1. CMS Upgrade Workshop - Fermilab 19.11.08 Trigger Studies Using Stacked Pixel Layers Mark Pesaresi https://twiki.cern.ch/twiki/bin/view/Main/MarkPesaresi https://twiki.cern.ch/twiki/bin/view/Main/MarkPesaresi

2. Mark Pesaresi2 Tracking Trigger Aim is to assess the performance and viability of a stacked pixel layer or layers as part of a L1 tracking trigger by the determination of track p t Study attempts to simulate the implementation of such a trigger Generation of trigger primitives using digi information Performance of the algorithm in finding high p t tracks Investigate methods of sensor readout and hit correlation for the on-detector implementation Performance of high p t track reconstruction for a trigger when using two or more stacked layers Complements previous study reported on last December using a stacked strip layer in the outer tracker

3. Mark Pesaresi3 Geometry 0.9 2.14 2.5 Current Pixel System Stacked Pixel Layer @ 25cm Considering a single stacked pixel layer at r=25cm, length=221cm Current pixel system included in geometry Outer geometry unnecessary at this point Using latest version of Strawman B in CMSSW_1_8_4

4. Mark Pesaresi4 Sensor Geometry Strawman B parameters modified in pixbar.xml and trackerStructureTopology.xml Sensor choice:tilted at 23° – to reduce cluster width by minimizing Lorentz drift 100μm thickness 28mm x 72.8cm sensor dimensions z overlap – to fill gaps in z 100 μm x 2.37mm pixel pitch 256 x 30 pixels per module Sensor separation varied between 0.5-4mm Modification made to geometry to aid trigger studies – not yet part of StrawmanB z offset – to match columns in top and bottom sensors with increasing eta 23° z overlap z offset

5. Mark Pesaresi5 Simulation Overview adc cut & sorting Sorted Digis [detId, row, column, adc] correlation algorithm Stubs [detId high, row high, column high, adc tot, row difference, column difference, simTrackId high, simTrackId low ] Stacked Layer Digis [detId, row, column, adc] adc digi > 30 sorted by detId into modules with upper and lower sensors hits between upper and lower sensors are correlated to check for high p t tracks modifiable search window cuts can be applied

6. Mark Pesaresi6 Correlation Algorithm Row difference calculation Since the sensors are tilted, there is a difference between the position of the higher and lower sensor hits for a high p t track which is also dependent on the position of the incident track on the sensor The fixed offset as a function of the row number can be applied to calculate the true row difference Equivalent to an on detector map between the hit position on the higher sensor to a set of positions on the lower sensor Column difference calculation Column difference is not symmetrical – dependence on whether hit is in detector +/-z. Can be exploited to maximise rate reduction. 0 256 pixel row 114 pixel row 125

7. Mark Pesaresi7 Correlation Algorithm Stub generation A stub is created when both the row and column difference lie within a given range. e.g. row offset = 3 0 ≤ row window ≤ +1 0 ≤ column window ≤ +1 Upper Lower Pass Fail 100μm

8. Mark Pesaresi8 Algorithm Performance Separation [mm]Max Efficiency [%]Fake [%] (or average number/event) Reduction Factor 0.599.050.73 (12.22) 8.04 1.099.354.14 (25.58) 22.26 2.097.74517.83 (18.74) 95.99 3.096.0039.08 (23.76) 210.28 4.092.9547.27 (32.39) 254.35 Max Efficiency: Average maximum efficiency for a high p t track to form a stub. Inefficiencies due to sensor doublet acceptances and algorithmic efficiency (window cuts) Fake: Average fraction of stubs per event generated by correlating hits from different tracks Reduction Factor: Average data rate reduction factor per event (N Stubs / N Digis ) where N Digis is number of hits with charge >adc digi for the whole stacked layer Performance of a detector stack at r=25cm for sensors with pitch 100μmx2.37mm. Correlation cuts optimised for high efficiency

