The LiC Detector Toy program

Transcription

1 The LiC Detector Toy program M Regler, W Mitaroff, M Valentan, R Frühwirth and R Höfler Austrian Academy of Sciences, Institute of High Energy Physics, A-1050 Vienna, Austria, EU regler@hephy.oeaw.ac.at Abstract. LiC is a simple but powerful and flexible software tool, written in MatLab, for basic detector design studies (geometries, material budgets) by determining the resolution of reconstructed track parameters. It is based on a helix track model including multiple scattering, and consists of a simplified simulation of the detector followed by track reconstruction using the Kalman filter. After a short description of LiC s main characteristics, we demonstrate its capabilities by applying this tool in a performance study of the LDC and SiD detector concepts at the International Linear Collider (ILC). 1. The Monte Carlo tool A simple but powerful and flexible software tool (LiC Detector Toy 1 ) for detector design, modification and upgrade studies has been developed. It aims at investigating the resolution of reconstructed track parameters in the vertex region for the purpose of comparing and optimizing the track-sensitive devices and the material budgets of various detector set-ups. This is achieved by a simplified simulation of the set-up yielding the measured coordinates, followed by full single track reconstruction. The detector model corresponds to a collider experiment with a solenoid magnet, and is rotationally symmetric w.r.t. the beam axis; the surfaces are either cylinders (barrel region) or planes (forward and backward regions). The magnetic field is homogeneous and parallel to the beam axis, thus implying a helix track model. All material causing multiple scattering is assumed to be concentrated within thin layers; it can either be averaged over a surface, or can be modeled individually. The simulation generates a charged track from a primary vertex, performs helix tracking with breakpoints due to multiple scattering, and simulates detector measurements including systematic or stochastic inefficiencies and uniform or Gaussian observation errors, but no other degradation of data. Supported are silicon strip detectors (single or double sided, with any stereo angle), pixel detectors, and a time projection chamber (TPC). The simulated measurements are then used to reconstruct the track by fitting its 5 parameters and 5 5 covariance matrix at a given reference cylinder, e.g. the inner surface of the beam tube (optionally converted to a Cartesian space point & momentum representation). The method used is a Kalman filter [1, 2] with linear approximation to the track model, the expansion point being defined by the simulated track parameters at the outer surface of the beam tube; process noise is calculated from the material budget as seen by the simulated track. Sensitive tests of goodness of the fits (χ 2 distributions and pull quantities) are implemented. 1 LiC stands for Linear Collider, but the tool is general-purpose.

2 The algorithms used in the tool are on a solid mathematical basis. The software is written in MatLab, a high-level matrix algebra language and IDE [3]. The tool is deliberately kept simple and can without effort be adapted to meet individual needs. Its main purpose, however, is to supply a tool for non-experts, without any knowledge of algorithmic details. Once the detector description ( input sheet ) has been set up, individual detector layers can easily be moved, removed or modified, and the result of these changes can quickly be evaluated. For ease of use, the program is integrated into a graphical user interface (GUI), Figure 1. Figure 1a: LiC Detector Toy GUI the main menu. The tool was beta released at the VCI 2007 [4]. For a thorough description of its functionality and usage see refs. [4, 5]. Figure 1b: setting parameters. 2. Track resolution study This study is based on about 2 18,700 (LDC barrel), 22,400 (SiD barrel) and 8,840 (LDC forward/backward) tracks, respectively, simulated and fitted by the LiC Detector Toy program. Definitions of the barrel and forward/backward regions in terms of the dip angle λ π/2 ϑ polar are given in section 3. The true and fitted track data are passed to and further analyzed by a Java program, running within JAS3 and using AIDA [6]: calculating the deviations of fitted w.r.t. true transverse momenta p T = (p fitted T p T ), and the impact parameters δ T and δ 0 (transverse and in space, respectively); histogramming p T /p T, p T /p 2 T, δ T and δ 0 for separate intervals of true p T ; extracting the rms or mean from each histogram; then using parametrizations (subsection 2.2) to fit rms( p T /p T ), rms( p T /p 2 T ), rms(δ T), and mean(δ 0 ) as functions of the central value of each p T interval see Figures Section 3 presents preliminary results, and section 4 the conclusions LDC and SiD detector descriptions The geometry and material constants of the ILC Large Detector (LDC) and Silicon Detector (SiD) concepts have been taken from their 2006 Detector Outline Documents [7]; recent updates are taken into account. Visualization snapshots of the layouts and summaries of the detector descriptions are shown in Figure 2.

