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

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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
CHAPTER 5: Estimating of the Jet Energy Scale Calibration Factor 951.41.31.21.1∆E b10.90.80.70.60.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4∆E lFigure 5.16: The distribution of the χ 2 (∆E l , ∆E b ) which is obtained by the sum of theχ 2 distributions for all selected events.direction of ∆E l , are taken into account to make the projected distribution in thedirection of ∆E b axis.Each of the two projected distributions is fitted with a second-degree polynomial aroundthe minimum as shown in Figure 5.17.2∆ χ120100806040203×1000.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4∆ E l2∆ χ4500040000350003000025000200001500010000500000.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4∆ E bFigure 5.17: The projected distribution of the χ 2 (∆E l , ∆E b ) into the (left) ∆E l and(right) ∆E b axis which are fitted with a second-degree polynomial. The results areobtained for 100pb −1 of simulated proton collisions.The parameters of the fitted parabolas are used to extract the estimated light aswell as the b jet energy corrections, expressed as ∆ε l est and ∆ε b est , respectively. Theminimum of the parabolas refer to the final estimation of the jet energy correctionswhich are found to be∆ε l est = −10.12 ± 1.11%,and∆ε b est = −1.31 ± 1.72%,
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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 3Object ReconstructionThe e
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