9 Performance of the prototypes
9.1 Electron energy calibration by 2016 CERN 8-module data
Energy calibration is a vital task in studying the performance of a calorimeter. A common subject of calibrating a sampling calorimeter is how to trace back the original energy of the incident particle from the information collected in the active layers. Thanks to the multi-layer design of HGCAL, shower development information can be retrieved from the detector. Hence, various calibration methods with different strategy toward the shower information can be studied and compared.
In [12], a generalization of the dEdx calibration method called the sampling frac-tion(SF) method was used to perform a careful MC study using a 30 layer non-uniform calorimeter. The result shows a generally better performance of the SF method than the dEdx calibration. This study aims to reproduce the method by the 2016 test beam data.
9.1.1 Data set
Both Data and MC of the 6 energies of the electron beam mentioned in 8.1are used. The selections is also the same in 8.1.
• Event selection: Require the Rimp of first layer < 20 mm.
• Hit selection: Collects only cell with energy higher than 2 MIPs, this selection is applied to all cells.
The statistics of the data set before and after the event selection are shown in Table 9.1.
†The delta ray is a secondary electron with enough energy which can be detected by the detector.
Delta ray can be easily produced by a charged pion which interacts electromagnetically.
e- Energy Total events Passed events
Table 9.1: Data statistics - energy calibration
9.1.2 dEdx method
The dEdx calibration make use of the silicon layers as MIP counter and calibrate the energy deposition in the absorber layers. The dEdx value of the absorber layers can be calculated from the X0 information for the setup. The MIP number in the absorber is taken from the average number between two active layers.† Hence, multiplying MIP counts and the expected energy deposition gives the energy in the absorber layers. At the end, all energy deposited in both active and passive layers are summed up and reconstructed energy is obtained.
EdEdx is the reconstructed energy by dEdx method.
i is the layer label, Ni is the number of mips in the absorber layer. The N0 is assumed to be 0.
Epassive is the expected energy deposition by 1 MIP, while Eactiveis the total energy recorded in the silicon layer.
The distribution of reconstructed energy is shown in Figure9.1. Both Data and MC are considered. A Gaussian fitting is done around the peak range so the low energy tail bias is avoided. The energy resolution of the detector in dEdx method is obtained by the Gaussian sigma in such energy, which will be shown later in 9.1.4 to compare with result from the SF method.
9.1.3 Sampling fraction (SF) method
The SF method is a generalization of the dEdx method in the sampling calorimeter which has different thickness abosrber layers. The method in the thesis is proposed in [12], where a dedicated MC study is performed. This will be the first test to validate the idea of the paper with the real data.
†First layer is a special case in the setup, since no silicon layer is placed bofore the absorber. However, one can just assume no MIP is generated before reaching the calorimeter.
Figure 9.1: dEdx EReco
The reconstructed energy of the dEdx method, both Data and MC are per-formed a Gaussian fit in the range [0.9,1.1] times the peak value. The black fitting is the fitting result of data, while the red fitting is for MC. The real beam energy of the 250 GeV data is slightly lower than the requested 250 GeV, which lead to the peak shift of the bottom right plot. (Table 9.2)
The definition of SF factor is quite simple:
SF = Eactive
Eactive+ Epassive or SF−1 = Eactive+ Epassive
Eactive (9.2)
Where Eactive is the visible energy in the prototype and Epassive is the energy in the ab-sorber layer. Although Epassivestay unknown in real life, the information can be obtained in MC. However, in the 2016 MC samples the information of the absorber layers is not stored. An assumption is made that there is no energy leakage in side or back of the calorimeter, thus the beam energy is directly used for the denominator of equation (9.2).
Hence, all the parameters (SHD, SF−1, Evisible) listed in the following paragraph are the value based on MC. Due the the nice agreement in all the energies of the electron, there is convincing reason to apply the parameters obtained in MC to calibrate the Data.
The linearity of the prototype can also be obtain from the Evisible fitting result, which is shown in the Figure 9.2.
Figure 9.2: Energy linearity by Evisible All the points are retrieved from MC.
The SF−1 and SHD are calculated event by event and form a distribution shown in Figure9.3and9.4, respectively. The mean value of the distribution is chosen†to represent the energy, which forms the plots of SHD to beam energy and SF−1 to beam energy. Thus, the beam energy can be describe as a function of SF−1 and SHD now.
