10. Bibliografía
11.1.4. Transcripción clase 4: 26 de Febrero de 2015
Assuming a radial symmetry of the hadronic cascades, the development of the average hadronic shower can be reconstructed by combining the shower start information with the T3B measurements. Hence, the time evolution of complete calorimeter profiles can be reconstructed. Here we focus on the comparison of the shower profiles of the instantaneous energy depositions with the intermediate and late depositions, as well as their reproduction by the simulation with various physics lists.
Reconstruction of the Calorimeter Profile
The longitudinal calorimeter profile gives the typical energy deposition in the different layers of the calorimeter, obtained by repeatedly measuring the response to a certain particle type at the same energy.
Contrary to that a longitudinalshower profile gives the typical response of the same calorimeter to the same particles, but measured with respect to the shower starting point. Assuming that all particles would start their shower in the first layer of the calorimeter, the shower profile and the calorimeter profile would be identical. However, hadronic interactions and as such the first hard interaction are statistical processes, and therefore the shower profile can only be measured if the shower starting point is known.
] I λ
Distance from Shower Start [
1 2 3 4 5
Mean time of First Hit [ns]
2 3 4 5 6 7 QBBC QGSP_BERT QGSP_BERT_HP data 60 GeV + π Radius: 4.7 cm to 20.1 cm
(a) Intermediate Shower Region
]
I
λ
Distance from Shower Start [
1 2 3 4 5
Mean time of First Hit [ns]
6 8 10 12 14 16 QBBC QGSP_BERT QGSP_BERT_HP data 60 GeV + π Radius: 20.2 cm to 38.7 cm
(b) Outer Shower Region
Figure 4.21: Changes of the Mean Time of first Hit over the distance from the shower starting position for the intermediate (upper plot) and the outer region (lower plot) of the shower radius.
With the help of the shower start finder algorithms the shower profile can even be reconstructed with only the T3B layer at hand. This is done by first filling a histogram with the distance between the shower starting layer in the CALICE W-AHCal and the T3B layer, weighted with the amplitude of the deposited energy in T3B. In this step the geometry of the single T3B strip is taken into account by scaling the energy deposition of the Time of first Hits according to geometrical coverage, as explained in subsection 4.2.5. As the shower starting position changes from event to event, the T3B layer samples the entire shower layer by layer. However, this implicitly assumes that the shower start is equally distributed over all W-AHCal layers, which it is not. Instead it falls exponentially with higher layer numbers, i.e. deeper shower starting positions. Therefore each layer of the histogram needs to be reweighted with the number of events having a shower start in that layer.
The shower profile and the shower start profile can be used to reconstruct the calorimeter profile. This is possible as the calorimeter profile is essentially just an overlay of several shower profiles which start in different depth of the calorimeter, each at a different rate.
The principle is explained with an imaginary 10 layer calorimeter in Figure 4.22. The upper plot (Figure 4.22(a)) shows the resulting shower start profile where each layer is assigned its unique color. As one can see, the shower start distribution falls with an exponential with negative exponent. The shower profile, as it can be reconstructed with the T3B layer, is shown in dark red in Figure 4.22(b), already weighted with the rate of a shower start in layer 1. Subsequently the green histogram again is the shower profile, but with a shower start not in layer 1, but in layer 2, once more weighted with the rate of shower starts in layer 2 and stacked on top of the distribution for layer 1. By adding up the shower profiles weighted with the rate of shower starts, the resulting overall shape gives the calorimeter profile.
Smearing of the Calorimeter Profile by the Limited Shower Start Identifi- cation Resolution
When reconstructing the calorimeter profile, the shower start profile is essential to correctly weight the individual shower profiles to the correct number of events. The shower start identification algorithms, however, have a limited resolution in the order of
σ = 2 layers. To study the effect on the resulting calorimeter profile of such a smearing, a simulation of a 60 GeV π+was created using the QBBCphysics list. To be independent
of detector effects, the pure undigitized data as it is created by Geant4 is used as a
input.
Figure 4.23 shows the calorimeter profiles. The one in red is obtained from the full information of all active detector layers and acts as a reference here. Below that there are three versions of a reconstructed calorimeter profile, obtained with the technique discussed above.
The difference between the three profiles, shown here in blue, green and black, is the resolution of the used shower start finder. The blue version has a resolution of
σ = 0 layers, which is identical to knowing the exact shower start position. Thus the shape is identical to the real shower profile obtained from the full detector information.
