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

98 CHAPTER 5: Estimating of the Jet Energy Scale Calibration Factor±1.0 RMS ±1.5 RMS ±2.0 RMS ±3.0 RMS∆ε exp∆ε expl(%) -8.83±0.31 -8.67±0.23 -8.17±0.19 -7.43±0.18b(%) -2.93±0.42 -2.08±0.36 -0.88±0.29 0.47±0.30Table 5.4: The expected residual corrections for light and b jets which are derived fromthe Gaussian fit over the various ranges of the fit.±1RMS to ±3RMS, which results in obtaining a small variation of about 1.4%. Forthe case of b jets, this variation is larger and reaches to about 3.4% when enlarging thefit range. This is due to the fact that, the distribution of the expected b jet residualcorrection, can not be fitted in the tail with a Gaussian function and the expected valueof the fitted Gaussian would change when increasing the fit range. This observationof the non-Gaussian effects in the tail, which is specific to the b jet distribution, canbe explained as follows. Since the b jets can decay to a lepton and the correspondingneutrino with a probability of 20%, hence the energy of the b jet is underestimateddue to the escaping neutrino. Hence, using the definition of the expected b jet energycorrection, one can have∆ε expb= E b quarkE b jet− 1 > 0,for those events where the b jet energy is underestimated. Therefore, these kind ofevents contribute to the tail in the distribution of the expected b jet energy correctionas shown in Figure 5.19. Therefore, in order to avoid the non-Gaussian effects inthe tail, the fit range is chosen to be ±1.5 times the RMS around the mean of thehistogram. However, the dependency of the fit results on the considered range of theGaussian fit can be taken into account as systematical uncertainty on the expectedvalues for the light and b jet energy corrections. Hence, for each of the expected lightand b jet distributions, the maximum variation among the various fit ranges comparedto the chosen fit range, being ±1.5RMS, is taken as the systematical uncertainty forthat particular distribution. The resulting systematical uncertainties for the expectedlight as well as b jet energy corrections, are listed in Table 5.5.Sys. Unc.δ sys. (∆ε expl)(%) ±1.2δ sys. (∆ε expb)(%) ±2.5Table 5.5: The systematical uncertainties on the expected light and b jet energy corrections.In order to compare the expected versus the estimated results, a new parameter,called the bias, is introduced which is defined as the difference between ∆ε estl/b and