El maestro en la práctica pedagógica y en la ECDF

beam energy [GeV]

10 20 30 40 50 60 70 80 90

rel. difference of relative resolution

0.2 0.4 0.6 0.8 1 Resolution Improvement

Weights derived from simulations with QGSP_BERT -

π

Data Neural Network SC: -

π

QGSP_BERT Neural Network SC: -

π

FTF_BIC Neural Network SC:

beam energy [GeV]

10 20 30 40 50 60 70 80 90

rel. difference of relative resolution

0.2 0.4 0.6 0.8 1 Resolution Improvement

Weights derived from simulations with FTF_BIC -

π

Data Neural Network SC: -

π

QGSP_BERT Neural Network SC: -

π

FTF_BIC Neural Network SC:

Figure 4.25: Energy resolution improvement with the weights of the neural network soft- ware compensation technique derived from simulated data of the hadronic physics lists QGSP BERT (left) and FTF BIC (right). Test beam data is shown in black circles, simulation data of the physics list QGSP BERT in red squares and FTF BIC in blue triangles.

data with the physics list FTF BIC results in a larger energy resolution improvement than simulated data with the physics list QGSP BERT, for both neural networks.

4.5

Summary

Three different software compensation techniques were developed for the energy recon- struction of pions in the CALICE analog hadron calorimeter. All methods use the fact that electromagnetic showers have other characteristics than hadronic showers. These differences can be used to estimated the sharing of energy between the electromagnetic and the hadronic fraction in a hadronic shower.

The local and one of the global software compensation techniques presented in this thesis, directly used the fact that electromagnetic showers have typically a higher energy density than hadronic showers. In the local software compensation this was used on the hit level. Each single hit energy was corrected with a weight, which was calculated from the value of the single hit energy density. In the global software compensation, the cluster energy was corrected for each event, i.e. a suitable weight factor, based on the value of the cluster energy density, was applied to the cluster energy. Weights of both techniques needed to be parameterized by a function, which was energy and energy density dependent. Different weight parameterizations were extracted from test beam and simulated data.

The third presented approach was a global software compensation technique based on a neural network. In this method the corrected reconstructed energy was estimated from a number of

shower variables. Since the correct training of the neural network required a quasi-continuous particle energy distribution, it could only be performed with simulated data.

The weights of all techniques and data samples were applied to all available sets of test beam and simulated data. Results for the energy resolution, the deviation of reconstructed energy from beam energy, and the energy resolution improvement, given by the ratio of the fitted Gaussian width of the reconstructed energy with and without software compensation, were discussed.

In the following, results obtained with the different techniques for various data samples are summarized in three parts, each illustrated by a schematic (Figures 4.26, 4.27 and 4.28).

• First, the differences between the performance of the local energy density software compensation technique, the global energy density software compensation technique and the neural network software compensation are discussed.

Figure 4.26: Illustration of the software compensation technique comparison, illustrated by the blue, green and red boxes.

The methods are compared for the same conditions as shown in Figure 4.26, i.e. for all techniques weights were extracted from simulated data and applied to all sets of simulated and test beam data. The sizes of the energy resolution improvements are listed in Table 4.2. It is largest for the neural network approach, followed by the local and then by the global energy density software compensation technique.

One of the main results of this thesis chapter is that all three presented software compen- sation methods are very successful in improving the energy resolution of test beam and simulated data. Additionally a good accuracy of the reconstructed energy was achieved. A decision about which of the presented software compensation techniques should be recommended for a usage in the future, depends on the particular application. The neural network approach led to the largest energy resolution improvement but its imple- mentation, due to additional needed data sets, was most resource intensive. Between

4.5 Summary 71

Table 4.2: Comparison of different software compensation methods for weights derived from simulated data.

Weight derived from simulated data

Local energy density SC Global energy density SC Neutral Network SC • Average energy resolution

improvement 20 % for test beam and 25 % for simulated data

• Average energy resolution improvement 18 % for test beam and 22 – 25 % for sim- ulated data

• Average energy resolution improvement 22 % for test beam and 30 % for simulated data

• Almost no beam energy de- pendence of energy resolution improvement of test beam data

the two methods based on energy density, the local method achieved a better energy resolution improvement. Furthermore it used the full capacity of the calorimeters’ fine granularity. However, the global energy density weighting approach led a constant improvement over the full applied energy range.

• Second, the performance with weights derived from test beam data and from simulated data is compared.

As illustrated schematically in Figure 4.27 this only includes techniques directly using the energy density. In case of simulated data the comments include both physics lists from which weights were derived.

