Correction Factors

The correction factors used in the unfolding process are based on MC simulation and therefore reflect eventual biases in the SM predictions; such biases need to be estimated and propagated to the correction factors. In addition, experimental uncertainties that affect the cross sections at reconstruction level need to be propagated to the correction factors.

Pileup Reweighting

As described in Section 5.2.2, simulated events are reweighted such that the distribution of the number of pileup interactions per event matches that in the dataset. A mismodeling in the pileup reweighting can lead to biases in the correction factors.

In order to compute the mean valueµ−1 of the Poisson distribution from which the number of pileup interactions is drawn, Eq. (5.1) is used. Thus, the number of pileup interactions that

are added to the hard-interaction event depends on the value of the inelastic cross sectionσ_inel. The modeling of proton-proton interactions in the event generator that is used to simulate pileup interactions, Pythia8, leads to an inelastic cross section that is slightly higher than the measured inelastic cross section [201]. A scale factor relatingσ^data_inel andσ^MC_inel is used in order to take this mismatch into account before pileup reweighting is performed. The scale factor is determined based on the observed number of primary vertices as a function ofµin data and in simulation.

The uncertainty on the scale factor of 3 % is propagated to the bin-by-bin correction factors by applying pileup weights based on varied scale factors in the computation of the correction factors and by comparing the resulting correction factors to the nominal values.

Vertex Selection

As described in Section 3.3.2, a multivariate algorithm is used to determine the Higgs boson production vertex. In approximately 75 % of simulated gluon fusion Higgs events, the correct vertex is chosen, defined by the selected reconstructed vertex being in a distance to the true vertex of less than 0.3 mm. The absolute uncertainty on this fraction was estimated to be 5 % by comparing the corresponding values in data and simulation usingZ→e⁺e⁻events in which the tracks of the electrons from theZ decay are disregarded, see also Figure 3.15.

The assumed location of the Higgs boson production vertex has impact on the reconstructed photon candidate four-momentum because it influences the pseudorapidity assigned to the photon candidate. Via the relation ET = E/cosh(η) as introduced in Section 3.3.3, this has an effect on the transverse energy of the photon candidates. Moreover, the selection of the Higgs boson production vertex has influence on the track-based isolation variable, for which exclusively the tracks assigned to the hard-interaction vertex are considered. Therefore, the uncertainty of the fraction f ofH→γγevents in which the correct vertex has been chosen needs to be propagated to the measured cross section. This requires the determination of the efficiencyεof the diphoton event selection as a function of f,

ε(f)= f·ε_corr+(1− f)·ε_wrong. (5.14)

In this equation,ε_corrand ε_wrong are the diphoton event selection efficiencies in the case of a correct selection of the Higgs boson production vertex, and in the case of an incorrect selection,

respectively. The uncertainty on f is propagated to the selection efficiencyε(f), and by extension to the correction factors, by comparing ε(f) for values of f that correspond to its up- and down-variations within the uncertainty∆f,ε(f±∆f).

Jets from Pileup Interactions

For an accurate determination of differential cross sections in jet-related variables, it is important to understand the impact of jets from pileup interactions: some jets that pass the selection criteria do not originate in the Higgs boson production vertex but result from pileup interactions. In simulation, particle-level information is exclusively stored for the hard interaction, and not for pileup interactions. Consequently, a jet is considered to be a pileup jet in simulation if it cannot be matched to any particle-level jet from the Higgs boson production vertex with a transverse momentum larger than 10 GeV within∆R<0.4. The fraction of selected jets stemming from pileup interactions in simulation is 6 % according to this definition. The efficiency with which pileup jets pass the jet selection cannot be expected to be identical in data and simulation. In order to estimate the effect of this potential difference on the bin-by-bin correction factors for jet-related distributions, 20 % of the selected pileup jets in simulation are randomly removed. This percentage corresponds to an estimate for the relative difference in efficiencies of pileup jets to pass the jet-vertex-tag requirement in data and simulation. The uncertainty from the contribution of pileup jets on the correction factors is assessed by comparing the nominal correction factors with those resulting from events with such modified sets of jets.

Photon Selection

The efficiency of the photon identification and isolation selection in simulation and in data are generally not identical. In order to correct for these differences between events in simulation and in data, scale factors are multiplied as additional factors to the weights of the simulated events. See Chapter 4 for details on the photon identification efficiencies and the corresponding scale factors, given by the ratio of identification efficiencies in data and in simulation. Both identification and isolation efficiency scale factors are known only with limited accuracy. The uncertainties on the identification and isolation efficiency scale factors are of the order 1 % in the relevant photon p_T region [147]. In Figures 4.25 and 4.26, the scale factors and uncertainties are

shown for identification efficiencies. In order to propagate uncertainties in the identification and isolation scale factors to the cross section measurement, the scale factors are varied within their uncertainties and the resulting correction factors are compared to the nominal correction factors.

Photon Energy Scale and Resolution

The uncertainty on the photon energy scale and resolution is not only relevant in the signal yield extraction as described in Section 5.6.1, but also in the determination of the correction factors.