9. Mark Pesaresi9 Algorithm Performance Separation [mm]Max Efficiency [%]Fake [%] (or average number/event) Reduction Factor 0.599.050.73 (12.22) 8.04 1.099.354.14 (25.58) 22.26 2.097.74517.83 (18.74) 95.99 3.096.0039.08 (23.76) 210.28 4.092.9547.27 (32.39) 254.35 Performance of a detector stack at r=25cm for sensors with pitch 100μmx2.37mm. Correlation cuts optimised for high efficiency Max Efficiency calculated using 20,000 single 50GeV Muon/Antimuon events with smearing Fake/Reduction Factor calculated using 100 MinBias events with an average of 400 interactions per bunch crossing with smearing Results optimised for high efficiency:Row window = 2 pixels Column window = 2 pixels @ 0.5mm 3 pixels @ 1mm, 2mm 4 pixels @ 3mm 6 pixels @ 4mm

10. Mark Pesaresi10 Algorithm Performance Cuts optimised for high efficiency: Row window = 2 pixels Column window = 2 pixels @ 0.5mm; 3 pixels @ 1mm, 2mm; 4 pixels @ 3mm; 6 pixels @ 4mm p T discriminating performance of a stacked layer at r=25cm for various sensor separations using 10,000 di-muon events with smearing Sensor separation is again an effective cut on p t – as with the stacked strips Again, the width of the transition region increases with separation. Due to: - pixel pitch - sensor thickness - charge sharing - track impact point Efficiencies decrease with sensor separation due to the larger column window cuts – sensor acceptances and fake containment are issues

11. Mark Pesaresi11 Implications In order to reduce Lorentz drift, sensors have been tilted – correlation requires that an offset must be programmed in order to match hits from high p t tracks - At its most basic, a calibration constant must be uploaded for each pixel row on a sensor - If technology changes, sensors may not need to be tilted Instead of the correlator performing a difference analysis on two hits, a programmable map between an address on the upper sensor and multiple addresses on the lower sensor would simplify implementation and reduce rate & fakes. Is this possible? If layer is part of a multi-stack detector, a high efficiency is preferable to large rate reductions. We only need to remove the majority of low p t tracks. Multiple stacks should remove the fakes if combinatorics are not too high. A 2mm separation at 25cm seems reasonable. To maintain high efficiencies, the column window cut must be kept wide. Can such a column window cut be implemented on detector?

12. Mark Pesaresi12 Next Steps Plenty of work to do still… e.g. Measure performance of a stacked layer as a function of radius Measure performance of a stacked layer as a function of pileup Measure performance of a stacked layer as a function of pixel pitch Check performance is maintained in different physics events, e.g. jets

13. Mark Pesaresi13 Double Stack Geometry 0.9 2.14 2.5 Current Pixel System Stacked Pixel Layer @ 25cm Considering now two stacked pixel layers at:r=25cm, length=221cm r=35cm, length=221cm Current pixel system included in geometry Outer geometry unnecessary at this point Using same sensor geometry for each layer Stacked Pixel Layer @ 35cm 1.8

14. Mark Pesaresi14 Stack Performance Cuts optimised for high efficiency: Row window = 2 pixels @ 25cm layer, 3 pixels @ 35cm layer Column window = 3 pixels @ 2mm; 2 pixels @ 1.45mm p T discriminating performance of stacked layers at r=25cm and r=35cm for various sensor separations using 10,000 di-muon events with smearing At a larger radius, a stacked layer with the same sensor separation will effectively cut at a larger p t Calculations indicate that a sensor separation of 1.45mm at 35cm will produce the same discrimination profile as a 2mm separation at 25cm - simulations agree with this calculation Having to build modules with different sensor separations may be undesirable for a future tracker

15. Mark Pesaresi15 Stack Performance Separation [mm]Max Efficiency [%]Fake [%] (or average number/event) Reduction Factor 2.0 (Upper Stack)99.0917.86 (10.91) 203.70 2.0 (Lower Stack)97.74517.83 (18.74) 95.99 Performance of detector stacks at r=25cm and r=35cm for sensors with pitch 100μmx2.37mm. Correlation cuts optimised for high efficiency Max Efficiency calculated using 20,000 single 50GeV Muon/Antimuon events with smearing Fake/Reduction Factor calculated using 100 MinBias events with an average of 400 interactions per bunch crossing with smearing Results optimised for high efficiency: Row window = 2 pixels @ 25cm layer, 3 pixels @ 35cm layer Column window = 2 pixels To simplify the simulations slightly, sensor separations of 2mm have been chosen for both layers