It can be concluded that the software compensation gives the best performance for both energy reconstruction accuracy and energy resolution, if the weights were applied to the same data sample type as the weights were extracted from, which is an expected result. It is important to stress that it is a great success that software compensation using weights extracted from simulated data also result in a significant improvement of resolution when applied to test beam data and vice versa. Obviously, the goodness of the results dependence on how accurate the simulated data described the test beam data in the first place. Models should describe data well on both the microscopic level, like local energy densities, and on shower shape level. There are ongoing activities between the CALICE collaboration and the developers of the hadronic models of Geant4 to improve the physics lists further. This is done on the side of the CALICE collaboration

Local Software Compensation based on energy density weighting

Global Software Compensation based on energy density weighting

Weights derived from simulated data Applied to test beam data Applied to simulated data with physics list QGSP_BERT Applied to simulated data with physics list FTF_BIC Weights derived from test beam data Applied to test beam data Applied to simulated data with physics list QGSP_BERT Applied to simulated data with physics list FTF_BIC

Figure 4.27: Illustration of test beam data and simulated data weight parameterization, illustrated by the light blue and orange circles.

through the comparison of many different shower variables of test beam data with simulated data using the available physics lists. The Geant4 developers, on the other hand, try to tune and adjust the implementation of their hadronic model descriptions to achieve a better agreement of test beam and simulated data.

• Third, the two physics list are compared with each other, as illustrated in Figure 4.28. It should be noted that it was not the goal of this thesis to study the performance of different physics lists. In that case, many more variables and physics lists should have been evaluated. Nevertheless, two physics lists were chosen to be presented in this thesis. Simulated data with physics list QGSP BERT led to a better description of the initial energy resolution of test beam data. The initial reconstructed energy was better described by simulated data with the physics list FTF BIC.

For the software compensation, weights extracted from simulated data of both physics lists achieved similar results for the energy resolution of test beam data. Using weights extracted from simulated data can lead to a bias in the reconstructed energy of test beam data. However, it was shown that this can easily be corrected. Furthermore, weights which were extracted from simulated data with the physics list FTF BIC gave better results for the linearity than weights which were extracted from simulated data with the physics list QGSP BERT. Also, the energy resolution improvement of simulated data was larger for all techniques with the physics list FTF BIC. Thus, it can be concluded that FTF BIC is slightly favored for the application in software compensation techniques.

4.5 Summary 73

Local Software Compensation based on energy density weighting Global Software Compensation based on energy density weighting Global Software Compensation based on neural network

Weights derived from simulated data of physics list FTF_BIC Applied to test beam data Applied to simulated data with physics list QGSP_BERT Applied to simulated data with physics list FTF_BIC Weights derived from simulated data of physics list QGSP_BERT Applied to test beam data Applied to simulated data with physics list QGSP_BERT Applied to simulated data with physics list FTF_BIC

Figure 4.28: Illustration of physics list comparison, illustrated by the pink and purple circles. However, the most important conclusion is that the large improvement in energy resolution was only achievable due to the construction of the calorimeter itself. Its high granularity made it possible to have a much better description of hadronic showers, since it provides a detailed three-dimensional picture of hadronic showers. For example, a software compensation technique for the CMS hadronic calorimeter led only to an energy resolution improvement of approximately 8 % [77]. The ATLAS hadronic calorimeter reached an energy resolution improvement due to calibration methods which included software compensation, dead material corrections, clustering corrections and other corrections for an imperfect reconstruction of

<20 % [78], compared to resolution improvements of up to 25 % obtained here with software compensation alone.

Chapter 5

Software Compensation in the CLIC ILD

and ILD detectors

The detectors developed and constructed by the CALICE collaboration are prototype detectors for the ILD and SiD detector systems of both ILC and CLIC, in the latter case called CLIC ILC and CLIC SiD. The analog hadron calorimeter with steel absorber plates, described in Section 4.1, represents the prototype for the ILD hadronic calorimeter. A prototype for the hadronic calorimeter for CLIC was recently built by the CALICE collaboration, taking the active layers and readout from the AHCAL and replacing the approximately 2 cm thick steel plates with 1 cm thick tungsten absorber plates.

In the previous chapter it was shown that software compensation improves the single particle energy resolution in the hadronic prototype calorimeter. Thus, it is an obvious step to implement software compensation in the event reconstruction software of ILD and accordingly CLIC ILD.

This chapter presents first, in Section 5.1, the studies on necessary requirements for software compensation in ILD and CLIC ILD. The second part, in Section 5.2, focuses on the energy resolution improvement for single hadrons and jets in the ILD calorimeter.

5.1

Calorimeter response to electrons and pions of ILD and

CLIC ILD

Software compensation works through the offline equalization of electromagnetic and hadronic detector response. It only can help to improve the energy resolution if thee/π ratio, intro-

duced in Chapter 3, is not equal to unity and differs by a large enough amount. Since the geometry and material of active and passive layers in the ILD detector design is comparable the one of the prototype, it is expected that thee/π6=1 for the ILD hadronic calorimeter in

simulations1, too. In case of the CLIC ILD hadronic calorimeter, this ratio is not a priory known, since a tungsten absorber, compared to steel like in the ILD case, will change the detector response. Therefore, a simulation study for its determination, as a necessary require- ment for the feasibility of software compensation, was performed.

