R AAHF ±
4.6 Run Selection and Performance Stability
points of CNTs are utilized for this cut. Table 4.5 shows the cut parameters about the isolation cut. In order to take account of the asymmetric distributions, asymmetric cut parameter sets are employed. Since there are overlap regions between modules in the azimuthal direction, it requires that two hits are displaced more than twice of the readout pixel size or on the same modules.
cdphi [rad]
-0.2-4 -0.1 0.0 0.1 0.2 10
10-3
10-2
10-1
cdphi [rad]
-0.20 -0.1 0.0 0.1 0.2 1000
2000
Figure 4.13: Left: cdphi distributions of the electrons from π0 decays (red) and charm electrons (blue) 1.0< pT <1.25 GeV/cin a single-track simulation. Right: the distribution of the inclusive electrons in the data.
Table 4.5: Requirements of rejection by the isolation cut.
barrel requirement
B0 -0.05<cdphi<0.2∩ |dz|<0.3∩ (dr>0.01 ∪ |dz|>0.085 ∪ (on same module)) B1 -0.02<cdphi<0.1∩ |dz|<0.3∩ (dr>0.01 ∪ |dz|>0.085 ∪ (on same module)) B2 -0.03<cdphi<0.045 ∩ |dz|<0.5 ∩ (dr>0.016 ∪ |dz|>0.2∪ (on same module)) B3 -0.03<cdphi<0.03 ∩ |dz|<0.5∩ (dr>0.016 ∪ |dz|>0.2∪ (on same module))
Around 80% of the conversion electrons and the electrons from π0 decays are rejected by the isolation cut, whereas only 10% of the charm and bottom electrons are rejected, shown in Sec. 4.8.7. By using the cut, the fraction of the heavy-quark electrons in the inclusive electrons increases up to more than 50% atpT > 1 GeV/c.
The efficiency of the isolation cut and the fraction in the inclusive electrons of each electron source are described in Sec. 4.8.7 and 4.8.8.
some runs were failed to measure. As is explained at Sec. 4.4.4, the beam center is calculated with the collision vertices reconstructed by the stand-alone tracks, but only 1/3 of events can succeed to measure the vertex. Therefore, when the number of events in a run is small, the beam center can not be measured with a good precision.
Figure 4.14 shows widths of the distributions of the reconstructed collision vertices.
The width is calculated by fitting the distribution with a Gaussian around the peak of the distribution. Only runs whose widths in the x and y directions are less than 300 µm are defined as good runs and the others are not used in this analysis.
run number
359 360 361 362 363
103
×
width [cm]
0.0 0.1 0.2 0.3
run number
359 360 361 362 363
103
×
width [cm]
0.0 0.1 0.2 0.3
Figure 4.14: Widths of the distribution of the reconstructed collision vertices inx (left) andy (right) directions.
4.6.2 Performance Stability
A DCA distribution and a survival fraction after the isolation cut for each of the good runs are checked. The DCA distribution in the data is necessary to be understand well in order to simulate the distributions of all electron sources. The survival fraction in the data is also necessary to be understand well since it affects yield of each electron source after the isolation cut. Therefore, a run which has a strange DCA distribution or a strange survival fraction can disturb the final result. Figure 4.16 shows mean values and widths of the DCA distribution of charged tracks withpT >1 GeV/c. The mean and width were calculated by fitting the DCA distribution with a Gaussian.
The mean should be independent of runs, and all the good runs satisfies following:
|m(run)−m|<3σm(run) + 5 [µm], (4.32) where m(run) and σm(run) are the mean and the fitting error for the mean of a run, and m is the mean of m(run) calculated by fitting with a constant. m is -17 µm. The mean is shifted from 0 since the reconstructed pT of a CNT is smaller
of the reconstructed path becomes larger than that of the actual path, and thus, the collision vertex tends to be outside of a circle of the reconstructed path, which means the DCA tends to be smaller than the actual DCA. Since the resolution of the DCA
Figure 4.15: An illustration of a reconstructed path and an actual path.
distribution is 130-140 µm, an effect of the deviation, 5 µm, is very small.
The widths slightly have a dependence on runs. Figure 4.17 shows the distribution of the widths. The red line is a fitting result by a Gaussian and 1σ of the Gaussian is around 8µm. The beam size changed from 120µm to 130 µm during a beam fill.
The variation of the widths can almost be explained by the variation of the beam size.
The ratio of the entries at a tail and peak regions of hadron DCA distribution is also checked. The ratio is very important for this analysis. The tail region is defined as |DCA| > 800 µm and the peak region is defined as |DCA| < 500 µm. The left panel in Fig. 4.18 shows the ratio of each run. Associated error bars correspond to statistical errors. The errors are calculated by assuming both the entries distribute independent normal distributions. The ratios are fitted by a constant and the fitting result is defined as a center value. The right panel in Fig. 4.18 shows a distribution
run number
359 360 361 362 363
103
×
DCA mean [cm]
-0.010 -0.005 0.000 0.005 0.010
run number
359 360 361 362 363
103
×
DCA sigma [cm]
0.00 0.01 0.02 0.03
Figure 4.16: Means (left) and widths (right) of DCA distributions of charged tracks for good runs.
of differences between the ratios and the center value normalized by their statistical errors. All of the normalized differences are within±3.
The survival fraction of charged tracks withpT > 1 GeV/cafter the isolation cut is calculated for each run. The left panel in Fig. 4.19 shows the fraction of each run.
Associated error bars correspond to statistical errors. The errors are calculated by assuming the distribution of the fraction is a binomial distribution. The fractions are fitted by a constant and the fitting result is defined as a center value. The right panel in Fig. 4.19 shows a distribution of differences between the fractions and the center value normalized by their statistical errors. Almost all of the normalized differences are within ±3.
4.6.3 DCA Distribution of Inclusive Electron
Figure 4.20 shows DCA distributions of inclusive electrons and hadrons forpT > 1.5 GeV/c.
The red and black lines show the distributions of electrons and hadrons. Mean and width values are different between the distributions. When the distributions are fitted by Gaussians, and their mean and width values are defined as the mean and RMS values of the Gaussians, the mean and width of electrons are -29.6 ± 1.5 µm and 149.4 ±1.3 µm and those of hadrons are -12.2 ± 0.1µm and 135.1 ± 0.1 µm. The difference of the mean values is derived from a difference of energy losses at VTX between electrons and pions, which is main component of hadrons. Since the main component of the inclusive electrons is the charm electrons, whereas, the main com-ponent of the inclusive hadrons is pions which are produced by beam collisions or decays of short-life hadrons, such as ρ or ω. Therefore, the width of the inclusive electrons is larger than that of the inclusive hadrons.
/ ndf
χ2 10.04 / 16
Constant 47.54 ± 3.33 Mean 0.01377 ± 0.00005 Sigma 0.000767 ± 0.000033
DCA sigma [cm]
0.00 0 0.01 0.02 0.03
20 40
/ ndf
χ2 10.04 / 16
Constant 47.54 ± 3.33 Mean 0.01377 ± 0.00005 Sigma 0.000767 ± 0.000033
Figure 4.17: Distribution of widths of DCA distributions of runs.
positrons. The right panel of Fig. 4.21 shows a ratio of the DCA distributions as a function of DCA. The ratio is fitted by a constant and the red line in the panel shows the result. χ2/NDF is good and the ratio is well approximated by a constant.
Therefore, there is not a clear difference between DCA distributions of electrons and positrons, and they can be handled together. The fitting result is not 1 since reconstruction efficiencies, especially detector acceptance, are different.