The Li C Detector Toy M Valentan M

The Li. C Detector Toy M. Valentan, M. Regler, R. Frühwirth Austrian Academy of Sciences Institute of High Energy Physics, Vienna The MATLAB program allows a fast evaluation of the optimal resolution for charged particles with uncorrupted data. Detector inefficiency and multiple scattering are included. Detector surfaces can be cylinders or planes. Input Simulation Event loop Detector Description • Coaxial cylinders - Stereo angle - in T • PC z dependent Frame Detector 1 Detector 2 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 By default the event loop first generates a vertex (uniformly distributed in a certain range). However, the user can enter the vertex positions (x 0, y 0, z 0), provided by an arbitrary vertex generator. • Plane wheels Track loop - Coordinates defined by two angles Inner Tracker (IT) Number of layers Radii [mm] Upper limit in z [mm] Lower limit in z [mm] Efficiency Rphi Efficiency 2 nd layer (eg. z) Stereo angle alpha [Rad] Thickness [rad. lengths] error distribution 0 normal-sigma(RPhi) [1 e-6 m] sigma(z) [1 e-6 m] 1 uniform-d(RPhi) [1 e-6 m] d(z) [1 e-6 m] : 5 : : : 90, 160, 300, 340 110, -90, 360, 640, 2730 90, -110, -360, -640, -2730 0, 0, 0. 95, 0 -1, 0. 95, -1 10*pi/180 0. 07, 0. 0175, 0. 14 1 50 50 Momentum variables • Arbitrary size and position Track parameters , , (according to the chosen multiplicity). The state vector is propagated to the beam tube, where it is transformed to variables similar to the DELPHIconvention , z, , including spatial variables. • 2 D measurement - single and passive layers steered by inefficiency Multiple scattering takes place on every massive barrier, using independent normal distributed random quantities (according to the Highland formula). A local cartesian coordinate system is used with one axis tangent to the track. • Strips or pads Track simulation Simulation Parameters Number of events rsp. tracks Momentum and direction Vertex Simulation features Test features Output features The track model is a helix. Tracking includes multiple scattering. • Start parameters uniformly distributed in the defined ranges • Simulation features: Arbitrary inefficiency without spatial or angular dependence Strip detectors (single layer and double sided; inner layer with any stereo angle) Pixel detectors (by crossing 2 strip detectors with strictly correlated inefficiency) Coordinates - Multiple scattering - Measurement errors Measurement of R and z' (according to stereo angle chosen) Strips, Pads or normal distributed uncorrupted data only • Test features: - Pulls and MC-pulls - ² Simulation of digital and normal distributed errors. The z dependence in the TPC can be used as an example for a template. • Output features: - Histograms of pulls - Histograms of residuals - 6 D cartesian, Harvester Reconstruction Track fitting uses the Kalman filter, a recursive least-squares estimator. It proceeds from the outermost layer towards the beam tube. Track loop Initialization of the track parameters with large errors Detector loop Propagate track parameters, using a reference track and a linearized model Output Pull quantities Test statistics (sample log file, 10000 tracks) Monte-Carlo pulls Phi mean: -0. 0014137 std: 0. 99745 z -0. 020775 1. 0021 Pulls at innermost detector RPhi z mean: 0. 0085271 0. 0029371 std: 0. 99706 0. 998 Chi^2 ndf: mean: theta 0. 006437 0. 99926 u beta -0. 0035657 0. 99836 kappa -0. 0024358 0. 997 At the beam tube v R , z – barrel region u, v - forward region -0. 0095907 0. 0042998 1. 0031 1. 0088 Average number of degrees of freedom 21. 8725 21. 9226 Extrapolation Linear error propagation Add multiple scattering MC residuals (fitted - true) Barrel region Forward region Scale factor relative to the barrel region: 50 Compute weighted mean of extrapolated track parameters and measurement Update Compute local χ2 statistic and accumulate total χ2 10000 track with 0. 7454< 2. 3562 10000 track with 0. 49087< 0. 098175 Up: Monte-Carlo residuals at the beam tube, computed from generated and fitted state vectors Left: Relative deviation p. T/p. T Right: Relative deviation p. T/p. T 2 Store final track parameters, error matrix and total χ2 Scale factor relative to the barrel region: 100