Calorimeter Depth [Layer]
0 2 4 6 8 10
# Entries [a.u.]
1
(a) Shower Start Profile
Calorimeter Depth [Layer]
0 2 4 6 8 10
Deposited Energy [a.u.]
0 0.5 1 1.5
2
(b) Calorimeter Profile as a Set of Stacked Shower Profiles
Figure 4.22: The principle on how the calorimeter profile (overall shape, lower picture) can be built from the shower profile (dark red, lower picture) and the shower start profile (upper picture). For details please refer to the text.
] I λ Calorimeter Depth [ 0 1 2 3 4 I λ
Energy [MeV] / Event / 0.13
0 20 40 60 60 GeV + π Calorimeter Profile
Full Detector Undigitized QBBC = 0.0 layer σ T3B Undigitized QBBC - = 1.0 layer σ T3B Undigitized QBBC - = 2.0 layer σ T3B Undigitized QBBC - T3B Reconstructed data
Figure 4.23: The calorimeter profile for a CALICE W-AHCal like detector, obtained from pure simulation without digitization of 60 GeV π+. The calorimeter profile is once
taken from all active layers, and three times reconstructed from the last layer using the shower start profile for reconstruction. The shower start profile has been smeared by Gaussian with a σ of 0, 1 or 2 detector layers.
The differences in the amount of deposited energy originates most likely from the different sensitivity of T3B and W-AHCal calorimeter layers, caused by differences in the geometrical structure and used materials in the cassettes. For green and black profiles the shower start finder has a Gaussian resolution of σ= 1 layer andσ = 2 layers respectively. One can see that the deterioration in the shower start identification resolution leads to a shift of the calorimeter profile peak towards the back of the calorimeter. Furthermore it leads to a downshift of the peak height.
Both effects can easily be explained when considering the effect of the smearing on the shower start distribution. Through the smearing an event with a shower start in layer N might be shifted downwards or upwards at the same probability. However, the shower start distribution itself is described by a falling exponential, i.e. the number of events with an early shower start is higher than the number of events with a late shower start. Hence by the smearing the average starting position is shifted downwards to the end of the calorimeter, and thus overestimating the number of events with an shower start there. As the peak of the real calorimeter profile is not at the beginning of the calorimeter, but after about 0.8λI, the number of events with a shower start at
that position is overestimated by the smearing, and thus weighted down.
For comparison Figure 4.23 also includes the fully reconstructed TofH-based T3B test- beam data in cyan. Its calorimeter profile is quite close to the black curve of undigitized simulated data with a Gaussian shower start resolution of σ= 2 layers. Therefore for all analysis presented in this thesis an Gaussian resolution of σ = 2 layers is assumed
for the shower start in simulated data (cf. section 4.3.1).
In the following, however, we will concentrate on the overall shape of the profiles. Thus the reduced height of the profile has no influence. Only the shift of the peak towards the end of the calorimeter introduces a systematic offset of about 0.3λI.
The Longitudinal Shower Profile
Using the technique described above, the shower profile of a 60 GeV π+was generated
for different time ranges. These were chosen to be sensitive to the three different contributions to the time structure of hadronic showers.
• 0−2.4 ns: The near instantaneous part caused by electromagnetic subshowers, strong hadronic interactions and intra-nuclear cascades.
• 2.4−16 ns: Intermediate part, caused mainly by neutron elastic scattering.
• 16−250 ns: Slow component. After the neutrons lost their energy through elastic scattering, they might be captured by a nucleus. The binding energy released by this neutron capture excites the nucleus, which then in turn emits detectable photons.
The resulting shower profile is shown twice in Figure 4.24. In the upper plot the profiles of the individual time ranges are stacked on top of each other, such that the overall shape is the sum of all time regions and as such the profile as seen by a real calorimeter. The profiles are displayed with their absolute energy deposition in terms of MIP per calorimeter layer. The lower plot is a copy of the one above, but the plots of the time ranges are normalized to individually give their relative energy deposition fraction per calorimeter layer, in order to be able to better compare their shape.
One thing that immediately stands out is the domination of the energy depositions within the first 2.4 ns, which is almost exclusively responsible for the overall shower shape. This is in agreement with the time development of the total energy deposition fraction, discussed in subsection 4.4.2.
