Impact of Pile-up

From 2010 to 2011 the amount of pile-up has significantly increased. During the 2010 data taking the average number of interactions per bunch crossing was two, while at the end of 2011 it increased to up to 20. Therefore for the analysis with 2010 data the dependence on pile-up could be neglected. In contrast, for the analysis with 2011 data the measured quantities on detector level are expected to be affected by pile-up, even if the cut on the JVF rejects jets coming from pile-up in the central region and the jet energies are corrected for an offset depending on the number of primary verticesN_{P V} and the number of interactions per bunch crossing µ. This can be ascribed to the fact that no algorithm exists to reject jets originating from pile-up outside the acceptance region of the inner detector. If the pile-up observed in data after applying the inclusiveZ/γ^∗(→ee) selection is correctly modelled by the MC event samples, the measured cross sections are expected to be independent from the amount of pile-up, since its impact is correctly taken into account in the unfolding.

A first check is performed by comparing the average number of interactions per bunch crossing and the number of primary vertices predicted by ALPGEN+HERWIG with the data, as shown in Fig. 7.2. For both distributions, the predictions from ALP-GEN+HERWIG are consistent with the data, which indicates that the re-weighting pro-cedure, as described in Sec. 7.2, works correctly.

Further tests are performed by comparing the predictions from ALPGEN+HERWIG with the data for a few key distributions after applying the inclusiveZ/γ^∗(→ee) selection for different pile-up scenarios. Three regions (low, medium and high) for the average number of interactions, as well as for the number of primary vertices are defined:

• Low µ: µ <6.5

9. Measurement with the Dataset of 2011

• Medium µ: 6.5≤µ <10.5

• Highµ: µ≥10.5

• Low NP V: NP V <5

• Medium NP V: 5≤NP V <8

• HighNP V: NP V ≥8

At first order, it is expected that the number of primary vertices is mainly influenced by in-time pile-up whereas µ is influenced by out-of-time pile-up. In order to disentangle both effects, four regions have been defined: low µor high µtogether with mediumNP V

to study the impact of out-of-time pile-up and mediumµ together with lowN_{P V} or high NP V for in-time pile-up.

In order to compare the different pile-up scenarios, the ratio between the distribution with requirements on µand N_{P V} and the inclusive distribution without requirements on µ and NP V is taken. The impact coming from electrons are removed by dividing each distribution by its respective number of inclusive Z/γ^∗(→ ee) events before calculating the ratio. Figure 9.5 shows the ratios to test the impact of in-time and out-of-time pile-up for the transverse momentum and the rapidity distribution of all jets. As expected, the largest impact of pile-up is found in the low p^jet_T region and in the forward region beyond the acceptance region of the tracker, where no cut on the JVF is applied. In addition the impact of in-time pile-up is much larger on the measured quantities. In general, a good agreement between the predictions from ALPGEN+HERWIG and the data are found, except for some phase-space regions (lowp_T and very high|y|). In order to provide more precise tests of the MC data agreement, the double ratio between the ratios from ALPGEN+HERWIG and data is built and shown in Fig. 9.6. The hatched bands reflect the pile-up component of the JES uncertainty.

As seen before the impact of pile-up on the measured quantities is well described by the predictions from ALPGEN+HERWIG, except for the region 20 GeV< p^jet_T <30 GeV, which supports the choice to perform the measurements only for jets with p_T >30 GeV.

But the deviations in this region are still covered by the pile-up component of the JES uncertainty. Also in the forward region the predictions from ALPGEN+HERWIG are consistent with the data within the large statistical and systematic uncertainties. Results of similar pile-up studies for the inclusive jet multiplicity are shown in Appendix B.1.1.

102

9.1. Uncorrected Distributions ALPGEN (Medium µ

PV) , High N Data 2011 (Medium µ

PV) , High N ALPGEN (Medium µ

(a) Inclusive jetpT, impact of in-time pile-up

[GeV]

(b) Inclusive jetpT, impact of out-of-time pile-up

yjet ALPGEN (Medium µ

PV) , High N Data 2011 (Medium µ

PV) , High N ALPGEN (Medium µ

(c) Inclusive jety, impact of in-time pile-up

yjet

(d) Inclusive jety, impact of out-of-time pile-up

Figure 9.5.: Ratios of (a),(b) the transverse momentum and (c),(d) the rapidity distributions of all jets with and without requirements on µ and NP V in data and simulation to test the impact of (a),(c) in-time pile-up and (b),(d) out-of-time pile-up. The distributions are divided by the respective number of inclusive Z/γ^∗(→ee) events before calculating the ratios.

9. Measurement with the Dataset of 2011

(a) Inclusive jetpT, impact of in-time pile-up

[GeV]

(b) Inclusive jetpT, impact of out-of-time pile-up

yjet

(c) Inclusive jety, impact of in-time pile-up

yjet

(d) Inclusive jety, impact of out-of-time pile-up

Figure 9.6.: Double ratio between the ratios from ALPGEN+HERWIG and data for (a),(b) the transverse momentum and (c),(d) the rapidity distributions of all jets to test the impact of (a),(c) in-time pile-up and (b),(d) out-of-time pile-up. The hatched bands reflect the pile-up component of the JES uncertainty.

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9.2. Corrections for Detector Effects

9.2. Corrections for Detector Effects

Similar to the 2010 analysis, the final cross sections are quoted on particle level to facilitate the comparison with pQCD predictions and with measurements from other experiments.

Therefore, the measurements are corrected for detector effects back to particle level. This correction accounts for resolution effects, non linearities and efficiencies of theZ/γ^∗and jet identification and reconstruction. In contrast to the 2010 analysis, the nominal correction is done using the iterative (Bayes) method [131] based on the ALPGEN+HERWIG signal MC event sample. The iterative (Bayes) method has been optimised using more refined corrections and a better method to choose the optimal number of iterations. In addition, the available MC statistics has significantly increased, which allows for measurements with a higher level of accuracy.

In the following subsections the implementation of the iterative (Bayes) method and the method to evaluate the optimal number of iterations are presented. The systematic uncertainties due to the unfolding procedure are discussed in Sec. 9.3.5.