Transcripción clase 2: 19 de Febrero de 2015

The raw information on energy deposition obtained from the Geant4 simulation

is digitized to include detector and electronic effects in several stages. This includes the conversion of the deposited energy to photon equivalents while taking the photon statistics of the scintillator with the attached SiPM into account. Another effect considered during the digitization is the correct modelling of the time distribution of the photon equivalents. However, the first step is the spatial conversion into T3B like tiles, together with the time partitioning into bins of 800 ps, modeling the accuracy of the used oscilloscopes.

Spatial and Time Partitioning

In the simulation the T3B layer is not divided into several tiles, but instead consists of a complete layer of scintillator material. Using the geometry information of the actual T3B layer with respect to the CALICE AHCAL, each simulation step is - based on its position - matched to one of the 15 30×30×5 mm3 _{scintillator tiles. If the hit was}

outside the T3B strip it is discarded.

The oscilloscopes used for the data acquisition have a sampling frequency of 1.25 GS/s corresponding to 800 ps. Hence, the simulation has to use the same binning. This is done by creating an array of hits similar to a histogram with a bin size of 800 ps for each tile position. Using the timestamp of the hit the correct bin of the histogram is identified, and the hit is added to it under consideration of its energy.

Scintillator Photon Conversion

The energy deposition of the simulation has to be converted into the same unit as the one used by the actual data, which is provided in terms of detected photons equivalents (p.e.).

As Birks’ Law was already applied in the Geant4 simulation, the number of

created photons scales linearly with the energy deposition and can be described by a single conversion coefficient cGeV,p.e..

However, the value of the conversion factor depends among other effects on the number of photons created in the scintillator, the distribution of these photons in the scintillator as well as the fill factor and quantum efficiency of the SiPM. Thus its determination is tedious and error prone. Instead the conversion is done by using the MIP energy scale as intermediate step. For this scale, both the number of detected photons and the deposited energy is known, as described in the following

The conversion factorcGeV,MIPresponsible for the conversion of the deposited energy

to the MIP scale, where 1 MIP is once more defined as the most probable value of the energy deposition distribution of a minimum ionizing particle, is determined by the simulation of muons. The fit on the resulting Landau distribution yields a value of

cGeV,MIP= 805 keV/MIP.

The second conversion factor for converting from the MIP scale to photon equivalents

probable value of the resulting Landau distribution defines the MIP scale and results in a conversion factor of cp.e.,MIP = 25 p.e./MIP. Note that this value is higher than the

17.8 p.e./MIP of the Time of first Hit which were presented in subsection 4.2.3, as the Time of first Hit is not defined over the entire time but over the shorter time window of 9.6 ns.

Following both steps, the energy conversion of the amplitudeA in a single T3B tile is done by: A[p.e.] =A[GeV]cp.e.,MIP p.e. MIP cGeV,MIP _GeV MIP Photon Statistics

A minimal ionizing particle passing through a T3B scintillator tile will create a few thousand photons. However, as stated in the previous section the average number of photons actually detected by the SiPM is only around 20. Consequently, the probability of detecting a photon is small and one cannot predict the exact number of photons that will be detected, even if the amount of created photons is known. This is a typical example for a Poissonian distribution.

During the digitization, the original amplitude Araw is corrected for this photon

statistic process. As the amplitude is given in units of photons equivalents, the first step is to round its value to the nearest integer. In the next step a Poissonian distribution with the resulting amplitude Araw as mean is created. By using this distribution as

a probability density function, one single random integer number is generated. This number is the new amplitudeAdigi.

Trigger Jitter and SiPM Afterpulsing

Within the simulation the time scale is well defined. The particle is created at the same location with the same momentum at the exact same point in time. At the testbeam, however, are a set of different contributions that have negative impact on the detector resolution. Most of these effects were already discussed in the context of the Time of first Hit in subsection 4.2.6. With the exception of the time slewing due to different amplitudes, a feature unique to the Time of first Hit and thus not affecting the resolution of single p.e., all these effects have to be applied on the simulation, as well. This is true for SiPM specific features, especially the afterpulsing, as well.

Both the time smearing and the afterpulsing effects can be seen in Figure 4.15, which shows the sum of 1 p.e.hit histograms of a 180 GeV muon run. As muons should deposit their energy instantaneously without any late components, the tail of the distribution shows the effect of afterpulsing. Around the peak the distribution is shaped like a Gaussian, which is the time jitter of the detector.

In order to correctly mimic these effects in the digitization, each photon equivalent is smeared according to this muon distribution. The result is a 1 p.e. hit histogram which is very close to the one originating from real testbeam data.

Time of 1p.e. Hit [ns] 0 50 100 150 200 250 Normalized Entries / 100ps -4 10 -3 10 -2 10 -1 10 180 GeV µ

central Tile only

Sum of all 1p.e. Hits of all Events

Figure 4.15: Sum of all 1p.e. hit histograms for a muon. Histogram is normalized to number of entries = 1.