The LCW weights are defined with respect to the electro-magnetic scale energy of the topo-clusters and can there-fore be applied in any arbitrary order. This allows system-atic checks of the order in which the corrections are applied.
There are four cluster properties used in the LCW calibra-tion scheme:
1. The energy density in cells in topo-clusters.
2. The cluster energy fraction deposited in different calori-meter layers.
3. The isolation variable characterising the energy around the cluster.
4. The depth of the cluster barycentre in the calorimeter.
In addition, the cluster energy after each correction step and the cluster location can be compared in data and Monte Carlo simulation.
Fig. 53 Calorimeter cell energy density distributions measured at EM scale used in the GCW jet calibration scheme in data (points) and Monte Carlo simulation (shaded area) for calorimeter cells in the barrel presampler (a), the second layer of the barrel electromagnetic calorimeter (b), the second layer of the barrel hadronic Tile calorime-ter (c), the second layer of the endcap electromagnetic calorimecalorime-ter (d), the first layer of the endcap hadronic calorimeter (e) and the first layer
of the forward calorimeter (f). Anti-kt jets with R= 0.6 requiring pjetT >20 GeV and|y| < 2.8 calibrated with the GCW+JES scheme are used. Monte Carlo simulation distributions are normalised to the number of cells in data distributions. The ratio of data to Monte Carlo simulation is shown in the lower part of each figure. Only statistical uncertainties are shown
14.2.1 Cluster isolation
Figure 54 shows the distributions of the cluster isolation variable for all topo-clusters in calibrated jets with pTjet>
20 GeV and|y| < 2.8 for topo-clusters classified as electro-magnetic (a) and hadronic (b).
The cluster isolation variable is bounded between 0 and 1, with higher values corresponding to higher
isola-tion (see Sect.13.2.2). Most of the topo-clusters in lower energetic jets have a high degree of isolation. The peaks at 0.25, 0.5 and 0.75 are due to the topo-clusters in bound-ary regions which are geometrically difficult to model or regions with a small number of calorimeter cells. Such topo-clusters contain predominantly gap scintillator cells or are located at the boundary of the HEC and theFCAL calorimeters.
Fig. 54 Distributions of the isolation variable for topo-clusters classi-fied as electromagnetic (a) and as hadronic (b) in data (points) and Monte Carlo simulation (shaded area). Topo-clusters associated to
anti-ktjets with R= 0.6 with pTjet>20 GeV and|y| < 2.8 calibrated with the LCW+JES scheme are used
The features observed are similar for topo-clusters classi-fied as mostly electromagnetic and those classiclassi-fied as mostly hadronic. A reasonable agreement between data and Monte Carlo simulation (see Fig.54) is found. The agreement in the peaks corresponding to the transition region between calorimeters is not as good as in the rest of the distribu-tion.
Figure55shows the mean value of the topo-cluster iso-lation variable as a function of the topo-cluster energy for all topo-clusters in jets with pjetT >20 GeV and |y| <
2.8 for topo-clusters classified as electromagnetic (a) or as hadronic (b). The Monte Carlo simulation consistently pre-dicts more isolated topo-clusters than observed in the data, particularly at topo-cluster energies E < 2 GeV and for both hadronic and electromagnetic cluster classifications. This feature is present in all rapidity regions, except for very low energy topo-clusters classified as mostly electromagnetic in very central jets.
14.2.2 Longitudinal cluster barycentre
Figure 56 shows the cluster barycentre λcentre (see Sect.
13.2.1) distributions for all topo-clusters in LCW calibrated jets with pjetT >20 GeV and|y| < 2.8 and for both cluster classifications. Most topo-clusters classified as electromag-netic have their centre in the electromagelectromag-netic calorimeter, as
expected. Those topo-clusters classified as mostly hadronic are very often in the electromagnetic calorimeter, since these low pTjets do not penetrate far into the hadronic calorime-ter. However, a structure is observed, related to the position of the different longitudinal layers in the hadronic calorime-ter. This structure is more prominent when looking at indi-vidual rapidity regions, being smeared where the geometry is not changing in this inclusive distribution. Good agree-ment is observed between data and Monte Carlo simula-tion.
Figure57shows the mean value of distributions of λcentre
as a function of the cluster energy for all topo-clusters in jets with pTjet>20 GeV and |y| < 2.8, again for both types of topo-clusters. In this case, topo-clusters classified as mostly electromagnetic have their barycentre deeper in the calorimeter on average as the cluster energy increases. A dif-ferent behaviour is observed for clusters tagged as hadronic, for which the mean depth in the calorimeter increases un-til approximately 2 GeV, at which point the mean depth decreases again. The shape of the mean depth as a func-tion of energy is different for different jet rapidities due to the changing calorimeter geometry. However, the qualitative features are similar, with a monotonic increase up to some topo-cluster energy, and a decrease thereafter. This is likely due to an increased probability of a hadronic shower to be split into two or more clusters with increased shower en-ergy. A good agreement is observed between data and Monte Carlo simulation.
Fig. 55 Mean value of the cluster isolation variable for topo-clusters classified as electromagnetic (a) and as hadronic (b) as a function of the topo-cluster energy measured at the EM scale, in data (closed
cir-cles) and Monte Carlo simulation (open squares). Topo-clusters asso-ciated to anti-ktjets with R= 0.6 with pTjet>20 GeV and|y| < 2.8 calibrated with the LCW+JES scheme are used
Fig. 56 Distributions of the longitudinal cluster barycentre λcentrefor topo-clusters classified as electromagnetic (a) and as hadronic (b) in data (points) and Monte Carlo simulation (shaded area).
Topo-clust-ers associated to anti-kt jets with R= 0.6 with pjetT >20 GeV and
|y| < 2.8 calibrated with the LCW+JES scheme are used
Fig. 57 Mean value of the longitudinal cluster barycentre λcentreas a function of the cluster energy measured at the EM scale for topo-clusters classified as electromagnetic (a) and as hadronic in data (b) in
data (closed circles) and Monte Carlo simulation (open squares). Topo-clusters associated to anti-ktjets with R= 0.6 with pjetT >20 GeV and
|y| < 2.8 calibrated with the LCW+JES scheme are used
14.2.3 Cluster energy after LCW corrections
In this section the size of each of the three corrections of the topo-cluster calibration is studied in data and Monte Carlo simulation. This provides a good measure of how the differ-ences between data and Monte Carlo simulation observed in previous sections impact the size of the corrections applied.
Figure58shows the mean value of the ratio of the cali-brated topo-cluster energy to the uncalicali-brated topo-cluster energy after each calibration step as a function the topo-cluster energy and pseudorapidity. Only topo-topo-clusters in LCW calibrated jets with pjetT >20 GeV are considered. For the results shown as a function of topo-cluster energy the rapidity of the jets is, in addition, restricted to|y| < 0.3.
The agreement between data and Monte Carlo simula-tion is within 5–10 % for the full topo-cluster pseudorapidity range ηtopo-clusterand is generally better for lower topo-clust-er entopo-clust-ergies whtopo-clust-ere the correction for the out-of-clusttopo-clust-er entopo-clust-ergy dominates. As the topo-cluster energy increases the largest corrections become the hadronic response and the dead ma-terial corrections.
An agreement to about 1 % is observed in a wide region in most of the barrel region after each correction. The agree-ment between data and Monte Carlo simulation is within 2 % for all topo-cluster pseudorapidities after the hadronic and the out-of-cluster corrections. Larger differences are ob-served between data and Monte Carlo simulation in the
tran-sition region between the barrel and the endcap and in the forward region once the dead material correction is applied.
14.3 Jet energy scale uncertainty from in situ techniques