16. Mark Pesaresi16 Double Stack Simulation Overview sorting/clustering correlation algorithm Tracklets stubs on each layer can be clustered or processed to remove duplicates in this case only 1 hit/column is passed – similar to how on detector correlation might work stubs between upper and lower layers are correlated in eta and phi – performance is trigger hardware dependent modifiable search window cuts can be applied Stubs (Lower Stack) [detId, row, column] Sorted Stubs (Lower Stack) [global coordinates] Sorted Stubs (Upper Stack) [global coordinates] Stubs (Lower Stack) [detId, row, column]

17. Mark Pesaresi17 Double Stack Correlation Algorithm Correlate stubs in upper sensor with stubs in lower sensor – use upper sensor as seed (fewer stubs, fewer fakes) Stubs Upper Stack Lower Stack Vertex Window cut in η applied – wide enough to allow for vertex smearing Window cut in ϕ applied – wide enough to allow for low p t tracks and scattering

18. Mark Pesaresi18 Double Stack Correlation Algorithm Window cut in η applied – wide enough to allow for vertex smearing Window cut in ϕ applied – wide enough to allow for low p t tracks and scattering Distributions of Δη and Δ ϕ between upper and lower stack stubs using 10,000 single 5-50GeV Muon/Antimuon events with smearing

19. Mark Pesaresi19 Double Stack Algorithm Performance Using double stack correlation window cuts |Δη| < 0.2, |Δ ϕ | < 0.015 Tracklet p t resolution vs. track p t and η when using a 3-point pt reconstruction measurement for 10,000 0-30GeV di-muon events with smearing If the stubs are correlated, we can use the two stubs plus the vertex as r, ϕ points for a 3- point track p t measurement – assumes track originates from (0,0)

20. Mark Pesaresi20 Double Stack Algorithm Performance Using double stack correlation window cuts |Δη| < 0.2, |Δ ϕ | < 0.015 p T discriminating performance using double stacks for 10,000 0-30GeV di-muon events with smearing With a momentum measurement using two stacks, an effective cut on track p t can be placed Maximum efficiency is still determined by that of the single stack A better track pt resolution using the double stack means that the transition region can be reduced We would like to have better efficiencies at low p t – this would require stacks with smaller sensor separations (or larger windows) increasing the number of stubs per layer and the number of combinatorics for the double stack algorithm

21. Mark Pesaresi21 Next Steps Investigate performance at high pileup – measure number of combinatorial fakes, pt resolution, robustness to displaced vertices / secondary interactions Measure vertex resolution, angular/z resolution at calorimeters Measure performance of two stacks as a function of radius separation Measure performance of two stacks as a function of pileup Check performance is maintained in different physics events Eric Brownson (Vanderbilt) is currently working on replicating the TDR L1 muon trigger rate plot at LHC luminosity. plan is to work in collaboration to get the corresponding plot at SLHC luminosity then use the tracking trigger developed here to measure the effect of combining such a trigger with the L1 muon trigger

22. Mark Pesaresi22 Summary Strawman B has been used as the basis to commence trigger studies using a stacked pixel layer at 25cm Algorithm to correlate digi hits from high p t tracks has been written Performance of algorithm in ideal conditions measured - >95% maximum efficiency of detecting high p t tracks, ~ x100 reduction in data rate Stubs from two stacked layers have been correlated Example layers at 25cm and 35cm demonstrate that high p t tracks can be detected with >90% maximum efficiency p t of single muons has been measured with ~4% resolution Still need to check number of combinatorial fakes, robustness of p t measurement in high pileup events Still plenty to investigate… Effect of occupancy on performance Effect of changing layer radii Effect of changing pixel pitch, short/long pixel strips Possibility to extend layers to high eta …

23. Mark Pesaresi23 Backup – Single Stack Performance Effect of changing window cuts on discrimination curves Efficiencies are unchanged with larger column windows Efficiencies are recovered (at larger separations) when row window is increased but also has the effect of decreasing the p t cut p T discriminating performance of a stacked layer at r=25cm for a sensor separation of 4mm and various algorithm cuts using 10,000 di-muon events with smearing

