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

108 CHAPTER 5: Estimating of the Jet Energy Scale Calibration FactorOnly e+jets t¯t events are taken into account in order to make the pull distributions.No background is considered because not enough simulated events are available.Running the method to estimate the residual jet energy callibration factors on eachof the pseudo-experiments, one can obtain 77 different values as the estimation of thelight and b jet energy corrections, corresponding to each of the pseudo-experiments.The obtained results are used to make the pull distribution.Now it can be explained that the index i in the definition of the pull variable, refers tothe i-th pseudo-experiment. Also the sign represents the average of the estimatedresults over all pseudo-experiments.By definition, the pull distribution is peaked at zero and can be fitted with a Gaussianfunction. If the estimation of the statistical uncertainties is correct, then the fittedGaussian would have a variance equal to one. Otherwise there would have been an underestimationor overestimation of the estimated statistical uncertainties, if the widthof the fitted Gaussian would have a larger or smaller width, respectively.The distribution of the pull variable for the estimated light and b jet energy correctionsis shown in Figure 5.22.Entries 77Entries 77# pseudo experiments1210862χ / ndf14.29 / 14Constant 7.512 ±1.446Mean -0.0703 ±0.1968Sigma 1.383 ±0.232# pseudo experiments1086χ 2/ ndf6.115 / 14Constant 7.917 ±1.264Mean -0.05784 ±0.18518Sigma 1.458 ±0.17844220-10 -8 -6 -4 -2 0 2 4 6 8 10ii(∆ε l -)/δ∆ε l0-10 -8 -6 -4 -2 0 2 4 6 8 10ii(∆ε b -)/δ∆ε bFigure 5.22: The pull distribution of the estimated (left) light and (right) b jet energycorrections. The distributions are fitted with a Gaussian function.As it is shown in the statistical boxes of the pulls in Figure 5.22, the width of thefitted Gaussian functions is about 1.4 for both estimators. These non-unity widths canbe used to correct the statistical uncertainties of the light and b jet energy corrections,which have been found for 100pb −1 of integrated luminosity in Section 5.4, resulting inand∆ε l est = −10.1 ± 1.5%,∆ε b est = −1.3 ± 2.4%.Therefore, at 7 TeV center of mass energy with the use of a sample of simulatedevents corresponding to an integrated luminosity of 100pb −1 , the residual jet energycorrections can be estimated with a statistical precision of about 1.5% and 2.4%, forlight quark and b quark jets respectively. While using the full sample of simulatedevents which corresponds to an integrated luminosity of about 9400pb −1 , the residualjet energy corrections can be estimated with a statistical precision of about 0.18% and