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

Table 3.5: List of variables calculated for each tangentvariablen cn mn rn tχ 2 plαpdefinitionNumber of common hitsNumber of missing hitsNumber of hits with residual below a certain thresholdNumber of tubes passed by tangentSum of quadratic residualsThe lever arm between the reference tubes1 st Hesse parameter of track2 nd Hesse parameter of trackfind the muon track, a list of variables shown in Tab. 3.5 is determined for eachinvestigated tangent. To be identified as a track, the tangent has to fulfill thefollowing constraints:n r ≥ 3n t ≥ 3n rn t≥ 0.75.If more than one tangent fulfills these requirements, the one with the smallestχ 2 p /(n r − 2) and the smallest n m is chosen. Once the pattern has been recognized,the track is fitted, if n c reaches a minimal number of hits which is set to n c,min = 4by default.3.5.6 Track FitThe track fit is done via a χ 2 minimization. The χ 2 of a track is given by thesum of its quadratic residuals δ, which are given for each hit by the differencebetween the measured drift radius r and the calculated track distance to the wire d:δ = r(t c ) − d(α,p), weighted by the resolution σ:χ 2 =N∑δ 2 iσ 2 i=1 iN∑ (r i − |ξ i cos α + ζ i sinα − p|) 2=. (3.5)i=1σ 2 iξ i and ζ i are the corresponding wire coordinates in the 2D-plane of each hit. All Nhits identified by the pattern recognition are taken into account. To determine theminimal χ 2 , the parameters α and p are combined to a vector ⃗q:( α⃗q = .p)For a minimum, one can thus demand:∂χ 2∂⃗q= 0. (3.6)38