1. The LiC Detector Toy 4 th SiLC Meeting Barcelona, 18 – 20 December 2006 The LiC Detector Toy A mini simulation and track fit program tool for fast and flexible detector optimization studies M. Regler, M. Valentan and R. Frühwirth Institute of High Energy Physics of the Austrian Academy of Sciences, Vienna

2. The LiC Detector Toy 4 th SiLC Meeting Barcelona, 18 – 20 December 2006 Abstract The “LiC Detector Toy” allows investigation of the track parameter resolution via Monte Carlo, for the purpose of optimizing a detector set-up. It features: Simulation of the track sensitive part of a ring or linear collider detector with a solenoid magnetic field, and its material budget; Support of measurements by semiconductor pixel and strip detectors, and a TPC; Track reconstruction by a Kalman filter, including tests of goodness of the fits. Written in MatLab ® (a language and IDE by MathWorks).

3. The LiC Detector Toy 4 th SiLC Meeting Barcelona, 18 – 20 December 2006 Motivation Compare track parameter resolutions of various detector set- ups, for both barrel and forward/backward regions; Optimize size and position of the track sensitive devices, and of the detector material budgets; A simple tool – easy to understand, handle and modify; Can easily be adapted to meet individual needs; Can be installed on a desktop or laptop PC; Quick results by “shorter than a coffee break”; Live demonstration at a conference possible; An integrated graphics user interface (GUI) available.

4. The LiC Detector Toy 4 th SiLC Meeting Barcelona, 18 – 20 December 2006 Program Features (general) Measurements by single or double layers, or by a TPC; Efficiencies uncorrelated (strips), or strictly correlated (pixels); passive layers defined by zero efficiency; Thickness of scatterers given in radiation lengths; Homogeneous magnetic field (by a solenoid), rotational symmetry w.r.t. the z-axis of the detector set-up; however, an asymmetry w.r.t. the z coordinate possible; Start parameters for simulated tracks are user-defined: –Vertex position range (on z-axis), –Transverse momentum range, –Range of polar angle θ, –Number of tracks from the vertex; Goodness of the fit monitored by pull quantities and χ².

5. The LiC Detector Toy 4 th SiLC Meeting Barcelona, 18 – 20 December 2006 Program Features (barrel region) Coaxial cylinder layers of arbitrary length and position; Any number of passive layers; Measurement of two coordi- nates: azimuth (RΦ), position along the cylinder (z); Optional stereo angle for strip detectors (z’ instead of z); Resolution in TPC Gaussian, and may depend on z.

6. The LiC Detector Toy 4 th SiLC Meeting Barcelona, 18 – 20 December 2006 Program Features (fwd/bwd region) Circular plane layers, perpendicular to z-axis; Arbitrary z position and inner/outer radius; Any number of passive plane layers; Measurements of two coordinates (u and v), directions depend on intersection point, defined by angles δ 1, δ 2. u x v δ1δ1 y δ2δ2

7. The LiC Detector Toy 4 th SiLC Meeting Barcelona, 18 – 20 December 2006 Simulation Single tracks originating from a vertex, assumed at (0, 0, z); Solenoid magnetic field, rotational symmetry w.r.t. z-axis; Exact helix track model, with kinks for multiple scattering; Multiple scattering at discrete “thin” layers: –Measurement layers and scattering material treated separately, –Correct path length traversed, material budget averaged over layer, –Scattering angles Gaussian distributed (in the track’s local coordinate frame) according to the Highland formula; Gaussian (TPC) or uniformly distributed measurement errors; Systematic and/or stochastic inefficiencies included.

8. The LiC Detector Toy 4 th SiLC Meeting Barcelona, 18 – 20 December 2006 Reconstruction No Pattern Recognition ! Track fit by an exact Kalman filter: –Inclusion of multiple scattering (“process noise”), –Fitting performed from outside inwards; Linear track model: –Expansion point is a “reference track” (method similar to that of the DELPHI experiment); Parameters: –Fitted parameters defined at the inside of the innermost layer, –DELPHI-like parameter vector and error matrix: { Φ, z, θ, β = φ-Φ, κ = ±1/R H } with sign(κ) = sign(dφ/ds), and corresponding 5x5 covariance matrix; –Optional CMS-like Cartesian parameters and errors: { x, y, z, p x, p y, p z } with a 6x6 covariance matrix of rank 5.

9. The LiC Detector Toy 4 th SiLC Meeting Barcelona, 18 – 20 December 2006 Sample Detector Setup Inspired by LDC concept with “Paris” TPC and additional silicon trackers (to be refined); scale units in mm.

