EUDET beam telescope Geant 4 simulation of spatial resolution Daniel Scheirich, Zdeněk Doležal, Tobias Haas*, Peter Kodyš, Pavel Řezníček Faculty of Mathematics and Physics Charles University, Prague *DESY EUDET Kick-off meeting, DESY 15-17 February 2006

Motivation and History 2 Motivation and History JRA1 is supposed to deliver beam telescopes for DESY and other beam tests DESY electron beam suffers from multiple scattering Geant 4 simulation needed Existing model developed for DEPFET beam tests Modification of the model for EUDET telescopes under way First results will be shown now

Outline Program structure Model validation Geometry of the beam test 3 Outline Program structure Model validation Geometry of the beam test Un-scattered particles Electron beam simulation Residual plots for 2 different geometries CERN 180 GeV pion beam simulation First results for EUDET geometry Conclusions

Geant 4 simulation program More about Geant 4 framework at www.cern.ch/geant4 C++ object oriented architecture Parameters are loaded from files G4 simulation program g4run.mac class TPrimaryGeneratorAction g4run.config class TGeometry … class TDetectorConstruction class TDetector … detGeo1.config C++ object oriented architecture, using Geant 4 framework Geometry parameters are loaded from files: easy way to change a test configuration no need to re-compile the whole program Two important classes that loads config files: TPrimaryGeneratorAction holds an information about particle, energy, energy cuts, … TDetectorConstruction provides routines to create detector model ALL geometry parameters loaded from files Each instance of TGeometry class represents one type of detector (f.i. telescope) Each instance of TDetector represents one detector in beamtest (f.i. TEL0) FILE geometry.config: possitions of detectors and sensitive wafers detGeo2.config … geometry.config det. position, det. geometry files sensitive wafers

5 Model validation Simulation of an electron scattering in the 300m silicon wafer Angular distribution histogram Comparison with a theoretical shape of the distribution. According to the Particle Physics Review it is approximately Gaussian with a width given by the formula: Motivation Scattering in simple wafer – WELL KNOWN PROBLEM Can be compared where p,  and z are the momentum, velocity and charge number, and x/X0 is the thickness in radiation length. Accuracy of 0 is 11% or better.

Example of an electron scattering 6 Example of an electron scattering Angular distribution electrons Electrons move along x-axis Blue area represents a silicon wafer Electrons leave wafer in many different directions Scatter angles are put into histogram Silicon wafer

7 Non-gaussian tails Gaussian fit Theoretical shape Good agreement Some numbers will be shown on the next slide Non-gaussian tails

Results: simulation vs. theory 8 Results: simulation vs. theory 0… width of the theoretical Gaussian distribution …width of the fitted Gaussian accuracy of 0 parametrisation (theory) is 11% or better According to PPR: accuracy of theta0 is 11% or better We are safely in the error range TABLE: Last column is the most interesting Good agreement between the G4 simulation and the theory

Geometry of the DEPFET beam test 9 Geometry of the DEPFET beam test (DEPFET) Beam is parallel with x-axis Two and two telescopes, DUT in the center and all is enclosed by scintillators We will discuss results for different distances b and e Geometry parameters: Lars Reuen Electron beam: 3x3 mm2, homogenous, parallel with x-axis

Geometry of the beam test: example 10 Geometry of the beam test: example The same thing in VRML

Configurations used for the simulation 11 Configurations used for the simulation as planned for January 2006 TB – info from Lars Reuen, October 2005 Geometry 1 Module windows: 50 m copper foils no foils 150 m copper foils We have tested 2 geometries: Telescopes close together – GEOMETRY 1 Telescopes far from each other – GEOMETRY 2 Another tested parameter: window thickness MOTIVATION: Use no windows and put the telescopes into one black box OR use current configuration with separate modules Geometry 2 Module windows: 50 m copper foils

Unscattered particle (geometry only) 12 Unscattered particle (geometry only) Intersects of an unscattered particle lie on a straight line. A resolution of telescopes is approximately pitch/(S/N) ~ 2 m. Positions of intersects in telescopes plane were blurred with a Gaussian to simulate telescope resolution. These points were fitted by a straight line. For better understanding of results we will discuss different contribution to the final beam test ressolution. Non-scattering particle: contribution of telescope intrinsic resolution (resolution of one telescope) Non-scattering particle = straight line Every deviations are caused by telescopes’ position errors

13 Residual R(y) in DUT plane Stars represents intersects of actual track Black crosses represents errors according to GAUSSIAN distribution, histograms bellow THOSE BLACK CROSSES are fitted (red line) We are interested in the residual in the DUT plane

Residual distribution in DUT: unscattered particle 14 Residual distribution in DUT: unscattered particle 2 cut : width 100% :  =0.9912 m 70% :  =0.9928 m Example of residual plots: geometry 1 Chi square cuts were applies to exclude bad fits First row is without any chi2 cut As chi2 cuts are applied width of residual plots in telescopes’ plane decreases while in DUT plane REMAINS THE SAME. Note that THESE distributions (telescopes) are no longer GAUSSIAN I will show some numbers -> NEXT SLIDE 50% :  =0.9918 m 30% :  =0.9852 m

Unscattered particles: residual plots 15 Unscattered particles: residual plots Geometry 1  = 1.19 m  = 1.60 m  = 1.60 m  = 1.18 m  = 0.99 m Geometry 2 SUMMARY for two geometries ALSO no significant change => we can’t reduce this effect by changing telescopes’ distances  = 1.05 m  = 1.68 m  = 1.68 m  = 1.05 m  = 0.99 m

