LHC-B. 60 silicon vertex detector elements. (strips not to scale) [cm] [cm] = 1265 strips

Transcription

1 LHCb , TRAC November Comparison of analogue and binary read-out in the silicon strips vertex detector of LHCb. P. Koppenburg 1 Institut de Physique Nucleaire, Universite de Lausanne Abstract This note presents single hit resolutions in the LHCb silicon strip vertex detector for various read-out schemes, depending on the number of bits used in digitization. A scan of reconstruction eciencies and ghost hit rates for various signal/noise ratios is presented. More detailed results can be found on: 1 Patrick.Koppenburg@ipn.unil.ch

2 Contents 1 Introduction 2 2 Simulation Simulation of the signal read-out schemes Binary read-out Analogue read-out Digital read-out Eects of noise Resolutions Ghost hits and lost tracks Average number of hit strips Conclusions and further ideas 8 A parameter 9 1

3 LHC-B 60 silicon vertex detector elements φ strip detector r strip detector (strips not to scale) = 896 strips = 1265 strips µm 80 µm 40 µm 60 µm µm [cm] µm [cm] 6.0 Figure 1: Vertex detector elements 1 Introduction During this year, the new r? geometry [1] of the vertex detector (SMVD) was introduced and various read-out schemes presented [2]. Some additional simulations and tests were needed to make a nal decision for the Technical Proposal. This note presents some results of a simulation of the charge deposition of tracks in the silicon detector. The single-hit resolutions for various read-out schemes, depending on the number of bits used in digitization and the consequences of electronic noise from amplier and detector are discussed. 2 Simulation 2.1 Simulation of the signal The simulation is based on a simulation of the DELPHI Very Forward Tracker by Heinz Pernegger [3]. Essentially r-strips are considered in this context. The detector is described by an innite electrode plane and a plane of strips parallel to it, at a distance equal to the thickness of the detector (T = 150 m) (see gure 2). Three strip pitches of 40, 60 and 80 m, corresponding to the strip-pitches used in the SMVD r-detector planes (gure 1) are tested. Possible eects of the curvature of the r-strips are neglected. The detector is supposed to have a homogeneous electrical eld V =T where V is the full depletion voltage, set here to 50 V. A single track is simulated as a straight line in the detector plane. Since detector planes are perpendicular to the beam axis (z), in r-detectors the incidence angle is equal to the -angle of the track. A typical distribution is reproduced in gure 3. Overlapping signals from two tracks are not considered. A Landau-distributed number of electron-hole pairs is generated along the track. For low-angle ( 0) tracks, the distri- 2

4 Pitch = 40 µm z T =150 µm ds x x Track α Figure 2: Simulation of charge segments in the detector bulk Figure 3: Typical incidence angle distribution for B! events generated with SICB [4]. All forward B events are considered in the rst plot, only those with both pions in the detector acceptance in the second. 3

5 bution peaks at e (1:8 fc) 2. The path of the particle is split in 1 m long segments (called ds in gure 2). In each segment a Landau-distributed 3 number of pairs is generated. Diusion is simulated by a Gaussian displacement dx of the segment. The smearing is a function of the drift distance in z and the depletion voltage V 4. The nal signal (without any noise) of each strip is the sum of all charges within the acceptance of the strip (so 40, 60 or 80 m). No insensitive regions are considered and the complete created charge is detected. Simulation of noise At rst order, the noise distribution has a Gaussian shape [5]. Noise was simulated by adding a Gaussian distributed number to the collected signal of each strip. Throughout, all results are related to the width of this distribution. 2.2 read-out schemes The read-out schemes dier by the number of bits used in the digitization of the signal. We call binary a 1-bit digitization of the analogue signal (strip was hit or not) and digital a b-bit digitization where b is small (typically 2 or 4). In the analogue read-out scheme, the signal is considered as a real number, which is equivalent with a b-bit digitization where b is big (typically 8 or 16) Binary read-out For the binary read-out scheme, clusters of adjacent strips in which the collected charge is above a threshold T Str B are considered. The reconstructed x intercept position of the track is the geometrical center of the cluster. Figure 4 shows the RMS of the dierence between this reconstructed position and the position of the simulated track in the middle of the layer versus the track incidence angle and for strip-pitches of 40 and 80 m. One can see that this resolution is oscillating between 6:5 and 11:5 m. The maximum RMS is reached when the average number of hit strips is close to an integer n (for 40 m-strips n = 2 at 220 mrads, n = 3 at 460 mrads... See gure 7). There the number of hit strips is independent of the position and the resolution is close to pitch= p 12 = 11:55 m. The minimum is reached when the probability to hit n or n + 1 strips is identical. The number of hit strips gives then an additional information that improves the resolution Analogue read-out The analogue read-out scheme oers the possibility of an improvement in both resolutions and reconstruction eciencies. We apply a threshold T Str A on strips to form clusters and a threshold T Cl A on the total charge of the cluster. To optimize the resolution, a generalized parameter is used (see appendix A). In absence of noise, the resolution can reach 2 m for high angle tracks Digital read-out For a digital b-bit read-out scheme, the analogue value is converted to an integer number in the range [0; 2 b? 1]. Essentially 2 and 4-bit read-out are presented. Since the results for 4-bit and analogue read-out are close, there is no need to investigate larger numbers of bits. 2 This value is probably slightly under-estimated. One would rather expect 2:0 fc, hence e. This does not aect results, since only the signal/noise ratio is relevant. 3 The average value being set as the generated total number of pairs divided by the number of segments. 4 This width is about 4:7 m for the maximal drift distance of 150 m. The RMS considering all segments is 3:3 m. 4

