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

74 CHAPTER 5: Estimating of the Jet Energy Scale Calibration Factor• Θ(t h , b h ) which is the space angle between hadronic top quark and hadronic b,• Θ(t h , b l ) which is the space angle between hadronic top quark and leptonic b,• Θ(t h , e) which is the space angle between hadronic top quark and electron,• Θ(W h , b h ) which is the space angle between hadronic W boson and hadronic b,• Θ(W h , b l ) which is the space angle between hadronic W boson and leptonic b,• Θ(W h , e) which is the space angle between hadronic W boson and electron,• Θ(b h , b l ) which is the space angle between hadronic b and leptonic b,• Θ(b h , e) which is the space angle between hadronic b and electron,• Θ(b l , e) which is the space angle between leptonic b and electron,• Θ(q, ¯q) which is the space angle between light quarks appearing in the decay ofhadronic W boson.Most of the above mentioned variables are not independent and contain the sameinformation. This can be seen by looking at their linear correlations which are shownin Table 5.1. Since the masses of the W boson and the top quark are going to be usedas constraints in this analysis, as will be explained in the following sections, it is alsorequired that the selected variables are not highly correlated with the W boson andtop quark masses. The last two rows of Table 5.1 contain the correlation factors amongall considered space angle variables with the masses of the W boson and top quark.The space angle variables are required to have a mutual correlation factor amongthemselves less than 40%. They are also asked to be correlated with the W boson andthe top quark masses less than 20%. Since the separation powers of each individualvariable are of the same order, taking into account the requirement on the correlationfactor, only 5 variables among the above mentioned space angle variables are selectedto be used in the training of the MVA method. In addition, there are two morevariables which are selected for training. A first one, which is defined as the transversemomentum of the hadronic top quark candidate relative to the sum of the transversemomenta of all hadronic top quark candidates pth TΣp T. Since with the four leading jets,there are four different ways to combine three of them to reconstruct a top quarkcandidate, then the sum in the denominator is performed over the transverse momenta