Figure 9.3: SF−1
The distribution of sampling fraction in all energies(left), the low energy has a broader distribution. The lines in the plot represent the mean value of the distribution. A obvious trend that the < SF−1 > lowers as the energy raises. (right)
Figure 9.4: Shower depth
The shower depth distribution is shown in the left plot. Low energy electron has earlier shower maximum, and the peak shift deeper in X0 as the energy goes high. The averaged SHD in each energy < SHD > as a function of beam energy is shown in the right plot.
†Based on the method proposed in [12].
Moreover, the relation between SF−1 and the SHD is also studied to check if SF−1 is affected by the shower development, which is shown in Figure 9.5.
Figure 9.5: SF−1 slope
The profiles of the SF−1 with fixed SHD in different energy are shown (left).
Each of the point is the mean of the SF−1 distribution and the vertical error bar is the statistic error of the distribution. The slope of the linear function with respect to energy is then converted into the right plot.
From all the MC studies, 3 functions are obtained: Ebeam(SF−1,SHD) , EReco(Evis) , Slope(EReco).
For the data, each event gives a measurement of Evisible and SHD, which can be used as the starting point of the calibration. The steps to reconstruct the energy is listed below:
• step 1: Get an initial guessed energy from Evis by 570(the slope in Figure 9.2), named Eguess.
• step 2: From Eguess, an expected SF−1 and the slope of how SF−1 is affected by SHD can be obtained.
• step 3: Correct the SF−1 by the measured SHD and calculate EReco by revised SF−1.
• Note that if one is not satisfied by the result, the calculated EReco can go back from step 2 and correct the SF value again. This process can be iterated till the final SHD is sufficiently close to the measured SHD. This can end up forming an iteration method and allowing the search of best correction for EReco. (While in the thesis, the EReco is corrected just once.)
The result of the reconstruction is shown in Figure 9.6.
Figure 9.6: SF EReco
The reconstructed energy of the SF method, both Data and MC are per-formed a Gaussian fit in the range [0.9,1.1] times the peak value.The black fitting is the fitting result of data, while the red fitting is for MC. The energy shift in the bottom right plot is again related to the real beam energy. See Table 9.1.
9.1.4 Comparison
Two main results of comparing dEdx method and SF method will be shown: EReco peak precision and the energy resolution of the 2 methods.
In the EReco plot, the dEdx method is raised by a factor of 1.03 so the high energy points can reach the correct beam energy, which make the comparison between 2 methods at the same starting point.
A dedicated correction is performed on 250 GeV beam which the beam energy is considered inconsistent with the required energy. From the information in Table 9.2, the beam experts pointed out the beam energy is not always as the request energy. The reason is the setting of the upstream magnets.† Start from 200 GeV beam, a 2 GeV difference is observed. The bias become larger as the beam energy goes further higher.
†This table is provided by the SPS beam line and basically covers all the possible beam energy which has been used. Although this is the status of October 2018, the beam line status remain alike in 2016.
Hence, the dEdx and SF results are shifted by simple multiplication as shown in the Figure 9.7, but the resolution is not affected. See Figure9.8 for resolution comparison.
The resolution is fitted by Equation 1.8, σEE = √SE LNE LC.
Beam file Energy Final Energy
H2B CMS HGCAL 012 20 20
H2B CMS HGCAL 011 30 30
H2B CMS HGCAL 010 50 49.99 H2B CMS HGCAL 009 80 79.93 H2B CMS HGCAL 003 100 99.83 H2B CMS HGCAL 000 120 119.65 H2B CMS HGCAL 007 150 149.14 H2B CMS HGCAL 006 200 197.32 H2B CMS HGCAL 005 250 243.61 H2B CMS HGCAL 004 300 287.18 Table 9.2: 2018 October beam status
Figure 9.7: EReco precision
The plot show the peak correctness in the reconstructed energy. MC in the left and Data in the right. The respond before and after the general correction of the dEdx method is shown in MC. The last point of 250 GeV has also been adjusted as mentioned.
The results shows a general better performance in the SF method. In the low energy region, the SF method is more precise. Another substantial result is the constant term in energy resolution is lower, which shows it can benefit the high energy measurement.
As a result, SF method is a successful method to reconstruct the energy in sampling calorimeter with non-uniform thickness absorber layers.
Figure 9.8: Final resolution
The MC behavior is shown in the left and the data in the right. The fitting result of the stochastic term, noise term and constant term is labeled.