LiC Detector Toy - Tracking detector optimization with fast simulation and its application to the ILD design

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by  Manfred Valentan

LiC Detector Toy - Tracking detector optimization with
fast simulation and its application to the ILD design
9 Manfred Valentan,Meinhard Regler, Winfried Mitaroff and Rudolf Fru¨hwirth
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0 Austrian Academy of Sciences – Instituteof High Energy Physics
2 Nikolsdorfer Gasse 18, A-1050 Vienna, Austria, EU

n
a The“LiC DetectorToy”isafast single-track simulation andreconstruction tool, aim-
J ing at theoptimization of tracking detector design, i.e. geometric layout and material
7 budgets. Its implementation is based on the MatLab system. Improvementsover the
2 last year include correct handling of complex forward regions (arbitrary mixture of
cylindrical and plane surfaces), enhanced detector description, flexible data presenta-

] tionofresults(e.g. fittedtrackresolutionsandimpactparameters),andsupportbyan
t
e integratedGUI.Inadditionanon-GUIversionrunningunderopen-sourceOctavehas
d been implemented. The tool has recently been used for fixing the “reference design”
- layout of thesilicon tracker (SIT,SET and FTD) of theILD detector concept.
s
n
i 1 Simulation and reconstruction
.
s
c
i The “LiC Detector Toy” (LDT) – a simple but powerful and flexible software tool for
s
y detector design, modification and upgrade studies – aims at investigating the resolution
h of reconstructed track parameters for comparing and optimizing the track-sensitive devices
p andmaterialbudgetsofvariousdetectorlayouts. Thisisachievedbyasimplifiedsimulation
[
of the investigated setup, followed by full single track reconstruction.