24. Mark Pesaresi24 Backup – Single Stack Performance 123 1 19.0541.9642.085 2 44.07595.58595.89 3 45.15597.74598.07 Row Width Column Width Efficiency of a 50 GeV muon/antimuon generating a stub in the stacked layer [%] Data rate reduction factor achieved on MinBias events at SLHC pileup 100 MinBias events with an average of 400 interactions per bunch crossing with smearing 20,000 single 50GeV Muon/Antimuon events with smearing 23 2 104.694.4 3 96.486.0 Row Width Column Width Choosing a sensor separation of 2mm, the effect of the window cuts has been determined

25. Mark Pesaresi25 Backup - Some Numbers Typical MinBias event at SLHC luminosity: 1455 tracks > 2 GeV 4 tracks > 8 GeV (in region |eta| < 2.14) Using a stacked pixel layer at 25cm (|eta| < 2.14) with pixel pitch 100μmx2.37mm and 2mm sensor separation [row window=2, column window=3] 140 stubs includes 25 fake stubs includes 20 duplicate stubs Every event is triggered A second stacked layer would reduce the number of fakes, the number of tracks (if p t threshold is raised) and allow sufficient resolution for matching to other sub- detectors.

26. Mark Pesaresi26 Backup - Sensor Readout A method for reading out stacked sensors for hit correlation is required - Readout and decision every bunch crossing - Low power G.Hall – July 2008

27. Mark Pesaresi27 Backup - Sensor Readout Module divided into 64 blocks of 4 rows per column Requires minimum 10 address lines: 6 bit block address 4 bit pattern e.g. x000,00x0,0xx0, etc. Assumes that only 1 block is hit per column – reasonable since <1 pixel hit per column on average 4 x 100μm 2.37mm Correlator Block1 Block0

28. Mark Pesaresi28 Backup - Sensor Readout Analysis modified to simulate this method of correlation Sort data into blocks Correlate hit blocks Readout block stubs and pattern data Run original algorithm Correlate blocks with pattern data Readout stubs On-detectorOff-detector Blocks are correlated in a similar way to before with a block (row) difference and a column difference. As before, an offset is required to match the blocks correctly Cuts can be placed on the window width for both blocks and columns Investigated how well top method worked and the data rate reductions possible

29. Mark Pesaresi29 123 1 49.3859.6460.03 2 78.7295.0395.59 3 80..5797.1897.75 Block Width Column Width Efficiency of a 50 GeV muon/antimuon generating a stub in the stacked layer [%] Data rate reduction factor achieved on MinBias events at SLHC pileup 100 MinBias events with an average of 400 interactions per bunch crossing with smearing 20,000 single 50GeV Muon/Antimuon events with smearing 23 2 9.204.78 3 8.374.47 Block Width Column Width Choosing a sensor separation of 2mm, the effect of block cuts have been determined Results are for block correlation followed by standard algorithm with [row window=2, column window=3] Backup - Sensor Readout

30. Mark Pesaresi30 Backup – Sensor Readout Require at least a factor 10 reduction in rate to read out detector. Achievable with a block width cut of 2. For reasonable efficiencies, a column width cut of at least 2 is still required. How can this be performed easily on detector? Offsets are still needed when applying correlation to blocks – can this be implemented on detector? A small fraction of columns contain more than one hit per BX (in some cases up to 6 hits). Is this important, can it be reduced or ignored? Largest cause is due to hits on block boundaries e.g. |0000|000x|x000|0000|

31. Mark Pesaresi31 Backup Fast Sim gives an average occupancy of 0.05% (up to 0.15% instantaneous) at an average of 400 interactions per event for a layer at 25cm extending to |eta| < 2.14 Assume Full Sim will give x3 occupancy 0.15% x 17,448,960 channels = 26,173 hit channels 30k channels require 2813, 2.56Gbps links assuming 12bit address per channel at 20MHz Link Power: 5.6 kW (322uW/ch) – Geoff suggests a budget of 300μW/ch for the p t layers Cutting the number of channels to readout by x10 using hit correlation brings link power for the p t layers down to reasonable values Total Hits Block Stubs Pixel Stubs

32. Mark Pesaresi32 Backup Layer Occupancy (No. digi hits in layer / total channels in layer) Module Occupancy (No. digi hits in occupied module / total channels in module) Note: Full Sim occupancies estimated at 3x these values 100 MinBias events, ~400 interactions per bx with smearing