Setup of a Drift Tube Muon Tracker and Calibration of Muon ...

χ 2N [a.u.]Probability103×10hc2p0Entries 242297Mean 0.4942RMS 0.3255χ 2N [a.u.]per d.o.f.22203×10hc2ndf0Entries 242297Mean 1.134RMS 1.02481816614121048624200 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1P(χ 2 )00 2 4 6 8 10 12χ 2 /dofFigure 3.16: The fit quality is checked by a look at the χ 2 distributions. Left: theχ 2 -probability shows a flat distribution as expected, with only a slight rise in the sideregions. Right: the χ 2 per degrees of freedom has a mean value close to 1.calibration was performed. Altogether 182728 events could be reconstructed. Theangular distributions of reconstructed tracks were already presented in Fig. 3.14.They show the expected behavior. The quality of the reconstruction was checked aspresented in the following section.3.8.3 Fit QualityAs described in Section 3.5.6, the track fit is done using a χ 2 -minimization. Thequality of the fit can be controlled by inspecting the distribution of χ 2 per degrees offreedom. The mean value of this χ 2 -distribution should be close to 1. Also, the χ 2 -probability can be used to investigate the fit quality. For a given number of degreesof freedom and a given χ 2 , the probability can be calculated, their distributionshould be homogeneous between 0 and 1. Fig. 3.16 shows the χ 2 -distribution andthe χ 2 /dof for real data. The χ 2 -distribution shows the desired behavior exceptfor the side regions. The excesses at zero and one can be explained by tracks thatwere reconstructed wrongly. This can be either due to a wrong pattern recognition(excess at zero) or a too good fit on fake drift circles, e.g. from δ electrons or crosstalk (excess at one). However, the mean value of χ 2 /dof shows the expected meanvalue around 1.If statistics are high enough, the calculated drift distances to the fitted trackshould be distributed homogeneously between 0 and the tube radius (18.15 mm).Fig. 3.17 shows this distribution. Besides a small discrepancy for very small driftcircles it is in good agreement with the expectation. This can be easily understoodby looking again at the TDC count to distance relation. For small drift distances,the TDC count to distance relation rises very steeply, meaning that a small deviationin the drift time has a large effect on the drift radius. Hence, small uncertaintiesoccur in this region. Since no negative drift distance can occur, the drift distanceis much likely to be overestimated in this region. This can be recognized by the48