Two main categories of systematic uncertainties are consid-ered. The first category contains those which affect the refer-ence pT of the recoil system. The second category includes those that affect the MJB variables used to probe the leading jet pT, introduced mostly by effects from analysis cuts and im-perfect MC modelling of the event.
The systematic uncertainty on the recoil system includes the following contributions:
1 Absolute JES uncertainty
The standard absolute JES uncertainties obtained from the combination of γ–jet and Z–jet techniques (see Sect.13.1) are included for each jet composing the recoil system. Fig-ures30and31show the MJB variations obtained by scaling the non-leading jet energy and momentum scale by ±1σ for each of the individual systematic uncertainties in the γ –jet and Z–jet calibrations, for the four jet calibration schemes.
Each source of systematic uncertainty is described in Sect.
9.5 and Sect. 10.4, respectively. This uncertainty ranges from 0.2% to 0.4% for Z–jet and 0.6% to 1.0% for γ–jet in the jet pTrange of 0.5–1.2 TeV for the two jet sizes of R= 0.4 and 0.6.
2 Relative JES uncertainty
Relative jet response uncertainties evaluated in the dijet
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Fig. 30: Multijet balance with the nominal and varied Z–jet in situ calibrations as a function of the recoil system precoilT for anti-kt jets with ((a),(b)) R = 0.4 and ((c),(d)) R = 0.6, calibrated with the ((a),(c)) EM+JES scheme and with the ((b),(d)) LCW+JES scheme. The varied distributions are obtained by fluctuating the jet energy scale for the non-leading jets by ±1σ for each of the systematic uncertainties for the Z–jet calibration and repeating the analysis over the data sample. The bottom panel shows the relative variations of the MJB with respect to the nominal case. The uppermost (lowermost) thick line in the bottom panel shows the total variation obtained by adding all the positive (negative) variations in quadrature.
intercalibration (Sect.8.4) are included in a similar manner for each jet with |η| < 2.8 in the recoil system.
3 Close-by jet uncertainty
The jet response is known to depend on the angular distance to the closest jet in (η, φ ) space [3], and the response vari-ation is expected to be more significant for jets belonging to the recoil system. Any discrepancy between MC simu-lations and data in describing the jet response with close-by jets therefore results in an additional systematic uncer-tainty. The measurement performed to evaluate the effect and the resulting systematic uncertainty are described in Sect.17. The close-by jet effect on MJB, shown in Fig.32, is obtained by scaling the jet energy and momentum for each recoil jet using the results in Sect.17.
The flavour composition of the jets could affect the agree-ment between MC simulations and data, and in principle cause an additional contribution to the JES uncertainty. Previous stud-ies with 2010 data [3], however, show that the resulting uncer-tainty on MJB is less than 1%, and is therefore ignored in this evaluation of systematic uncertainties.
The jet response is corrected for energy deposited by addi-tional proton–proton collisions in the same bunch crossings us-ing the pile-up offset correction described in Sect.6. The resid-ual pile-up effect on MJB is checked by comparing the MJB values using sub-samples of data and MC simulations with dif-ferent NPV and µ values. The result shows that the agreement between MC simulations and data is stable within its statistical
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Fig. 31: Multijet balance with the nominal and varied γ–jet in situ calibrations as a function of the recoil system precoilT for anti-kt jets with ((a),(b)) R = 0.4 and ((c),(d)) R = 0.6, calibrated with the ((a),(c)) EM+JES scheme and with the ((b),(d)) LCW+JES scheme. The varied distributions are obtained by fluctuating the jet energy scale for the non-leading jets by ±1σ for each of the systematic uncertainties and repeating the analysis over the data sample. The bottom panel shows the relative variations of the MJB with respect to the nominal case. The uppermost (lowermost) thick line in the bottom panel shows the total variation obtained by adding all the positive (negative) variations in quadrature.
uncertainty, and therefore an uncertainty due to pile-up is not considered.
The second systematic uncertainty category includes sour-ces that affect the MJB variable which is used to probe the high-pT jet energy scale. As said earlier, those are mainly due to effects from analysis cuts or imperfect MC modelling with the following considerations:
1 Analysis cuts
A systematic uncertainty might be induced by event selec-tion cuts on physical quantities that are not perfectly de-scribed by the MC simulation. In order to evaluate this sys-tematic uncertainty, all relevant analysis cuts are varied in a range where the corresponding kinematic variables are not strongly biased and can be examined with small
statisti-cal fluctuations (see Table7for the range of variation). For each value of the cuts, the ratio of the value of MJB in data and simulation is evaluated. The maximum relative devia-tion of this ratio from the default value is taken as the sys-tematic uncertainty from the source under consideration.
2 Jet rapidity acceptance
The analysis uses only jets with |y| < 2.8 in order to re-duce the impact of the large JES uncertainties in the for-ward region. This selection, however, can cause additional systematic uncertainty because the fraction of jets produced outside the rapidity range can be different in the data and MC simulations, and hence affect the MJB values. This ef-fect is checked, as is done in Ref. [3], by looking at the MJB for events with precoilT > 210 GeV, as a function of
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Fig. 32: Relative uncertainties on the MJB due to the systematic uncertainty sources considered in the analysis as a function of the recoil system pTfor anti-kt jets with ((a),(b)) R = 0.4 and ((c),(d)) R = 0.6, calibrated with the ((a),(c)) EM+JES scheme and with the ((b),(d)) LCW+JES scheme. The black line shows the total uncertainty obtained as a sum of all uncertainties in quadrature.
Table 8: Representative values of systematic uncertainties in the precoilT range 500 GeV < precoilT < 1.2 TeV for all effects con-sidered in the analysis.
Source EM+JES LCW+JES
Jet size R= 0.4 R= 0.6 R= 0.4 R= 0.6
Absolute JES 0.8% 0.7% 0.7% 0.7%
Relative JES 0.3% 0.4% 0.5% 0.4%
Close-by jet 0.6% 0.3% 0.6% 0.4%
Jet pTthreshold < 0.4%
α cut < 0.1%
β cut < 0.2%
pTjet2/precoilT cut < 0.1% 1.5% < 0.1% 1.2%
UE/radiation model < 0.5%
Fragmentation model 1.0% 0.3% 1.0% 0.5%
the total transverse energy (Σ ET) summed over all jets with
|y| > 2.8. The majority of events have a very small Σ ETand the effect turns out to be negligible.
3 Underlying event, fragmentation and ISR/FSR model-ling
Imperfect modelling of the UE, fragmentation and ISR/FSR may influence the multijet balance by affecting variables used to select events and kinematic properties of the lea-ding jet and the recoil system. The systematic uncertainty for each of the mentioned sources is estimated by evaluat-ing the data-to-MC ratio of the MJB, measured usevaluat-ing the default simulation based on PYTHIAand simulations using alternative MC generators. For the systematic uncertainty contribution from fragmentation, the HERWIG++ samples are used as an alternative. For the underlying event and ra-diation modelling systematics, the PYTHIAPERUGIA2011 samples are used. The systematic uncertainty introduced by these effects is 2 % or smaller in all cases except the lowest precoilT bins below 300 GeV.
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0.95