10. The LiC Detector Toy 4 th SiLC Meeting Barcelona, 18 – 20 December 2006 Sample Input Sheet (barrel) 22 Number of layers:5 23 Radii [mm]:90,90,160,300,360 24 Upper z limit [mm]: 110,-90, 360, 640, 2730 25 Lower z limit [mm]: 90,-110,-360,-640,-2730 26 Efficiency RPhi:0,0,0.9,0.9,0 27 Efficiency 2nd:-1 28 Stereo angle alpha [Rad]:pi/2 29 Thickness [rad. lengths]:0.14,0.14,0.0175,0.0175,0.14 30 Error distribution:1 31 0 normal sigma(RPhi) [1e-6m]: 32 sigma(2nd) [1e-6m]: 33 1 uniform d(RPhi) [1e-6m]:50 34 d(2nd) [1e-6m]:50

11. The LiC Detector Toy 4 th SiLC Meeting Barcelona, 18 – 20 December 2006 Sample Input Sheet (barrel) 50 Start parameter range 51 52 Transverse momentum [GeV/c]:5,20 53 Angular range in theta [Rad]:pi/4, 3*pi/4 54 Range in z [mm]:0,5 55 56 Flags (0 disabled, 1 enabled) 57 58 Sketch of arrangement:0 59 Simulation:1 60 Multiple scattering:1 61 Measurement errors:1 62 Reconstruction:1 63 Tests:1 64 Chi2:1 65 Display bad pulls:0 66 Pulls histograms:1 67 Residuals histograms:1 68 Vertex output:0 69 70 Number of tracks:1000

12. The LiC Detector Toy 4 th SiLC Meeting Barcelona, 18 – 20 December 2006 Sample Input Sheet (fwd/bwd) 23 Number of layers:4 24 z positions [mm]:550,800,1050,1300 25 Inner radius [mm]:51,72,93,113 26 Outer radius [mm]:270,290,290,290 27 Efficiency u:0.95 28 Efficiency v:0.95 29 Angle 1st coord. (u) [Rad]:-20*pi/180 30 Angle 2nd coord. (v) [Rad]:20*pi/180 31 Thickness [rad. lengths]:0.01 32 error distribution:1 33 0 normal-sigma(u) [1e-6m]: 34 sigma(v) [1e-6m]: 35 1 uniform-d(u) [1e-6m]:50 36 d(v) [1e-6m]:50

13. The LiC Detector Toy 4 th SiLC Meeting Barcelona, 18 – 20 December 2006 Goodness Tests: Pull Quantities

14. The LiC Detector Toy 4 th SiLC Meeting Barcelona, 18 – 20 December 2006 Fit Results: MC Residuals Note: dip angle λ = π/2 - θ

15. The LiC Detector Toy 4 th SiLC Meeting Barcelona, 18 – 20 December 2006 Summary of various set-ups and dip angle λ parameter regions

16. The LiC Detector Toy 4 th SiLC Meeting Barcelona, 18 – 20 December 2006 Subsequent Vertex Fit Fitted tracks as input to the VERTIGO/RAVE vertex reconstruction toolkit; Interface is the Harvester’s standard CSV text format; Successfully tested with 10- and 1000-prong events. Tracks from barrel region Tracks from forward region

17. The LiC Detector Toy 4 th SiLC Meeting Barcelona, 18 – 20 December 2006 GUI snapshot: startup panel

18. The LiC Detector Toy 4 th SiLC Meeting Barcelona, 18 – 20 December 2006 GUI snapshot: set parameters

19. The LiC Detector Toy 4 th SiLC Meeting Barcelona, 18 – 20 December 2006 GUI snapshot: display geometry

20. The LiC Detector Toy 4 th SiLC Meeting Barcelona, 18 – 20 December 2006 GUI snapshot: run the program

21. The LiC Detector Toy 4 th SiLC Meeting Barcelona, 18 – 20 December 2006 GUI snapshot: results of the run

22. The LiC Detector Toy 4 th SiLC Meeting Barcelona, 18 – 20 December 2006 References http://forum.linearcollider.org ==> Fast Simulations ==> LiC Detector Toy (permanently kept up-to-date);http://forum.linearcollider.org http://wwwhephy.oeaw.ac.at/p3w/ilc/reports/ LiC_Det_Toy/UserGuide.pdf (User Guide);http://wwwhephy.oeaw.ac.at/p3w/ilc/reports/ LiC_Det_Toy/UserGuide.pdf A live presentation will be given at the Vienna Conference on Instru- mentation (VCI), 19-24 February 2007 (http://vci.oeaw.ac.at/2007). Acknowledgements Thanks are due to Winfried Mitaroff for contributions to the helix tracking algorithms, as well as for editing these slides, and to Manfred Krammer for their presentation in Barcelona.