In addition, the shape of the instantaneous part is characterized by a faster rise, with a peak after already around 0.3λI, whereas the intermediate and the slow component
both have their peak only at around 0.6λI. This behaviour is caused by the dense
but range limited electromagnetic part of the shower, which mainly contributes to the instantaneous shower component.
Based on the shower profiles, the calorimeter profile can be constructed. In this process the statistical fluctuations seen in the shower profiles are washed out by their repeated overlay.
Differences with respect to the shower radius are shown by splitting the longitudinal calorimeter profile into three regions:
• The central part consisting of the two inner most tiles, covering −1.5−4.6 cm.
] I λ Shower Depth [ 0 1 2 3 4 I λ
Energy Deposition [MIP] / 0.129
-3 10 -2 10 -1 10 1 10 2 10 3 10 0.0 ns to 2.4 ns 2.4 ns to 16.0 ns 16.0 ns to 250.0 ns Shower Profile 60 GeV data Radius [cm]: -1.5 to 41.8 ] I λ Shower Depth [ 0 1 2 3 4 I λ
Energy Deposition Fraction / 0.129
0 0.02 0.04 0.06 0.08 0.1 0.0 ns to 2.4 ns 2.4 ns to 16.0 ns 16.0 ns to 250.0 ns Shower Profile 60 GeV data Radius [cm]: -1.5 to 41.8
Figure 4.24: The shower profile for 60 GeVπ+ data, split into different times. In the
upper plot the three parts are shown in terms of their total energy deposition of MIP per layer, stacked on top of each other to get the total shower profile. In the lower plot the same distributions are shown, but scaled to the relative energy deposition fraction per layer, acting as a shape comparison.
• The outer part with the tiles 8 to 15, covering 20.2−41.8 cm.
The distribution of the three radial regions ranges again split into the same three time ranges introduced above are shown in Figure 4.25. The normalization is again that each profile sums up to 1, i.e. it shows the relative energy deposition per layer within the specific time and radial range.
For high shower radii, there are no statistically significant differences in the calorime- ter profile for the three different time ranges. They all tend to peak around 1.7λI. For
the intermediate and the slow time region there is a slight tendency for the peak to wander to the back of the calorimeter when moving from the outer shower radius to the center. However, there is a significant change in the shape of the instantaneous part, where the peak moves forward to be at around 1λI for the central part. This is a
clear sign of the electromagnetic sub-showers fraction, as electromagnetic showers tend to be very dense in the W-AHCal, as one calorimeter layer already has almost 3 X0.
] I λ Calorimeter Depth [ 0 1 2 3 4 I λ
Energy Deposition Fraction / 0.129
0 0.01 0.02 0.03 0.04 0.05 0.0 ns to 2.4 ns 2.4 ns to 16.0 ns 16.0 ns to 250.0 ns Calorimeter Profile 60 GeV data Radius [cm]: -1.5 to 4.6 ] I λ Calorimeter Depth [ 0 1 2 3 4 I λ
Energy Deposition Fraction / 0.129
0 0.01 0.02 0.03 0.04 0.0 ns to 2.4 ns 2.4 ns to 16.0 ns 16.0 ns to 250.0 ns Calorimeter Profile 60 GeV data Radius [cm]: 4.7 to 20.1 ] I λ Calorimeter Depth [ 0 1 2 3 4 I λ
Energy Deposition Fraction / 0.129
0 0.01 0.02 0.03 0.04 0.0 ns to 2.4 ns 2.4 ns to 16.0 ns 16.0 ns to 250.0 ns Calorimeter Profile 60 GeV data Radius [cm]: 20.2 to 41.8
Figure 4.25: Shape comparison of the longitudinal calorimeter profile for 60 GeVπ+
data split into different time ranges. The three plots show different segments of the shower radius.
