Measurement of the Jet Energy Scale in the CMS experiment ... - IIHE

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80 CHAPTER 5: Estimating of the Jet Energy Scale Calibration FactorPurity10.90.80.70.60.50.40.30.20.10Likelihood0.2 0.4 0.6 0.8 1EfficiencyFigure 5.7: The purity versus efficiencyplot when cutting on the MVA output forthe selected e+jets t¯t events with a correctjet-parton combination.Figure 5.8: The purity versus efficiencyplot when cutting on the MVA output forall selected e+jets t¯t events.Also shown in Figure 5.8 is the distribution of the purity versus efficiency when cuttingon the Likelihood response which is plotted for all selected e+jets t¯t events, includingthose with no correct jet-parton combination. Considering these kind of events, theefficiency of selecting the correct combination with the use of the Likelihood method,when no cut is applied on the Likelihood response, reduces to about 17% which isobtained as 34% × 51% ∼ 17%.5.1.6 Reconstructing W Boson and Top Quark MassesNow that the reconstructed jets are associated to the hadronic quarks which areproduced in the decay products of the hadronic top quark of an e+jets t¯t event,t → Wb → q¯qb, one can reconstruct the W boson four-vector by summing the fourvectorsof the two light jets. The four-vector of the top quark can be subsequentlyreconstructed by adding the four-vector of the hadronic b jet to the reconstructedhadronic W boson. Furthermore, one can measure the invariant masses of the W bosonand top quark from their reconstructed four-vectors. In Figure 5.9, the masses ofthe W boson and the top quark are shown for those events where the MVA successfullyreturned the true jet-parton combination. It is observed that the reconstructedW boson mass is peaked around 89 GeV while the parameter which has been usedfor the W boson mass when simulating the events was chosen to be 80.4 GeV. Alsothe mean value of the distribution of the top quark mass is shifted from the valueused in the simulation procedure, being 172.5 GeV, to a reconstructed value which isfound to be about 181 GeV. One should note that the events which are used to fill themass distributions with, are those events where the MVA successfully chose the truejet combination. If all selected events were taken into account, tails would appear onboth histograms.This observation leads to the fact that, the jet energies which are used to build the Wboson and top quark four-vectors are over-estimated which yields the obtained higherinvariant mass values compared to the input masses. Therefore this motivates to build
CHAPTER 5: Estimating of the Jet Energy Scale Calibration Factor 81a method to correct the jet energies so that the known measured values of the W bosonand the top quark masses can be re-obtained.#eventsEntries 5006350Mean 89.15300RMS 13.452502001501005000 20 40 60 80 100 120 140 160 180 200m W(GeV)#events240 Entries 5006220200Mean 180.9180RMS 20.171601401201008060402000 50 100 150 200 250 300 350 400m top(GeV)Figure 5.9: The distributions of the reconstructed W boson mass (left) and the topquark mass (right) for the selected events where a true jet-parton matching is returnedby the MVA method.5.2 Kinematic FitFor a given event, four-vectors of the reconstructed objects are measured. The sameevent may contain particles, such as neutrinos, for which a direct measurement is notpossible. With the assumption of certain hypotheses, the measured as well as the unmeasuredquantities are supposed to fulfill the kinematic constraints which are usuallydeduced from the event hypothesis. Since there are uncertainties on the measuredquantities, the constraints are not exactly satisfied. The constraints can then be usedto slightly change the measured values within their uncertainties. The concept of anevent-by-event least square fitting together with the application of Langrange Multiplierscan be utilized to insure that the measured as well as the unmeasured quantitiesfulfill the kinematic constraints. This procedure is referred to as a kinematic fit.The kinematic fit method has been frequently used in various physics analyses performedin different collaborations [15]. Since at an electron-positron collider, the initialenergy and momentum of the incoming particles are well known, it is possible to applyconstraints like energy and momentum conservation via a kinematic fit method to extractfitted values for the unmeasured quantities in the final state. Also the kinematicfit technique can be used for calibration purposes. For example, the electromagneticcalorimeter of the BaBar experiment is calibrated by means of the kinematic fit technique[102]. Using the radiative Bhabha events e − e + → e − e + γ, given that the momentaof the incoming and outgoing electrons and positrons, as well as the photon’s angularposition are measured, the photon energy can be obtained via a kinematic fit. This fitresults in an absolute measurement of the photon energy which then can be comparedto the measured photon energy to obtain calibration constants.At hadron colliders like the LHC, it is not possible to apply energy-momentum constraintssince the initial kinematic properties of the colliding partons arrising from
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Vrije Universiteit BrusselFaculteit
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IntroductionThe Standard Model of p
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Chapter 1The Standard Model of Part
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CHAPTER 1: The Standard Model of Pa
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Chapter 2The CMS experiment at the
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CHAPTER 2: The CMS experiment at th
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Bibliography[1] M. E. Peskin and D.
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BIBLIOGRAPHY 133[40] The ALICE Coll
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BIBLIOGRAPHY 135[76] The CMS Collab
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SummaryJets appear in the final sta
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Measurement of the Jet Energy Scale in the CMS experiment ... - IIHE

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