it is checked whether one of them satisfies the following requirements:
• The electron candidate has a pT larger than 25 GeV and lies in a detector region allowing a reliable electron identification, that is,|η|<2.47 and excluding 1.37<|η|<1.52.
• The electron candidate matches to the object that fired the trigger, i.e. its angular distance
∆Rto the fired trigger is sufficiently small. In this analysis, the threshold is chosen to be
∆R<0.1.
• The electron candidate passes tight electron identification criteria, see Section 3.3.3.
If the considered electron candidate fulfills these requirements, and the invariant mass of the system of the two electron candidates is close to theZ-boson mass of 91.2 GeV [6], it is likely
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Figure 4.4.|Efficiency corrections for a bias due to a pre-selection based on f1. The correction is shown for converted and unconverted photons as a function of pTand in four different|η|regions.
that the electron candidate is indeed one of the two electrons from a Z →e+e− decay. As a consequence, this electron can be used as atagfor the other electron candidate, which is called theprobe. Since all selection criteria so far have been applied to the tag electron candidate, the corresponding selection of probe electron candidates remains unbiased. Therefore, the probes can be used to determine identification efficiencies. An electron candidate that is used as a probe in a given pairing of electron candidates can also be used as a tag itself in the same pairing if it passes the corresponding tag selection criteria. Generally, all possible combinations of electron candidates are considered.
To a large degree, the electron-extrapolation method of measuring photon identification efficiencies follows that of the electron identification efficiency measurement [150], which is outlined below. The major difference is that the selected probe electrons are transformed to pseudo-photons, which allows measuring the efficiency of the photon identification algorithm.
The measurement of the electron identification efficiency is based on invariant-mass distribu-tions for two different probe selections, corresponding to the numerator (identification selection applied) and denominator (no identification selection applied) of the efficiency. After subtracting the background in the invariant-mass spectrum, stemming predominantly fromW±+jets events with a leptonically decayingW±boson and from multi-jet events, the ratio of the integrals of the numerator and the denominator distributions around theZ-boson mass peak corresponds to the electron identification efficiency, as illustrated in Figure 4.5.
The background subtraction is performed in a simple signal-plus-background fit, considering electron-candidate pairs with an invariant massmeewithin 65 GeV≤mee≤250 GeV. The shape of theZ→e+e−signal mass distribution is based on simulation. A template for the background shape is taken from data, using inverted isolation and identification criteria in order to obtain a sample enriched in background events. Basic track quality selection criteria are applied to all candidates. In order to contribute to the background sample, a candidate must fail at least two rectangular selection requirements on shower and track properties. Additionally, if the candidate’s transverse energy is below 30 GeV, the calorimeter-based isolation variable defined in a cone of radius 0.3, topo-Econe 30T , must exceed 2 % of the candidate’s transverse momentum.
The background template is sketched in Figure 4.5 as gray area. The numerator and denominator in the efficiency measurement are computed in a mass region close to theZ-boson mass in order to be less sensitive to mismodeling of the background template and because only a small fraction
(a) (b)
Figure 4.5. |Sketch of the determination of the identification efficiency with a tag-and-probe method.
Shown are two invariant-mass distributions of di-electron candidates. In each of these, theZ→e+e−signal, colored blue (dark and light), is stacked on the background, colored gray. The black line corresponds to the sum of both distributions. No identification selection is applied in the right distribution(b), while in the invariant-mass distribution in(a), the probe must pass the identification selection. In order to be less sensitive to background effects, the efficiency is determined in a small mass range around theZ-boson mass peak. The signal that is used for the numerator and denominator computation (Nnum,Nden) is colored dark-blue, while the signal that is disregarded for the efficiency determination is colored light-blue. The ratio of the dark-blue areas of the right and left plot correspondingly corresponds to the efficiency.
of electron-positron pairs fromZ→e+e−events have a mass that differs considerably frommZ. Nominally, the mass range for the computation of the numerator and denominator signal yield is 70 GeV≤mee≤110 GeV.
This description of the determination of electron identification efficiencies translates easily to the determination of photon identification efficiencies, with the difference that the photon identification selection is applied to pseudo-photons which correspond to transformed probe electrons. Transformations have been derived for several kinematic regions of the probe electron.
Another modification with respect to the measurement of electron identification efficiencies as described above is that an isolation requirement is imposed on both the denominator and the numerator level in the case of the determination of photon identification efficiencies, i.e. the probe pseudo-photons must be isolated.
In Figures 4.6 and 4.7, examples of measured invariant-mass distributions for the numerator and denominator probe selection are shown. As explained in Section 4.2, sets of electron shower-shape transformations are derived to map electron shower shower-shapes to those of converted and unconverted photons individually. For Figures 4.6 and 4.7, the mappings to shower shapes of
un-converted photons are applied to probe electrons, allowing the measurement of the identification efficiency for unconverted photons.
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Figure 4.6. |Examples ofmeedistributions for unconverted pseudo-photon probes with 35 GeV<pT<
40 GeV and|η|<0.6. In(a)the denominator selection consisting of an isolation requirement is applied, while in the numerator selection in(b)also the photon identification requirement is applied. The ratio in the lower panel shows the agreement between the distribution observed in data with the fitted signal-plus-background distribution.
In the low-pT region, e.g. 25 GeV< pprobeT < 30 GeV (see Figure 4.6) the only distinct accumulation of events is the peak at mZ. An additional feature of the distribution occurs at largerpT, e.g. 100 GeV<pprobeT <125 GeV (see Figure 4.7): At a mass of roughlymee = 2pprobeT a second, smaller and broader maximum is visible, resulting from non-resonant Drell-Yan events, i.e.qq¯→γ∗/Z∗ →e+e−. While in the case of resonant production withmee≈mZ, the invariant mass of the final-state electrons for generic Drell-Yan di-electron production is given by
m2ee=2ptagT pprobeT h
cosh(ηtag−ηprobe)−cos(φtag−φprobe)i
, (4.9)
where piT, ηi, and φi correspond to the transverse momentum, the pseudorapidity and the azimuthal angle of the tag and the probe electrons. The mean value of the difference (ηtag−ηprobe) is zero, while for (φtag−φprobe) it is 180o. Hence, the mean value for the invariant mass of electron-positron pairs from non-resonant Drell-Yan production amounts to aboutmee≈2pprobeT in the case of unboosted di-electron systems, i.e. pT(e+e−)≈0. As can be seen in Figure 4.7,
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Figure 4.7. |Examples ofmeedistributions for unconverted pseudo-photon probes with 80 GeV<pT<
100 GeV and 1.81<|η|<2.37. In(a)the denominator selection consisting of an isolation requirement is applied, while in the numerator selection in(b)also the photon identification requirement is applied. The ratio in the lower panel shows the agreement between the distribution observed in data with the fitted signal-plus-background distribution.
this corresponds to the mass value at which the second peak is centered.