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

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68 CHAPTER 5: Estimating of the Jet Energy Scale Calibration Factorthe mass constraints of both the W boson and the top quark on t h → W h b → q¯qb h andrequiring the reconstructed jets to fulfill the constraints, while allowing the measuredenergies to change within their resolutions, would result in obtaining jets with modifiedenergy. The method of applying mass constraints, which makes use of the LagrangeMultipliers, is called a Kinematic Fit and is introduced in Section 5.2.In addition to the baseline event selection cuts described in the previous chapter, someextra cuts are applied on the selected events which are introduced in Section 5.3. Themethod to estimate the residual jet energy calibration factors is described in Section 5.4and the statistical properties of these estimators are discussed in Section 5.5. Finally,the method is applied on the proton-proton collision data which has been collected bythe CMS experiment during the physics runs in 2010. The plots which compare thesimulation versus data are shown in Section 5.6.5.1 Multi-Variate Analysis Method (MVA)In the final state of the e+jets t¯t decay, t¯t → e¯ν e q¯qb¯b, there are four quarks producedwhich should result in at least four reconstructed jets in the detector. If no tagging toolsare used to distinguish between light jets, originating from the quarks which appear inthe decay products of the hadronic W boson, and b jets, originating from the b quarkswhich appear in the decay products of both the hadronic and the leptonic top quarks,one can not differentiate between them. Therefore in order to label the jets and assignthem to the four quarks, there are 4! = 24 different ways to do the assignment giventhat only four reconstructed jets are taken into account. Since the order of the jetswhich are assigned to the light quarks is not important when reconstructing the Wboson momentum, they can be used interchangably. Hence the number of differentways to assign four reconstructed jets to the four quarks is divided by 2 and reduces to12. The quarks which are produced in the decay products of e+jets t¯t event, initiatefrom heavy particles such as W boson and top quark. Hence the four leading jets thatare the jets with the maximum p T among the reconstructed jet collection, could begood candidates to represent the four quarks and thus are used to do the assignment.It should be noted that there are usually more than four jets reconstructed in the eventdue to radiations, hence the four leading jets are not always the correct jets as willbe discussed in Section 5.1.1. Another important note to be emphasized is that theelectron fakes a jet but is removed from the list of reconstructed jets.To summarize the above discussion, there exist 12 different combinations in order toassociate four leading jets to the four quarks arrising from the e+jets t¯t decay. Among12 possible combinations, only one combination represents the correct assignment.Since the determination of the correct combination of jets is essential for the rest ofanalysis, specific efforts should be made in order to select the correct combination.In order to select the correct jet-parton combination among 12 combinations, when nosimulation information is available, it is possible to take randomly one combination.The probability of selecting the correct jet combination randomly is 1 ∼ 8% as only12one among twelve comibnations is the right candidate in each trial. The probability ofselecting the right jet combination is further improved by considering the kinematicsof some variables that can differentiate between the right and wrong jet combinations.
CHAPTER 5: Estimating of the Jet Energy Scale Calibration Factor 69This is the subject of the methods, generally called Multi-Variate Analyses (MVA),which combine the information of different variables and extract a value that candiscriminate between the right and wrong jet combinations.There are many MVA methods implemented in order to separate signal, which is inthis case a right jet combination, from backgrounds, which are the other eleven wrongjet combinations [100]. The Likelihood ratio method is used in this analysis in orderto label the jets and select the correct jet combination.5.1.1 Jet-Parton Matching AlgorithmWhen analyzing simulated samples for which the information from the generator levelcan be accessed, a Monte Carlo truth jet-parton matching can be introduced. Evenin case of access to the full information of the partons produced in the final state,including their four-vectors, no unambiguous definition of matching is present. Thereare many algorithms to associate the reconstructed jets to the generated partons [101].In general they match jets to partons based on the spatial distance between them. Theone, which is used in this analysis, is called ptOrderedMinDist and explained brieflyhere.The algorithm starts by making a p T -ordered list of partons produced in the final state.Then it looks for the closest reconstructed jet to the leading parton by matching themin (η, φ) space. A reconstructed jet is assigned to the leading parton if∆R = √ (η parton − η jet ) 2 + (φ parton − φ jet ) 2 < 0.3.In case such a jet is found, the jet is matched to that parton and is subsequentlyremoved from the list of the reconstructed jets. The algorithm continues by taking thesecond leading parton in the event. In this procedure, if there is no jet found close tothe parton, the parton remaines unmatched.Applying the above mentioned jet-parton matching algorithm, it is found that in only26% of the selected e+jets t¯t events, a correct jet-parton matching exists. This relativelylow fraction of selected events, for which the four leading jets are matched to the fourquarks arrise in t¯t → eν e q¯qb¯b, can be explained as follows. In most of the e+jets signalevents, one can find energetic jets originating from Initial State Radiation (ISR) whichfinally appear in the list of four leading jets. The appearance of the ISR jets in the listof four leading jets consequently spoils the procedure of matching of the hard-scatterpartons to the four leading jets. This physics result can be understood by looking atthe plot in Figure 5.1.According to Figure 5.1, which shows the multiplicity of the generated ISR jets withp T > 30 GeV per selected signal event, the fraction of the selected e+jets t¯t eventsthat contain at least one ISR with a p T exceeding 30 GeV would reach to 74%.Also it can be calculated how often an ISR jet is reconstructed among the four leadingjets. As understood from Figure 5.2, which shows the number of ISR jets that can bematched to the four leading jets per selected signal event, in 56% of all selected e+jetst¯t events, there is at least one ISR that is matched to a jet among the four leading jets.Therefore, the presence of ISR jets among four leading reconstructed jets in signalevents can partially explain why in a large fraction of the selected events, the four
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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 2The CMS experiment at the
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Chapter 6ConclusionThe Standard Mod
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CHAPTER 6: Conclusion 129The method
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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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