Systematic variations of the photon energy scale and resolution lead to migrations in and out of the fiducial region and between bins of the p^H_T and|yH|distributions. The uncertainty on the energy scale and resolution is propagated to the correction factor uncertainties by computing the difference between the nominal correction factors and the correction factors based on the up-and down-variations of energy scale up-and resolution.

Jet Calibration and Flavor Tagging

When considering differential distributions inp_T^j1 orN_b−jets, the systematic uncertainties of the jet energy determination and jet modeling need to be propagated. The calibration of jet energies is outlined in Section 3.3.4. The relevant uncertainties include, but are not limited to, uncertainties within thein situcalibration procedure, uncertainties that account for potential mismodeling of the pileup effects, as well as uncertainties in the jet composition. In the case ofN_b−jets, also uncertainties related to a potential mismodeling of theb-tagging efficiency need to be propagated to the correction factors for the N_b−jets distribution. The uncertainty on the correction factors is determined by quadratically adding differences between the nominal correction factors and correction factors resulting from variations of the relevant jet-related parameters.

Theoretical Uncertainties

The correction factors are sensitive to the modeling of the underlying physics. Several modeling aspects are taken into account in order to estimate the theoretical uncertainty on the correction factors.

Because correction factors for the various Higgs boson production modes differ to some extent, the corrections factors are sensitive to the relative contributions, as can be seen in Eq. (5.11).

The cross sections for the individual production modes that enter this equation are based on SM predictions. By computing the differences between the nominal correction factors and correction factors that are based on varied contributions from different production modes, the uncertainty on the production mode contributions are propagated to the correction factors. In Table 5.3 the up-and down-variations applied to the cross section of six of the production modes independently are shown. These variations are based on References [202–204]. When scaling the cross section of a particular production mode up or down, the cross sections of all other production modes are kept at their SM value. The production modes with the smallest cross sections are not listed in Table 5.3 and are not considered in the variation scheme, that is, their contributions are assumed to be correctly described by the SM. This is justified by their small cross section; variations of these cross sections would result in negligible effects on the correction factors.

σpm±∆σpm

σpm ggF VBF W H ZH ttH¯ bbH¯

Up 1.145 1.203 1.433 1.468 1.500 1.220 Down 0.855 0.797 0.567 0.532 0.700 0.780

Table 5.3. |Orthogonal variations (scaling factors, SM corresponds to 1) of the cross section contributions of individual Higgs boson production modes that are used to determine the modeling uncertainty on the correction factors due to a limited knowledge about the relative contributions from different production modes. Each production mode contribution is varied independently. Values for all production mode variations exceptt¯tHandbbH¯ are based on Reference [202]. Thet¯tHandbbH¯ variations are based on References [203] and [204], respectively.

Another source of theoretical uncertainty is the sensitivity of the correction factors to the diff er-ential distributions in simulation. In order to directly assess the impact of poter-ential mismodeling of the predicted distributions on the unfolded results, alternative sets of correction factors are derived based on distributions from simulated events in which event weights are modified such that the resulting p_T^H and|y_H|distributions at reconstruction level correspond to the observed distributions. The reweighting factors are derived from a fit of an appropriate function to the observed spectrum and correspond to the ratio of the fitted function to the SM expectation. The resulting reweighting factors, which are smoothed before application, are shown in Figures 5.4a and 5.4b for p^H_T and|y_H|, respectively. Three varied sets of correction factors are produced: one in which only the p^H_T distribution is modified, one in which only the|y_H|distribution is modified, and one in which both p^H_T and|y_H|distributions are modified. The maximal deviation of the

three resulting varied correction factors from the nominal correction factor is taken to be the corresponding uncertainty on the correction factor.

0 50 100 150 200 250 300 350

H

pT

0.2 0.4 0.6 0.8 1 1.2 1.4 1.6

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(a)

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2 2.4

H|

|y 0.2

0.4 0.6 0.8 1 1.2

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(b)

Figure 5.4. |Factors for an event reweighting based on(a) p^H_T and(b)|y_H|in simulatedH→γγevents.

By comparing correction factors based on reweighted samples to correction factors from the nominal SM prediction, the impact of a potential mismodeling of differential distributions in simulation on the correction factors is estimated.

Furthermore, an uncertainty due to a potential mismodeling of the underlying event and the parton shower has been taken into account. This uncertainty has been estimated by comparing the nominal correction factors, which are based on the use of Pythia8, with those for which Herwig++was used as parton shower simulation. For the estimation of this uncertainty, only the effect on the dominant Higgs boson production mode, gluon fusion, was considered. Other production modes, having considerably smaller cross sections, have been omitted here due to the large computational effort that would be necessary for the evaluation of an uncertainty that generally has a small impact on the total uncertainty on the correction factors. Due to a relatively low number of simulated events with Herwig++ as parton shower simulation and resulting statistical fluctuations in some phase-space regions, the uncertainty per bin are estimated based on a linear fit to the distribution of differences between correction factors based on Pythia8 and Herwig++.

The three theoretical uncertainties on the correction factors as described above are combined by taking the envelope of these. A further theoretical uncertainty, an uncertainty related to the

limited knowledge of the Dalitz-events fraction among selected events, is taken into account separately. The sensitivity of the correction factors on the assumed value for the fraction of Dalitz events is estimated by comparing the nominal correction factors to correction factors which are based exclusively on non-Dalitz events.