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

CHAPTER 5: Estimating of the Jet Energy Scale Calibration Factor 107(%)est∆ε l-2-4(%)est∆ε b42-60-8-2-10-4-12-14-18 -16 -14 -12 -10 -8 -6 -4 -2 0 2 exp∆ε l (%)-6-8-10 -5 0 5 10 exp∆ε b (%)Figure 5.21: The calibration curves representing the estimated residual jet energycorrections as a function of the expected jet energy corrections when applying severalinclusive shifts on the input energy of the reconstructed jets. A line with a unity slopeis overimposed for comparison.in a calibration curve with a non-unity slope. This can be fixed as explained below.The non-unity slope of the calibration curves can be solved by the use of successiveiterations, which means the estimated jet energy corrections found in a first iterationare applied on the initial jet energy scales. In a second iteration, the residual jet energycorrections can again be estimated, starting with the corrected jets of the first iteration.Ideally, in a second iteration no residual jet energy correction should be needed, giventhat the estimated jet energy correction is equal to the expected jet energy correctionin the first iteration. Othewise, the iteration procedure should be repeated until aresidual jet energy correction equals to zero is estimated. This means after applyingseveral iterations, the estimation converges to the line ∆ε estl,b = ∆εexp l,b, means the slopof the calibration curve becomes close to the unity.5.5.2 Pull DistributionIn order to evaluate if the statistical uncertainties on the estimators have been quotedcorrectly, one can start looking at the pull distributions which are defined as(∆ε i l,b − < ∆ε l,b >),δ∆ε i l,bwhere ∆ε l,b and δ∆ε l,b , as already used, are the estimated residual jet energy correctionsand their statistical errors, respectively. The index i is explained as follows.The initial simulated e+jets t¯t sample contains about 180000 events. In an analysiscorresponding to 100pb −1 , one would expect to obtain 2333 signal events, as it canbe deduced from the cross section of the e+jets t¯t process. Hence instead of giving aweight to the initial simulated events, one can repeat the whole analysis on the smallerbulks of simulated events, so-called pseudo-experiments, where each contain 2333 signalevents. Therefore, starting with the initial number of simulated signal events, onewould end with about 77 uncorrelated pseudo-experiments. Here no correlation meansthat a single signal event is not processed in no more than one pseudo-experiment.