6 Peak signal per track: RMS of noise per strip: Strip-pitch = 40 microns e 0 e Peak signal per track: RMS of noise per strip: Strip-pitch = 80 microns e 0 e RMS in microns RMS in microns analogue readout 4-bit digital readout 2-bit digital readout binary readout analogue readout 4-bit digital readout 2-bit digital readout binary readout Figure 4: Resolutions vs. pitches of 40 and 80 m. track incidence angle for various read-out schemes and strip 97/09/ /09/ Peak signal per track: e RMS of noise per strip: 600 e Strip-pitch = 40 microns Peak signal per track: e RMS of noise per strip: 1500 e Strip-pitch = 40 microns RMS in microns 8 6 RMS in microns analogue readout 4-bit digital readout 2-bit digital readout binary readout 2 analogue readout 4-bit digital readout 2-bit digital readout binary readout angle in mrads angle in mrads Figure 5: Resolutions vs. S=N 7. track incidence angle for a 40-m-pitch for S=N 18 and For 4-bit read-out, the same procedure as for analogue read-out is applied to the digital clusters, including a "digitized" parameter. For all tested noises, the optimal thresholds are found to be very close to the analogue thresholds. Throughout all 4-bit thresholds are equal to analogue thresholds. With a 2-bit read-out no ecient cluster threshold could be found and it was decided not to cut on cluster charges. The best strip-threshold was found to be equal to the binary threshold. The resolution improvement provided by 2-bit read-out in comparison to binary read-out is only due to the use of a "digitized" center-of-mass determination of the position. 5

7 Noise S=N pitch Binary Analogue [e] [m] = 0 Min Max = 0 Min Max Table 1: = 0, Minimal and maximal resolutions in m 3 Eects of noise 3.1 Resolutions Table 1 lists single-hit resolutions for various noise RMS and the considered strip-pitches. One can see that the values increase when noise increases, but the loss in resolution is not dramatic. It becomes important for high angle tracks, mainly because of poor reconstruction eciencies. Figure 5 shows resolutions for noise RMS of 600 (S=N 18) and 1500 e (S=N 7) in 40 m strips. 3.2 Ghost hits and lost tracks With noises up to 1000 e (S=N 11), it is possible to set thresholds in order to have a nearly 100% reconstruction and no ghost hits (i.e. noisy clusters above threshold). The only consequence of the thresholds is the loss in resolution discussed above. For N oise = 600 e, binary and 2-bit thresholds are set to T Str B = 2600 e (0:42 fc), while analogue and 4-bit thresholds are set to T Str A = 1100 e (strips) and T Cl A 3800 e (cluster). When noise becomes higher than 1000 e, threshold setting is a compromise between losing tracks and generating ghost hits. Figure 6 shows the percentage of reconstructed hits versus the number of ghost hits for high noises scanning various thresholds for between 0 and 200 mrads. With a binary read-out, 25 thresholds between 2000 and 6800 e were scanned, which leads to the curves shown in the rst plot. With analogue read-out, the curves show the "best" combinations of strips thresholds between 2500 and 3750 e and cluster thresholds between 3250 and 5250 e. The analogue read-out scheme always allows a slightly better noise rejection. Requiring a 98% reconstruction eciency leads to O(10) ghost hits per strips with a S=N ratio between 8 and 9. At S=N 7, this number increases to 80 and 120 for analogue and binary respectively and at S=N 6, it reaches 600 and 800 ghost hits. These numbers have to be compared with a typical number of about 340 real r-hits in channels. 6

