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

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

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All tracks from OD fith5All tracks from OD fith6N [arbitrary units]605040Entries 2192Mean -0.4299RMS 3.716c 363.5 ± 9.5mean -0.2555 ± 0.0776σ 2.877 ± 0.082N [arbitrary units]4540353025Entries 2192Mean -0.7274RMS 4.585c 410.1 ± 10.2mean -0.9334 ± 0.1172σ 4.486 ± 0.10230202015101050-10 -5 0 5 10∆θ [°]0-10 -5 0 5 10∆ϕ [°]Figure 5.26: Polar <strong>and</strong> azimuth angle differences for muon tracks reconstructed inboth OPERA <strong>and</strong> BorexinoTable 5.7: Borexino muon tracking resolution determined by the comparison withOPERA rock muonsAngle σ [ ◦ ] (OD) σ [ ◦ ] (ID) σ [ ◦ ] (GL)θ 2.88 ± 0.08 4.86 ± 0.16 3.01 ± 0.12ϕ 4.49 ± 0.10 4.76 ± 0.14 4.11 ± 0.10α 3.75 ± 0.02 3.70 ± 0.04 2.63 ± 0.02coordinate system. For a detailed description <strong>of</strong> the coordinate transformation seeAppendix D.5.5.1 Direct Angular ComparisonFor a direct comparison <strong>of</strong> the tracks reconstructed by Borexino <strong>and</strong> OPERA for thesame muon, the azimuth <strong>and</strong> polar angles ϕ <strong>and</strong> θ are obtained for all trackings. Thedistribution <strong>of</strong> differences between the corresponding angles is shown in Fig. 5.26exemplarily for the OD tracking. Performing a Gaussian fit gives a measure forthe angular resolution <strong>of</strong> the Borexino reconstruction. The results are presented inTab. 5.7. This shows excellent values for θ, however, the resolution <strong>of</strong> ϕ is ratherpoor. This can be explained by the method how ϕ is determined in Borexino: muontracks are determined by their entry <strong>and</strong> exit points to the detector. Since thedetector is spherical, small uncertainties in the determination <strong>of</strong> these points leadto large uncertainties in ϕ around the poles. This could be accounted for e.g. bylooking at a θ-dependency <strong>of</strong> σ ϕ .However, another analysis is chosen; the absolute angle α between both tracks ⃗tis determined. This can be done as follows:⃗t bx ·⃗t op = |⃗t bx ||⃗t op |cos α⇔α = cos −1 (sin θ bx sin θ op (cos ϕ bx cos ϕ op + sin ϕ bx sin ϕ op ) + cos θ bx cos θ op )93

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