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

76 CHAPTER 5: Estimating of the Jet Energy Scale Calibration Factorof the four possible top quark candidates. A second variable is derived from the b-tagging discriminant (β) of each of the two b jet candidates which exist in the final state.The variable which is used in the training is defined as the b-tagging discriminator ofthe hadronic b jet candidate multiplied by the b-tagging discriminator of the leptonicb jet candidate, hence β bh × β bl .The final selected variables which are used to train the Likelihood Ratio method, arelisted in Table 5.2. The mutual correlation factors between the selected variables andthe top quark and the W boson masses are also quoted. The separation power of eachindividual variable is calculated and given in the last row of Table 5.2.Θ(t h , W h ) Θ(t h , b h ) Θ(t h , b l ) Θ(t h , e) Θ(b l , e)p thTΣp Tβ bh × β blm W -0.7 +2.0 +0.9 -0.1 -2.5 +0.4 -0.7m top +3.6 +2.0 +1.7 +2.1 -1.5 +2.5 +0.9Separation Power 0.08 0.06 0.20 0.09 0.30 0.10 0.40Table 5.2: The correlation coefficients of the variables, which are selected to train theMVA method, with the masses of the W boson and the top quark. The separationpower of each variable is also shown in the last row. All numbers are quoted in %.The distribution of the selected variables, which are shown separately for the correctand the wrong combinations, can be found in Figure 5.4 and Figure 5.5. All selectedevents in which a correct jet-parton combination exists, are taken into account.5.1.5 The MVA PerformanceAfter training the Likelihood Ratio method using the input variables listed in Table 5.2,one can check the performance of the method by looking at some control plots. Forexample, the fraction of e+jets t¯t events for which the chosen jet combination returnedby the Likelihood Ratio method corresponds to the true jet-quark combination, couldbe a possible measure to check how well the MVA method works.Figure 5.6 shows the Likelihood Ratio response, which is defined to be the maximumvalue among twelve possible values, per event. Only those selected e+jets events forwhich the hadronic jets are matched to the hadronic quarks in t → Wb → q¯qb, contributeto this plot. In association with the Likelihood Ratio response, the chosenjet-parton combination is also returned by the Likelihood Ratio method, which waschosen either rightly or wrongly. The response for the events with either right orwrong jet combination chosen by the MVA is shown in Figure 5.6. Here, “Good” jetcombination, as labelled in the plot, is defined as the event where the correct combinationis chosen as the one where the hadronic jets are matched to the hadronic quarkst → Wb → q¯qb. Therefore even if the MVA is not able to assign the fourth jet amongthe four leading jets to the leptonic b quark arrising from the leptonic top quark, the