The study was based on the simulation and reconstruction ofe− andπ− events at two energies

(10 GeV and 30 GeV). In Section 3.4 is was explained that the electromagnetic fraction in hadronic showers increases for higher energies. Therefore the fraction of invisible to incoming particle energy decreases with higher particle energy and thee/πdiffers less from unity. Thus,

the difference of electromagnetic and hadronic detector response should be largest for lower energies and it is sufficient to determine the ratio in the lower energy range.

The events were simulated with detector models of ILD and CLIC ILD. The creation point of the particles was placed between the electromagnetic and the hadronic calorimeter in the central barrel region, since only the detector response of the hadronic calorimeter, needed to be investigated. To test whether the results were simulation model dependent, two sets of events with different physics lists (QGSP BERT and FTF BIC) were simulated. QGSP BERT is the default physics list for high energy experiments. Another physics list (FTF BIC) was included to check for possible effects which are hadronic model dependent. The reconstruction was performed with the official reconstruction software2. An event picture of such a single particle shower is shown in Figure 5.1.

Figure 5.1: Event picture of a pion of 30 GeV in the barrel of the CLIC ILD hadronic calorimeter. The creation point of the particle was between the electromagnetic and hadronic calorimeter. (left:) Full detector. (right:) Hadronic calorimeter.

The output of the Particle Flow reconstruction are objects with a reconstructed energy based on the same calibration scale, since both particle types are treated as hadrons. The distribu- tions of the reconstructed cluster energy was fitted with a Gaussian for all settings (particle type, particle energy, detector model, physics list). The mean value of the fitted Gaussian cor- responds to the reconstructed energy. By comparing the reconstructed energies for electrons and pions thee/π ratios were calculated, shown in Table 5.1 for the CLIC ILD detector and

in Table 5.2 for the ILD detector.

The simulation of the hadronic calorimeter response of CLIC ILD shows an e/π ratio of 2_{One change to the default PandoraPFA settings had to be applied. See Section B.2 for more detail.}

5.1 Calorimeter response to electrons and pions of ILD and CLIC ILD 77

Table 5.1: Detector response to simulated electron and pion events in the CLIC ILD hadronic calorimeter with the physics lists QGSP BERT and FTF BIC. Both particle types are recon- structed with the same calibration values.

Detector: ILD for CLIC

FTF BIC QGSP BERT

particle

energy 10 GeV 30 GeV 10 GeV 30 GeV

E_rec E_rec E_rec E_rec

e− 11.89±0.01 GeV 35.07±0.03 GeV 11.86±0.01 GeV 35.07±0.03 GeV

π− 10.67±0.02 GeV 33.48±0.04 GeV 11.38±0.02 GeV 36.33±0.04 GeV e/π

ratio 1.14±0.002 1.047±0.002 1.042±0.002 0.965±0.001

Table 5.2: Detector response to simulated electron and pion events in the ILD hadronic calorimeter with the physics lists QGSP BERT and FTF BIC. Both particle types are recon- structed with the same calibration values.

Detector: ILD for ILC

FTF BIC QGSP BERT

particle

energy 10 GeV 30 GeV 10 GeV 30 GeV

E_rec E_rec E_rec E_rec

e− 14.42±0.01 GeV 43.57±0.03 GeV 14.43±0.01 GeV 43.59±0.03 GeV

π− 10.33±0.03 GeV 34.38±0.07 GeV 10.68±0.03 GeV 36.62±0.06 GeV e/π

ratio 1.396±0.004 1.267±0.003 1.351±0.004 1.190±0.001

almost unity for the hadronic physics model of QGSP BERT. Thus, the electromagnetic and hadronic response of the detector are nearly the same and nothing has to be corrected. For the hadronic model of FTF BIC the ratios are bigger, but still to small to expect that a large energy resolution improvement due to the usage of software compensation could be achieved. The simulation results for the tungsten calorimeter are quite surprising, since the geometry was not constructed in the view of compensation. There are two possible explanations for the result: Either the material and geometry of hadronic calorimeter of CLIC ILD gives indeed an

e/π ratio close to one and the calorimeter is self-compensating or the simulation of particles

in tungsten with Geant4 is not adequate. For clarification, the currently designed hadronic CALICE prototype with tungsten absorber layers is going through an extensive test beam campaign, which started in September 2010 at the CERN SPS. The data is currently analyzed and a simulation model is under construction. Once the test beam data is understood and the simulations are validated, thee/π ratio can be calculated for test beam data and simulation,

and decided, which hadronic model describes the data best.

The hadronic calorimeter of ILD shows ane/π ratio of around 1.2 – 1.4. This value is large

enough to assume that a software compensation algorithm could be used to improve the energy reconstruction.