] I λ Calorimeter Depth [ 0 1 2 3 4 I λ
Energy Deposition Fraction / 0.129
0 0.01 0.02 0.03 0.04 0.0 ns to 2.4 ns 2.4 ns to 16.0 ns 16.0 ns to 250.0 ns Calorimeter Profile 60 GeV data Radius [cm]: -1.5 to 41.8 ] I λ Calorimeter Depth [ 0 1 2 3 4 I λ
Energy Deposition [MIP] / 0.129
-4 10 -3 10 -2 10 -1 10 1 10 2 10 0.0 ns to 2.4 ns 2.4 ns to 16.0 ns 16.0 ns to 250.0 ns Calorimeter Profile 60 GeV data Radius [cm]: -1.5 to 41.8
Figure 4.26: Longitudinal calorimeter profile for 60 GeVπ+data split into different time
ranges. The upper plot shows the shapes for the different time ranges, while the lower plot shows the total calorimeter profiles, stacked with the individual time contributions.
range and not seen for large radii, where the shape is dominated by pure hadronic interactions.
Putting all three shower radii into a single plot gives the overall longitudinal shower profile, shown again twice in Figure 4.26. As before, the upper plot shows the calorimeter profile, normalized for the individual time ranges, while the lower plot is the result of stacking the three time components on top of each other.
One can see that the peak of the instantaneous part is slightly shifted to the calorimeter front with respect to the other two time ranges due to the electromagnetic subshower part.
Comparison to Simulation
A comparison of the calorimeter profile obtained from data with the ones from the simulation, based on the three different physics lists QGSP BERT, QGSP BERT HP and QBBC, is shown in Figure 4.27 for the entire radial extend of the shower. As before the statistical fluctuations of the shower profile are smeared out by its repeated overlay in the construction of the calorimeter profile and are thus only visible in the statistical
] I λ Calorimeter Depth [ 0 1 2 3 4 I λ
Energy Deposition [MIP] / 0.129
5 10 15 20 25 data QBBC QGSP_BERT_HP QGSP_BERT Calorimeter Profile + π 60 GeV 0.0 ns to 2.4 ns ] I λ Calorimeter Depth [ 0 1 2 3 4 I λ
Energy Deposition [MIP] / 0.129 1
2 3 4 data QBBC QGSP_BERT_HP QGSP_BERT Calorimeter Profile + π 60 GeV 2.4 ns to 16.0 ns ] I λ Calorimeter Depth [ 0 1 2 3 4 I λ
Energy Deposition [MIP] / 0.129
0.2 0.4 0.6 data QBBC QGSP_BERT_HP QGSP_BERT Calorimeter Profile + π 60 GeV 16.0 ns to 250.0 ns
Figure 4.27: Shape comparison of the longitudinal calorimeter profile for 60 GeVπ+
data split into different time ranges. The three plots show simulation with different physics lists for the three time ranges.
errors.
In the early time range of 0 ns to 2.4 ns, shown in the upper of the three plots in Figure 4.27, the agreement between the two physics simulations of QGSP BERT and
QGSP BERT HP is clearly within statistical limits while QBBC deposits about 3% more
energy in the central region of 1−2λI. Except for the first layers, the calorimeter profile
of the testbeam data lies above the simulation, depositing about 10% more energy than the two QGSP based simulations around the peak of the profile. However, the overall
shape of the calorimeter response is in good agreement for all four data sets.
In the central plot, showing the intermediate time range of 2.4 ns to 16 ns, the change of the peak towards the calorimeter rear is reproduced well by all physics list. However, small differences between the physics lists and the testbeam data start to occur in the shape, as the profile of the testbeam data has a steeper rise towards the peak around 2λI as well as a faster drop towards the end than all of the physics lists. However,
the total amount of deposited energy is well described by QGSP BERT HP in the first
≈ 0.5λI and around 3 to 4λI, while the peak around 1.5 to 3λI is best described by
QGSP BERT and QBBC.
For the late components of 16 ns to 250 ns, shown in the lower plot, the differences between all four data sets are most significant. While the rise in the deposited energy per layer up to 1λI is reproduced well by all physics lists, for the profile above 1λI
QGSP BERT andQBBC overestimate the detector response by about 0.12 MIP/layer and 0.07 MIP/layer respectively. At the same time their profile peaks at 2.3λI (QGSP BERT)
and 2.0λI (QBBC) respectively, which is considerably after the one of the testbeam data,
which peaks at 1.8λI. QGSP BERT HP, on the other hand, constantly underestimates
the detector response by up to 0.15 MIP/layer in the region around 1.5λI. However,
towards the calorimeter rear the overestimation falls and is less pronounced, such that it is almost within statistical limits around 4.9λI. As the other physics lists, the position
of the peak of the profile of QGSP BERT HPis shifted towards the calorimeter end (2.1λI).