3 The LDC concept: The SiD concept: LDC Detector description Bz = 4 Tesla; efficiency Si = 95%, TPC = 100%; errors in m BARREL R[mm] Zmin[mm] Zmax[mm] Error distribution d[xo] Remarks Beam pipe 14 passive mm Be VTX pads 50*50 (25*25) equ. distrib..002 wafer + ladder VTX idem idem idem VTX 3 37 idem idem idem idem idem VTX 4 48 idem idem idem idem idem VTX 5 60 idem idem idem idem idem Support passive.070 arbitrary structures idem idem passive idem idem SIT strips 2* o, 10 o SIT idem idem idem TPC inn. wall passive pad rings <1580 idem idem ( z) 196 * 1,2 = 15, 1,2 = 50, 3.8 in R 1.25E-5 58 in z FORWARD Z[mm] Rmin[mm] Rmax[mm] Error distribution d[xo] Remarks FTD pads 50* FTD idem idem FTD idem idem FTD idem strips 2*90 idem ± 45 o FTD idem idem idem idem FTD idem idem idem idem FTD idem idem idem idem SiD Detector description Bz = 5 Tesla; efficiency Si = 95%; errors in m BARREL R[mm] Zmin[mm] Zmax[mm] Error distribution d[xo] Remarks Beam pipe passive mm + conus + conus Be + Ti VXD pads 20*20 equ. distrib wafer + ladder VXD idem idem idem idem idem VXD idem idem idem idem idem VXD idem idem idem idem idem VXD idem idem idem idem idem Dbl. support passive 2 * dbl. wall cylinders C fibre TRK strips single TRK idem idem idem TRK idem idem idem TRK idem idem idem TRK idem idem idem FORWARD Z[mm] Rmin[mm] Rmax[mm] Error distribution d[xo] Remarks not implemented so far SiD barrel region restricted to λ < 20 o, in order to avoid the supporting membranes of the VXD. Figure 2: Visual layouts and detector descriptions of the LDC (left) and SiD (right) concepts Parametrization of track resolutions The relative errors of the transverse momentum due to the magnet spectrometer resolution or caused by multiple scattering, respectively, are: σ(p T )/p T = A p T and σ(p T )/p T = B 1 + (m/p) 2 B The above terms are expected to add quadratically. However, for p T < 35 GeV, a simpler linear addition fits the data quite well and has been used: σ(p T )/p T = A p T + B, thus σ(1/p T ) σ(p T )/p 2 T = A + B/p T For lack of a theoretical model, the errors of the impact parameters w.r.t. the true vertex are heuristically parametrized for p T > 2.5 GeV as: σ(δ T,0 ) = a + b e p T /c (for high p T, the asymptotic value = a) In the forward/backward region, only linear parametrizations in p T > 2.5 GeV have been used; thus the divergent part of σ(p T )/p 2 T is cut away LDC and SiD track resolutions LDC and SiD barrel regions for p T = GeV (Figures at left): the data points correspond to LDC 50 50µm pixels (blue dots), LDC 25 25µm pixels (red squares), and SiD 20 20µm pixels (purple triangles), respectively, of the barrel vertex detectors - for a detailed description, see subsection 2.1. LDC forward/backward regions for p T = GeV (Figures at right): the data points correspond to dip angle ranges of 81 o < λ < 81.5 o (blue dots), 81.5 o < λ < 82 o (red squares), and 82 o < λ < 82.5 o (purple triangles).