Electron beam simulation 16 Electron beam simulation There are 2 main contributions to the residual plots RMS: Multiple scattering Telescope resolution Simulation was done for 1 GeV to 5 GeV electrons, 50000 events for each run Particles that didn’t hit the both scintillators were excluded from the analysis 2 cuts were applied to exclude bad fits 2 contributions to the residual plot width: Multiple scattering Detector resolution: beside telescopes there is also DUT resolution that contribute to the final test beam resolution

Example of 2 cuts 17 30% of events, 2 < 0.0005 An example of chi2 cut Colored areas contain 30, 50 or 70% of all events. Chi2 cut corresponds to the right border of an area. Chi2 is not normalized

18 Actual position DUT residual DUT plane Telescope resolution: Gaussian with  = 2 m An example of fitting: Stars represents intersects of an actual track. An error according to the Gaussian distribution with a sigma 2 microns is add to the actual intersects in telescope planes. A residual is distance between fitted straight line and actual position (as is shown in green circle).

Electron beam simulation: residual plots 19 Electron beam simulation: residual plots Example of residual plots Decrease of residual plots width after chi2 cuts were applied IS significant here And some numbers …

Electron beam simulation: residual plots 20 Electron beam simulation: residual plots … and some numbers. We can reduce DUT residual plot sigma from almost 40 microns to 21 (or less) microns by applying chi2 cuts BUT there is limit as will be shown further.

Residual-plot sigma vs. particle energy 21 Energy dependency: For higher energies multiple scattering runs lower that means narrower residual plots. For more strict chi2 cuts residual plots are narrower too. BUT: neither energy nor chi2 cut affect intrinsic DUT and TEL resolution. That’s why we CAN’T go under ~9 microns

Residual plots: two geometries 22 Residual plots: two geometries Ideal detectors telescopes resolution included Summary chart [čárt] RED lines: values of DUT residual plots sigma with ideal detectors BLACK lines: values of DUT residual plots sigma when all effects are included. EXPLAIN: cuts and energies Note: Significant difference between geometries for less strict cuts & lower energies For higher energies and more strict cuts difference decrease.

Residual plots: two geometries 23 Residual plots: two geometries Ideal detectors telescopes resolution included Summary chart [čárt] RED lines: values of DUT residual plots sigma with ideal detectors BLACK lines: values of DUT residual plots sigma when all effects are included. EXPLAIN: cuts and energies Note: Significant difference between geometries for less strict cuts & lower energies For higher energies and more strict cuts difference decrease.

Three windows thicknesses for the geometry 1 24 Three windows thicknesses for the geometry 1 Geometry 1 Module windows: no foils 50 m copper foils 150 m copper foils Shortly about window thickness dependency. Three thicknesses were simulated: 0, 50 & 150. All for geometry 1.

Residual plots: three thicknesses 25 Residual plots: three thicknesses Ideal detectors TEL & DUT resolution included We expect: no window is the best. Let’s see some numbers…

Residual plots: three thicknesses 26 Residual plots: three thicknesses Ideal detectors TEL & DUT resolution included We expect: no window is the best. For low energy and less strict cuts it’s true (SHOW) BUT: for the highest ENG and the most strict cut the values are almost the same, again. Let’s see some numbers…

Pion beam simulation CERN 180 GeV pion beam was simulated 27 Pion beam simulation CERN 180 GeV pion beam was simulated Geometries 1 and 2 were tested In addition: the same with pion beam.

Pion beam: residual plots 28 Pion beam: residual plots Ideal detectors TEL & DUT resolution included Let’s skip to the results: residual plots Pion has much lower multiple scattering. Resolution of detectors is much more important. Note: For ideal detectors chi2 cut affect residual plot width. For non-ideal it doesn’t. This effect is washed out by DUT intrinsic resolution.

Pion beam: residual plots 29 Pion beam: residual plots Ideal detectors TEL & DUT resolution included Numbers confirm it.

The latest results Final beam test geometry: similar to the Geometry 1 DUT is shifted to the front side The resolution of telescopes ~ 5 m

Unscattered particle 2 cut : width 100% :  =2.53  0.02 m Telescope resolution 5 m

Infinite energy extrapolation Telescopes resolution 5 m Plot 2 vs. 1/E2 Angular distribution width  due to a multiple scattering is proportional to 1/E

Infinite purity extrapolation Attempt to exclude scattered tracks by Chi2 cut – infinite purity

Infinite purity and energy extrapolation Even the most stringent cut cannot eliminate multiple scattering effects

35 EUDET Geometry The same thing in VRML

6 vs 4 telescopes unscattered particles 6 telescopes give better precision due to more measurement points 6 telescopes 1.0 mm 4 telescopes 1.3 mm

6 vs 4 telescopes scattering included, ideal telescopes 6 telescopes give worse precision due to more scattering 6: 5.9-1.0 mm 4: 3.8-0.6 mm

6 vs 4 telescopes scattering included, telescopes s~2.5 mm 6 telescopes give worse precision due to more scattering: more points won’t overweigh scattering 6: 6.0-1.46 mm 4: 4.0-1.45 mm

Distance dependence Distance matter, so all attempts should be made to get as close as possible

40 Conclusions Software for a simulation and data analysis has been modified for EUDET First results available: 4 telescopes better than 6 minimizing distance important To be done: Thorough analysis Magnetic field