1 The detector model correspondsto a collider experiment with a solenoid magnet, and is
v rotationally symmetric w.r.t. the beam axis (denoted z); the surfaces are either cylinders
3 (“barrelregion”)orplanar disks(“forward/rearregion”). The magneticfield B~ =(0,0,Bz)
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1 is homogeneous and parallel to the z-axis, thus implying a helix track model (radius RH).
4 All materialcausingmultiple scatteringis assumedto be concentratedwithin thin layers;it
. can either be averagedover a surface, or can be modeled individually.
1
Simulation generates charged tracks with user-defined ranges for the start parameters
0
9 (vertex position, momentum p or its transverse component pT, and polar angle ϑ); per-
0 formshelixtrackingwithbreakpointsduetomultiplescatteringaccordingtoRossi-Greisen-
v: Highland;a and simulates detector measurements including systematic or stochastic ineffi-
i ciencies, and uniform or Gaussian observation errors, but no other degradation of data. At
X
presentsupported is any combinationof Si stripdetectors (single or double sided, with any
r
stereo angle α), pixel detectors, and a time projection chamber (TPC).
a
Reconstruction is done separately for each track from all its simulated measurements
without pattern recognition, by fitting the five parameters and 5×5 covariance matrix at a
pre-definedreferencecylinder,e.g. theinnersurfaceofthebeamtube. Standardparameters
are [Φ,z,ϑ,β = ϕ−Φ,κ = ±1/RH] (Φ and ϕ denote the azimuth angles of position and
direction, respectively). The method used is an inwards-running Kalman filter [2, 3], with
linear expansion from a “reference track” being defined by the simulation; process noise is
calculatedfromthe materialbudgetasseenbythattrack. Sensitivetests ofgoodnessofthe
2
fits (χ distributions and pull quantities) are an integral part.
a Energylossduetobremsstrahlungofe± willbeincludedinafuturerelease.
LCWS/ILC2008
Thealgorithmsusedinthetoolstandonsolidmathematicalgroundandarefield-proven.
The software is based on MatLab(cid:13)R [4], a licenced high-level matrix algebra language and
IDE;usageissupportedbyagraphicuserinterface(GUI). Zoomable2Dand3Ddisplaysof
the setup andflexible data presentationofthe results areeasily at hand. The core program
hasrecentlybeenrefactoredtorunalsoincommandlinemodewithoutGUIunderOctave
[5], an open-source product which is source-code compatible.
Thetoolisdeliberatelykeptsimpleandcanwithouteffortbeadaptedtoindividualneeds.
Itsmainpurpose,however,istosupplyatoolfornon-expertswithoutalgorithmicknowledge.
Oncethedetectordescription(“inputsheet”)hasbeensetup,individualdetectorlayerscan
easily be added, moved, modified or removed, and the result of these changes can quickly
be evaluated. For more information see the User’s Guide [6].
2 Application to the ILD design
A first “ILD reference design” was proposed in Sept. 2008 at Cambridge (UK); however,
details of the Silicon Tracker layout were left open. Optimization brainstormings, based on
LDTv2.0andvalidatedagainstfullsimulation(Mokka–Marlin),tookplaceinSept/Oct.2008
at DESY, and in Dec. 2008 at the SiLC meeting in Santander. They helped defining the
layout eventually used by the benchmark MC runs for the LoI.
2.1 Barrel region (SIT and SET):
TheSiliconInnerTracker(SIT)isplacedbetweenVertexDetectorandTPC,andtheSilicon
External Tracker (SET) fills the gap between TPC and Electromagnetic Calorimeter. In
ordertoassesstheimpactofSITandSETontheoveralltrackingperformance,thestandard
layout is compared with two alternatives by removing either SIT or SET, but not both, for
radial tracks (ϑ=90◦) with momenta p=pT =1...1000 GeV/c.
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Figure 1 shows, for these 3 layouts, the resolutions of ∆pT/pT (left), transverse impact
parameter (middle), and z coordinate (right) as functions of pT.
Momentum res. at q=90(cid:176) Proj. impact res. at q=90(cid:176) z res. at q=90(cid:176)
10 5
orig. ILD
no SIT
10−4 no SET 8 4
V]
2D) [c/Ge(p/ptt sm(ip2) [m] 46 sm(z) [m] 23
s
2 1
0 0
100 101 102 103 100 101 102 103 100 101 102 103
Transverse momentum p [GeV/c] Transverse momentum p [GeV/c] Transverse momentum p [GeV/c]
t t t
Figure 1: Effectsofremovingeither SIT (red)orSET(green)w.r.t. standardlayout(blue).
Note from the right figure that the SET also contributes to the z coordinate resolution
because of its precise z measurement at long lever arm.
LCWS/ILC2008
2.2 Forward/rear region (FTD):
The Forward Tracking Detector (FTD) is placed between beam tube and inner wall of the
TPC.Itconsists,ineachz direction,of3pixeldisks(FTD1–3)and4stripdisks(FTD4–7),
the latter double sided with stereo angles α = 90◦. This standard setup is compared with
three alternatives which make use of strip disks with a small stereo angle α = 6◦, while
leaving everything else unchanged:
Layout symbolic FTD 4 FTD 5 FTD 6 FTD 7
Standard + + + + 90◦ 90◦ 90◦ 90◦
Setup 1 II II + II 6◦ 6◦ 90◦ 6◦
Setup 2 II II II + 6◦ 6◦ 6◦ 90◦
Setup 3 II II = II 6◦ 6◦ ¶ 6◦ 6◦ b
Theimpactonthe trackingperformanceofthese4setupsaretestedwithforwardtracks
(ϑ=7◦)ofmomentap=10...250GeV/c. Figure2showstheresolutionsof∆pT/p2T (left),
transverse impact parameter (middle), and z coordinate (right) as functions of p.
Momentum res. at q=7(cid:176) Proj. impact res. at q=7(cid:176) z res. at q=7(cid:176)
10−2
+ + + + (orig. ILD)
|| || + || (setup 1)
|| || || + (setup 2)
V] || || = || (setup 3)
2D(p/p) [c/Gett sm(ip2) [m] sm(z) [m]102
s 10−3 101
101 102 101 102 101 102
Absolute momentum p [GeV/c] Absolute momentum p [GeV/c] Absolute momentum p [GeV/c]
Figure 2: Alternative setups 1 (red), 2 (green) and 3 (black) vs. standard setup (blue).
Thus, it is possible to achieve better resolutions in transverse momenta and impact
parameters at high momenta, at the cost of only small losses in the resolution of z.
References
[1] Presentation:
http://ilcagenda.linearcollider.org/contributionDisplay.py?contribId=217&sessionId=21&confId=2628
[2] R.Fru¨hwirthetal.(ed.M.Regler,R.Fru¨hwirth): DataAnalysisTechniquesforHigh-EnergyPhysics,
2nd edition,CambridgeUniversityPress(2000), ISBN0-521-63219-6, 0521-63548-9(pbck).
[3] M.Regler,R.Fru¨hwirthandW.Mitaroff: Int.J.Mod.Phys.C7, 4(1996)521.
R.Fru¨hwirthetal.: Nucl.Instr.Meth.A 334(1993)528.
[4] D.HanselmannandB.Littlefield: Mastering MatLab 7,PearsonPrentice-Hall(2005).
See alsoMatLabon the web,http://www.mathworks.com/
[5] GNUOctavev.3on the web,http://www.gnu.org/software/octave/
[6] M.Valentan: “LiCDetectorToy” repository,http://wwwhephy.oeaw.ac.at/p3w/ilc/lictoy/
b Normallythe strips of one side are oriented radially, measuring the azimuthal arc RΦ, and the strips
oftheothersideareinclinedbyα. ¶OnlyFTD6ofsetup3hasitsstripsofonesideorientedtangentially,
measuringtheradiusR. Incaseofα=90◦,thisdistinctionbecomes dummy.
LCWS/ILC2008