4 The values are averages over p T intervals of width 2.5 GeV. The error bars shown reflect only the statistics normalized to bin content. Figure 3: rms( p T /p T) vs. p T for barrel (left) and forward/backward (right) regions. Figure 4: rms( p T /p 2 T) [GeV 1 ] vs. p T for barrel (left) and forward/backward (right) regions. Figure 5: rms(δ T) [mm] vs. p T for barrel (left) and forward/backward (right) regions. Figure 6: mean(δ 0) [mm] vs. p T for barrel (left) and forward/backward (right) regions.

5 3. Preliminary results The results extracted from Figures (subsection 2.3) are summarized below. Barrel regions (LDC: λ < 48 o, SiD: λ < 20 o ), p T = GeV: Detector, px size rms( p T/p T) rms( p T/p 2 T) [GeV 1 ] rms(δ T) 2 mean(δ 0) 2 LDC 50 50µm (4.6 p T ) 10 5 ( /p T ) µm 9.56 µm LDC 25 25µm (4.6 p T ) 10 5 ( /p T ) µm 5.91 µm SiD 20 20µm (2.4 p T ) 10 5 ( /p T ) µm 6.46 µm Forward/backward regions (81 o < λ < 82.5 o ), p T = GeV: LDC λ range rms( p T/p T) rms( p T /p 2 T) 3 rms(δ T) 2 mean(δ 0) 2 81 o < λ < 81.5 o (8.4 p T 2.83) GeV µm 70.7 µm 81.5 o < λ < 82 o (5.7 p T ) GeV µm 57.1 µm 82 o < λ < 82.5 o (5.0 p T ) GeV µm 53.4 µm 4. Conclusions In the barrel region and for transverse momenta p T < 35 GeV, the momentum resolution benefits dramatically from the low material budget of LDC s TPC. In contrast, SiD s all-si tracker suffers from repeated breakpoints due to multiple scattering which forbids fitting a sufficiently long undisturbed track segment (as in a TPC); we have proved for p T = GeV that hypothetically reducing SiD s material budget to a quarter would halve rms( p T /p T ). However, extrapolation to higher momenta shows a break-even at p T 50 GeV, as expected. The transverse impact parameters in the barrel region reflect directly the resolutions (i.e. the pixel sizes) of the corresponding vertex detector s innermost layer(s). In the forward/backward region λ > 81 o, the momentum resolution is sensitive to LDC s forward tracker strips stereo angle: ±45 o (i.e. perpendicular orientation) is a good compromise between optimal R Φ and R z resolutions. The transverse impact parameters and those in space are almost identical; emphasis must rather be given to z (not shown). For the extreme forward/backward region λ > 82.5 o (not shown), track reconstruction suffers extremely from inefficiencies, and might require non-standard treatment. References [1] R. Frühwirth et al.: Data Analysis Techniques for High-Energy-Physics, 2 nd edition (eds. M. Regler and R. Frühwirth), Cambridge University Press (2000). [2] M. Regler, R. Frühwirth and W. Mitaroff: Int.J.Mod.Phys. C7, 4 (1996) 521. R. Frühwirth et al.: Nucl.Instr. Meth. A 334 (1993) 528. [3] D. Hanselmann and B. Littlefield: Mastering MatLab 7, Pearson Prentice-Hall (2005). See also [4] M. Regler, M. Valentan and R. Frühwirth: The LiC Detector Toy Program, Proc. 11 th Vienna Conf. on Instrumentation (VCI) 2007, Nucl.Instr.Meth. A (in print). [5] User s Guide: [6] FreeHep software used: Java Analysis Studio (JAS3): Abstract Interfaces for Data Analysis (AIDA): [7] ILC Detector Outline Documents: LDC (July 2006): SiD (May 2006): 2 asymptotic value, 3 weighted average.