R AAHF ±
4.10 Systematic Error Estimation
[GeV/c]
pT
1 2 3 4
10-4
10-3
10-2
Figure 4.56: The fraction of fake tracks in the inclusive electrons as a function of pT.
tracks in this thesis. The rotated fake tracks can not simulate the fake tracks com-pletely. A large part of the fake tracks are created with a correlated hit such as a hit created by a particle with the same mother. On the other hand, the rotated fake tracks can not simulate these correlated fake tracks. Therefore, it can only provide a rough estimation. Figure 4.57 shows the DCA distribution of the rotated fake tracks of all charged particles withpT > 1 GeV/c. The distribution is fitted by a Gaussian at |DCA| < 0.15 µm. The mean is +81.6 µm and RMS is 175 µm. Then, the Gaussian fittings are repeated by changing the fitting range and by fixing the mean of the Gaussian on +81.6µm, which is the result of the fitting at|DCA| < 0.15µm.
The results are summarized in Table 4.10. When the mean of the Gaussian is changed to±100 µm, the changes of the fitting results are within the errors. The DCA distri-bution of the fake tracks is approximated by a Gaussian. The RMS of the Gaussian is set to 250 µm. In addition, the RMS is changed from 150 to 650µm in systematic error evaluation, described in Sec. 4.10. The mean of the Gaussian is also changed to
±100 µm.
DCA [cm]
-0.1 0.0 0.1
0 10 20
Figure 4.57: The DCA distribution of the rotated fake tracks withpT > 1 GeV/c.
Table 4.10: The results of the Gaussian fitting of the DCA distribution of the rotated fake tracks.
fitting range RMS of the Gaussian -0.15 < DCA <0.15 cm 175 ± 15µm -0.15< DCA < -0.02 cm 381± 266µm
0.02 < DCA < 0.15 cm 207 ± 34µm
and the variations of fb are evaluated, which correspond to the 1st to 7th items.
The 8th item corresponds to the error for the efficiency of the isolation cut. The evaluations are performed about following items:
1. Yield of each electron sources: Yield ratios of all sources are shifted one by one.
The shifts are performed for ±1 σ in Fig. 4.44. The shift of the fake track contribution is in Fig. 4.56.
2. The mean of DCA distributions: The mean in simulations was shifted to repro-duce the DCA distribution of the data, as is explained at Sec. 4.9.1. Figure 4.48 shows the mean values of the DCA distributions of the data and the simula-tion. The mean values in the simulation successfully reproduce that of the data, and is changed ±10 µm in the study of the systematic error estimation. The mean values of all electrons are changed at the same time except for the hadron contamination, conversion electrons, and fake tracks, whose mean values are evaluated independently.
3. The DCA resolution: The starting point of tracks in simulations are smeared to reproduce the width of the data. As is shown in Fig. 4.47, the width of hadrons in the simulation well reproduces that of the data, and the difference is∼5 µm.
Therefore, the width in the simulation is changed ±5 µm. The widths of all electrons are changed at the same time except for the hadron contamination, conversion electrons, and fake tracks.
4. The DCA distribution of conversion electrons: The mean and width are changed.
As is discussed at Sec. 4.9.4, the distribution is approximated by a Gaussian and its mean and width are calculated by the fitting functions of Eq. 4.64 and 4.65. The parameters at these equations are changed ±1 σ in this study.
5. The DCA distribution of fake tracks: The total yield, mean, and width are changed.
5-1. Mean: changed ±100 µm.
5-2. RMS: changed to 200, 300, 400, 500, 600, and 700 µm and calculated the standard deviation.
6. The DCA distribution of heavy-quark electrons :
6-1. Particle ratios (D+/D0,Ds/D0, Λc/D0,B+/B0,Bs/B0, Λb/B0).
6-2. pT spectra of charm and bottom quarks.
6-3. Charm and bottom masses.
Table 4.11: Summary of systematic errors.
pT range (GeV/c) 1.5-2.0 2.0-2.5 2.5-3.0 3.0-4.0 4.0-5.0 1 < 1% < 1% <1% < 1% <1%
2 ±1% ±3% ±7% ±3% ±6%
3 ±39% ±20% ±18% ±24% ±14%
4 (mean) ±1% < 1% <1% < 1% <1%
4 (RMS) ±1% < 1% <1% < 1% <1%
5-1 < 1% < 1% <1% < 1% <1%
5-2 ±2% < 1% <1% < 1% <1%
6-1 (D+/D0) ±3% ±1% ±1% ±1% <1%
6-1 (Ds/D0) < 1% < 1% <1% < 1% <1%
6-1 (Λc/D0) < 1% < 1% <1% < 1% <1%
6-1 (B+/B0) < 1% < 1% <1% < 1% <1%
6-1 (Bs/B0) < 1% < 1% <1% < 1% <1%
6-1 (Λb/B0) ±4% ±4% ±4% ±5% ±5%
6-2 (charm) ±8% ±7% ±8% ±10% ±1%
6-2 (bottom) ±36% ±38% ±40% ±43% ±41%
6-3 (charm) < 1% < 1% <1% ±4% ±9%
6-3 (bottom) < 1% < 1% <1% < 1% ±1%
7 ±6% ±12% ±9% ±6% ± 4%
8 ±27% ±9% ±8% ±8% ±6%
total 66% 46% 48% 54% 48%
7. Fitting range: The default fitting range is |DCA| < 1.0 mm. In addition, the fittings with the ranges of ±0.75 mm and±1.25 mm are performed.
8. The error derived from the error ofriso is also quadratically added in the system-atic error.
The changes of the results by +1σ and -1σ shifts about all items except for the RMS of the DCA distribution of the fake tracks andpT spectra and masses of charm and bottom quarks, are averaged and the averages are assigned both positive and negative sides of the systematic error since the changes are symmetric. The averages are quadratically added in the systematic error. As for the RMS of the DCA distribution of the fake tracks, the changes are evaluated with 6 patterns and their standard deviation is added in the systematic error. As for pT spectra of charm and bottom quarks, two spectra are utilized for both charm and bottom, and the changes by the spectra which shiftpT spectra of quarks larger are assigned. As for the quark masses, both of the changes are assigned. Since the variation of the pT spectra and masses are limited, the same errors are assigned for both positive and negative sides.