8 97/11/ Binary readout, 40 micron strips Strip thresholds ranging from 2000 to 6800 e Ghost hits per strips Reconstructed hits 97/11/ Analogue readout, 40 micron strips Strip threshold: e Cluster threshold: e Ghost hits per strips Reconstructed hits Figure 6: Ghost hits and reconstruction eciencies for binary and analogue read-out. Each curve corresponds to a given noise. 7

9 97/10/ analogue readout binary or 2-bit digital readout Peak signal per track: RMS of noise per strip: Strip-pitch = 40 microns e 0 e 4 analogue or 4-bit digital readout binary or 2-bit digital readout mean number of strips mean number of strips Peaksignal per track: RMS of noise per strip: Strip-pitch = 40 microns e 0 e angle in mrads Figure 7: Average number of hit strips per cluster without and with noise (S=N 18). In the rst plot the thresholds are identical for all read-out schemes and the curves are superimposed. 3.3 Average number of hit strips As one can see from gure 7, the average number of strips per cluster increases with the track angle. In absence of noise, it does not depend on the read-out scheme and begins at 1.5 strips per cluster for = 0 tracks. When noise is added, the increased strip thresholds reduce the number of strips per cluster. With sensible noises, the average number of strips per hit is around 1.2 for low angle tracks at all strip-pitches. At = 400 mrad it increases to 2.1, 1.7 and 1.5 for 40, 60 and 80 m strips respectively. These values are important for the data transmission, since after zero suppression and before clustering, the total number of signals to transmit is the total number of hits times the average number of hit strips per hit. Considering all tracks in an event, this average value is around Conclusions and further ideas The simulation of the deposited charge and noise in the microstrips of the vertex detector shows that with signal/noise ratios above 7, the ghost hit rates and the fraction of lost hits stay acceptable. The analysis of the various read-out schemes show great similarities between the binary and 2-bit digital schemes on one side and the analogue and 4-bit (or more) digital schemes on the other side. The analogue (or 4-bit) read-out allows a slightly better signal-noise separation and increases single-hits resolutions by a factor 2 for large angle tracks (over 200 mrads). For low angle tracks, there is no major dierence. Finally, due to the deposition of charge on several strips, the average number of strips over threshold per hit is around 1.5. Once the LHCb GEANT simulation includes the tracking with the r? hits, the eect of the detector parameters on o-line physics analysis can be determined. For example, of crucial 8

10 importance in the B! channel is ecient reconstruction of the decay vertex ; this will depend on the cluster resolution and the detector geometry. A parameter Considering tracks that hit two strips, it is observed that due to the Gaussian smearing of the collected charge along x, the fraction of the collected charge on each strip is not a linear function of the position of the track. The quantity = P H(2) P H(1) + P H(2) is calculated where P H(1) and P H(2) are the collected charges (Pulse Heights) on the left and right strip [6, 7]. The reconstructed position of the track is considered as a polynomial function x = f(). Compared to a linear center of mass (CM) method, this improves resolutions by 1 or 2 microns. For high tracks that hit more than two strips, the procedure can easily be generalized to n strips, dening P H(n)? P H(1) n = P H(1) + : : : + P H(n) When the number of hit strips becomes higher than 4, the improvement in resolution compared to the CM method is negligible. Acknowledgments The author would like to thank Hans Dijkstra, Thomas Ruf, Jan Buytaert and Oliver Cooke for their help and suggestions and to acknowledge the CERN Vertex Trigger group for the fruitful meetings. References [1] LHCb Collaboration. Trigger and Data Acquisition System for the LHCb experiment. LHCb /LHCC. CERN/LHCC [2] Hans Muller, Jan Buytaert, Hans Dijkstra, Thomas Ruf. Vertex trigger implementation. LHCb [3] Heinz Pernegger. Reconstruction of inclined tracks with large pitch silicon strip detectors. Submitted to Nucl. Instr. and Meth., feb /afs/cern.ch/users/p/perneg/public/nim paper3.ps. [4] Andrei Tsaregorodtsev. SICB user guide, GEANT3-based simulation package for the LHCb experiment. LHCb Collaboration, june [5] Teela Marie Pulliam. Noise Studies on Silicon Microstrip Detectors. Bachelor of science thesis, University of California, Santa Cruz, jun thesis.ps. [6] Anna Peisert. Silicon microstrip detectors. In Fabio Sauli, editor, Instrumentation in High Energy Physics. World Scientic, [7] E. Belau and al. Charge collection in silicon strips detectors. Nucl. Instr. and Meth., (214),