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.

The LiC Detector Toy

4th SiLC Meeting Barcelona, 18 – 20 December 2006


A mini simulation and track fit program toolfor fast and flexible detector optimization studies

M. Regler, M. Valentan and R. Frühwirth

Institute of High Energy Physics of theAustrian Academy of Sciences, Vienna



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).



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.



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.



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.



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 δ1, δ2.u

x

v

δ1

y

δ2



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.



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/RH } with sign(κ) = sign(dφ/ds), and corresponding 5x5 covariance matrix;

– Optional CMS-like Cartesian parameters and errors:{ x, y, z, px, py, pz } with a 6x6 covariance matrix of rank 5.



Sample Detector Setup

Inspired by LDC conceptwith “Paris” TPC and additional silicon trackers (to be refined);scale units in mm.



Sample Input Sheet (barrel)22 Number of layers: 523 Radii [mm]: 90,90,160,300,36024 Upper z limit [mm]: 110,-90, 360, 640, 273025 Lower z limit [mm]: 90,-110,-360,-640,-273026 Efficiency RPhi: 0,0,0.9,0.9,027 Efficiency 2nd: -128 Stereo angle alpha [Rad]: pi/229 Thickness [rad. lengths]:

0.14,0.14,0.0175,0.0175,0.1430 Error distribution: 131 0 normal sigma(RPhi) [1e-6m]:32 sigma(2nd) [1e-6m]:33 1 uniform d(RPhi) [1e-6m]: 5034 d(2nd) [1e-6m]: 50



Sample Input Sheet (barrel)50 Start parameter range51 52 Transverse momentum [GeV/c]: 5,2053 Angular range in theta [Rad]: pi/4, 3*pi/454 Range in z [mm]: 0,55556 Flags (0 disabled, 1 enabled)5758 Sketch of arrangement: 059 Simulation: 160 Multiple scattering: 161 Measurement errors: 162 Reconstruction: 163 Tests: 164 Chi2: 165 Display bad pulls: 066 Pulls histograms: 167 Residuals histograms: 168 Vertex output: 06970 Number of tracks: 1000



Sample Input Sheet (fwd/bwd)23 Number of layers: 424 z positions [mm]: 550,800,1050,130025 Inner radius [mm]: 51,72,93,11326 Outer radius [mm]: 270,290,290,29027 Efficiency u: 0.9528 Efficiency v: 0.9529 Angle 1st coord. (u) [Rad]:-20*pi/18030 Angle 2nd coord. (v) [Rad]:20*pi/18031 Thickness [rad. lengths]: 0.0132 error distribution: 133 0 normal-sigma(u) [1e-6m]:34 sigma(v) [1e-6m]:35 1 uniform-d(u) [1e-6m]: 5036 d(v) [1e-6m]: 50



Goodness Tests: Pull Quantities



Fit Results: MC Residuals

Note: dip angle λ = π/2 - θ



Summary of various set-ups and dip angle λ parameter regions



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



GUI snapshot: startup panel



GUI snapshot: set parameters



GUI snapshot: display geometry



GUI snapshot: run the program



GUI snapshot: results of the run



References• http://forum.linearcollider.org ==> Fast Simulations

==> LiC Detector Toy (permanently kept up-to-date);• http://wwwhephy.oeaw.ac.at/p3w/ilc/reports/LiC_Det_Toy/UserGuide

.pdf (User Guide);• 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.

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.

Documents

lic detector toy

detector material

detector setup

th silc meeting barcelona

linear collider detector

zaxis arbitrary z position

z resolution

vienna slide