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

Appendix DComparison of CNGS Tracks inBorexino and OPERAAs described in Section 5.5, a comparison of muons originating from the CNGSbeam that have crossed both the Borexino and the OPERA detector has been done.This section summarizes the necessary coordinate transformations for this task.BorexinoOPERAz bxy opx opx bxy bxCNGSz opFigure D.1: Relative coordinate systems of Borexino and OPERABoth the Borexino and OPERA coordinate systems are shown in Fig. D.1. Sincethe muon tracks are to be compared within Borexino, the Borexino coordinate systemis taken as the reference system. Assume, the offset between both detectors is∆x, ∆y and ∆z in the Borexino system, the transformation is trivial:x = x bx = ∆x − z op ,y = y bx = ∆y − x op ,z = z bx = ∆z + y op .For each muon track, OPERA provides five parameters: one slope and the accordingz-intercept for each the x −z and the y −z plane: s x , x op,0 , s y and y op,0 respectivelyas well as the inverse momentum 1 p . The z-intercept is not given for z op = 0, instead107