Section 4.3.6 showed all the required steps needed to correct the deposited energy in the PSD layers in MC due to a different energy loss observed for data. The reason of this difference was understood in terms of the position along the z axis of the primary particle interaction in DAMPE.
4.6.1 Selecting different samples in DAMPE
We selected two samples using the same cuts listed in section 4.3 but with a different trigger requirement. For one sample we ask the activation of the standard high energy trigger (HET) and for the second sample it is required the MIP trigger (at least one of the two MIP triggers) excluding the HET. The MC has access to all the information regarding the original simulated particle, also where it interacts (or “stops”) in DAMPE.
The distributions of the stop coordinate along z for the two samples are illustrated in Fig. 4.56 for several ranges of the true energy of the particle. One can notice the structure
h_StopZ_enebin_26 Entries 24331 Mean 3.138 Entries 24331 Mean 3.138 RMS 100.3 < 2371.37 GeV
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h_StopZ_enebin_38 Entries 11860 Mean 52.58
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p MC HET
Figure 4.56: Distributions of the z coordinate of the interaction relative to the primary proton particle in DAMPE. The distributions are shown for various true energy bins and for the two different MC samples considered: one requiring the HET (blue), one the MIP trigger (red), vetoing the activation of the HET. The statistics box relative to the MIP sample is also displayed.
of DAMPE from the HET distribution: the two first peaks at≈ -300 mm are relative to the two layers of the PSD, the 6 peaks after to the 6 points measured by the STK and after z = 0 the BGO. The particles selected with the HET interact also before the BGO and these can produce secondary particles (backsplash) closer to the PSD. The
CHAPTER 4. MEASUREMENT OF THE PROTON FLUX
MIP trigger aims to select also particles that do not interact with DAMPE, however the percentage of non interacting protons remains very low (it is only of few percent above 50 TeV in true particle energy) and it can be used to select a sample interacting only in the BGO. For the MIP sample it is possible to perform the same study on the PSD as illustrated in section 4.3.5 regarding the charge selection, looking at the PSDglobal variable, but without the use of a PSD correction in MC in this case. We fitted the PSDglobaldistributions with a Landau function in several energy bins and some example fits for proton MC and data are shown in Fig. 4.57. The black dashed line in Fig. 4.57 represents the chosen cut for the proton selection. The MPV and the width of the fits are shown in Fig. 4.58 as function of the energy, with a fit on the MC MPV and width.
The fit curve for the MPV in MC is called fselMIP and it is used to parametrize the
/ ndf
Figure 4.57: Fits for two energy ranges with a Landau function on the global PSD measurement for the MIP sample for data (left, with a red fit) and proton MC (right, with a blue fit). The charge selection cut values are depicted with a black dashed line.
charge cut for protons, asking:
PSDglobal <(fselMIP(Erec) + 0.5). (4.26) In this case the MC seems to reproduce much better the data and allows a proton se-lection without a PSD smear. However the MIP trigger data is prescaled by four in the latitude range [-20◦, 20◦] and for higher latitudes it is disabled so 28 months of statis-tics in data are not enough to parametrize well the PSDglobal distribution after 10 TeV.
Nevertheless it allows to be sensitive to the different interactions that the two samples undergo in DAMPE through the ratio NMIP(Erec)/NHET(Erec), where NMIP(Erec) is the
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Energy [GeV]
Figure 4.58: MPV (left) and width (right) of the Landau fit performed on the reconstructed charge in PSD trough PSDglobalfor the MIP proton sample. The MC MPV and width are fitted with a log polynomial function of order four.
number of proton events that are selected from the MIP sample (assuming a negligible helium background) and NHET(Erec) is the number of protons that are selected with the usual HET (with the helium background subtracted), both at a particular recon-structed energy Erec. The distribution of NMIP(Erec)/NHET(Erec) as a function of the reconstructed energy and the difference observed between data and proton MC is shown in Fig. 4.59. At∼100 GeV data and MC seems to deviate of a maximum of 6%. After it
Energy [GeV]
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Figure 4.59: Top: ratio between the number of selected MIP protons and HET protons in data (red) and in proton MC (blue) as a function of the energy. Bottom: difference in the ratio as a function of the reconstructed energy in the BGO.
CHAPTER 4. MEASUREMENT OF THE PROTON FLUX
is difficult to quantify the disagreement since the statistical uncertainty in the data even in four bins per decade are too big. It is difficult to translate this difference in a sys-tematic error on the modeling of the interaction in DAMPE. It is given in reconstructed energy and we do not know if there is a direct connection between this difference and the measured proton flux. However, an analysis based on the MIP trigger can help in this direction.
4.6.2 Cross-check with a parallel proton flux analysis
Requiring the activation of the MIP trigger, but vetoing the HET reduces way too much the statistics available to estimate the systematic error due to the different inter-actions. But assuming that the proton flux is isotropic at the studied energies, the data in the latitude range [-20◦, 20◦] allows us to perform a nearly independent proton flux measurement. In this case in Eq. 4.1 ∆T is 1.138·107 s, equivalent to 131 days. We decided to perform an analysis using the MIP trigger in a less tight way, applying the cuts described in section 4.3, changing only partially the cuts of group 4. We require at this stage:
• the activation of at least one of the MIP triggers (we will refer to the MIP trigger sample for simplicity, as in the previous section);
• the first-point STK cluster charge measured by the tracker is asked to be less than 600 ADC to reduce the contribution of|Z|higher than 2 particles;
• to use the combined information of longitudinal and transversal shower shape (same cut as with the HET sample usingζ) in order to remove the electron com-ponent in cosmic rays;
• select the proton sample as function of energy.
Like in section 4.3.6, a correction between proton MC and data in the PSD energy deposition has to be performed but the difference in the MPV and in the width of the Landau fit is lower than in the HET sample (for example at 1.7 TeV in reconstructed energy DiffMPV(MIP)∼1%, DiffMPV(HET)∼6%). Results of this smear and the charge selection adopted in this case are available in section B.3. Fig. 4.60 shows the acceptances as a function of the true energy of the particle for the two studied samples at each cut after the trigger requirement. One can notice that requiring the HET reduces of∼1/3 the effective acceptance at lower energy, for higher energies this reduction decreases but the acceptance seems not to reach any plateau. The MIP sample, not vetoing the activation of the HET, still shows a dependence of the energy when we select the proton sample. This is as expected looking at the templates fits in Fig. B.17, since the proton selection is done to reduce the helium contamination (the high energy trigger efficiency for helium is higher with respect to protons [96]). However the final acceptance goes more in a less energy dependent direction with respect to the HET sample. The events selected, after background subtraction, are shown on the left part of Fig. 4.61, whereas the migration matrix for the selected events is shown on the right part. The
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sr]×2Effective Acceptance [m
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rec)
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Figure 4.60: Effective acceptance of the cuts of group 4 for MC protons of the HET sample (left) and the MIP sample (right).
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