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

94 CHAPTER 5: Estimating of the Jet Energy Scale Calibration Factorthat point in the two-dimensional space of (∆E l , ∆E b ). These events are not selectedas mentioned before.The correction factors on the light jet energy ∆E l , and on the b quark jet energy ∆E b ,can be interpreted equivalently as the residual shifts on the light jet energy ∆ε l , andon the b quark jet energy ∆ε b , by means ofand∆E l ≡ (1 + ∆ε l ),∆E b ≡ (1 + ∆ε b ).Therefore, in each point of the two-dimensional grid (∆E li , ∆E bj ), the shifts on thelight and the b quark jet energy are applied by means of multiplying the followingfactors(1 + ∆ε li ),and(1 + ∆ε bj ),measby the initial measured light jet energy, called E l init , and the initial measured b jetmeasenergy, called E b init , respectively. In the multiplication factors, 0 ≤ i, j < 41 and thestart points are taken to be∆ε l(i=0) = −0.4,and∆ε b(j=0) = −0.4.Hence, the region which is scanned by the fit procedure includes the following pointsmeas measmeasmeas meas0.60E l init , 0.62E l init , . . .(1 + ∆ε li )E l init . . .,1.38E l init , 1.40E l init ;meas measmeasmeas meas0.60E b init , 0.62E b init , . . .(1 + ∆ε bj )E b init . . .,1.38E b init , 1.40E b init .In each point of the scanned region, the kinematic fit package returns a probabilitywhich is obtained from the χ 2 of the fit. Therefore, instead of a two-dimensionaldistribution of the fit probability P KinFit (∆E l , ∆E b ), one can have a two-dimensionaldistribution of the χ 2 values χ 2 (∆E l , ∆E b ). In each point of the two-dimensional grid,the χ 2 values of all selected events are summed which leads to obtain a two-dimensionalparabola in the dimensions of the residual light and b jet energy corrections. Thedistribution of the χ 2 (∆E l , ∆E b ) which is obtained by the sum of the χ 2 disribution ofthe individual selected event, is shown in Figure 5.16.The estimated residual light and b jet energy correction factors are determined atthe point with the minimum χ 2 fit probability, being the most central point in the plotshown in Figure 5.16.The two-dimensional χ 2 distribution is projected in the directions of ∆E l and ∆E bto obtain two separate one-dimensional distributions which are subsequently used toestimate the final residual corrections. The projection into the ∆E l axis is done usingthose events that participate in minimizing the χ 2 distribution in the direction of ∆E b .Also, the events which contribute to the bin of the minimum χ 2 distribution in the