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

N [a.u.]∆ α (x)2200020000da0Entries 88028Mean −0.000274818000RMS 0.0933516000const 1393 ±4.814000σ 0.004899 ±0.00000012000lg 0.03125 ±0.000171000080006000∆ α0.0003038±0.0000997400020000−1.5 −1 −0.5 0 0.5 1 1.5∆αFigure 3.11: Angular alignment of the CMT. The plot shows the comparison of theHesse parameter α for a single reconstruction of tracks in each of the two modules inthe x−z-plane without any prior calibration. The distribution is fitted with a Voigtian(red). The mean value as well as the mean from the fit show a good angular alignmentof the order of 0.3mrad.After the angular correction has been implemented, a possible translation of themodules is investigated. It is assumed that the position of module 1 is shifted by∆ξ in ξ and ∆ζ in ζ with respect to the true position. This shift is thus describedas a shift of the assumed coordinate system ξ ′ − ζ ′ of module 1 with:ξ ′ = ξ + ∆ξζ ′ = ζ + ∆ζ.Comparing the same muon track in both modules leads toξ cos α 0 + ζ sin α 0 − p 0 = ξ ′ cos α 1 + ζ ′ sin α 1 − p 1 ,and thus, assuming that α 0 and α 1 are equal, to∆p = ∆ξ cos α + ∆ζ sin α. (3.22)In reality α 0 and α 1 do not obtain the same value from the single fit. To obtaincomparable tracks, the reconstruction is redone for the second plane with a fixedparameter α = α 0 , leaving only one free parameter p 1 .∆p = p 1 − p 0 can now be determined from the single module reconstruction.Obtaining enough statistics allows to do a fit with free parameters ∆ξ and ∆ζ. Theoffset values found using this method are subtracted from the initial wire coordinatesand the new positions are again stored in TAlign. An exemplary fit for real data isshown in Fig. 3.15 in Section 3.8.2.3.6.2 Wire AlignmentOnce the relative position of the modules is determined, the alignment is continuedfor the single anode wires. The reconstructed data from the full 2D-planes of the42