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Analytical Method (AM) for DT Trigger Primitive Generation in Phase2: May 2020 results

See also: CMS DP-2020/XXX and CMS IN-2019/003 (CMS Private Document) Previous results reported have been reported here

INTRODUCTION

A full replacement of the muon trigger system in the CMS (Compact Muon Solenoid) detector is envisaged for operating at the maximum instantaneous luminosities expected in HL-LHC (High Luminosity Large Hadron Collider) of about 5-7.5x10³⁴ cm^-2s^-1. Under this scenario, the new on detector electronics that is being designed for the DT (Drift Tubes) detector will forward all the chamber information at its maximum time resolution. A new trigger system based on the highest performing FPGAs is being designed and will be capable of providing precise muon reconstruction and Bunch Crossing identification. An algorithm easily portable to FPGA architecture has been designed to implement the trigger primitive generation from the DT detector. This algorithm has to reconstruct muon segments from single wire DT hits which, for a given BX, come with a spread of 400 ns due to the drift time in the cell. This algorithm provides the maximum resolution achievable by the DT chambers, bringing the hardware system closer to the offline performance capabilities. The results of the simulation and of the first implementations in the new electronics test bench are shown.

Description of the algorithm: Analytical Method

The input information is the wire position of the hit cell and the hit time from the start of the LHC orbit. From this, and assuming a given laterality, the hit position can be reconstructed. For a given hypothesis of muon trajectory within a super-layer, which is a straight line, using information from 3 cells allows to solve for the collision time, as the dependence on track slope is factored out. In this way one can identify the bunch crossing (BX) of the corresponding proton-proton interaction where the muon was produced. In practice a selection is made of patterns of 4 tubes and their sub-patterns of 3 tubes over 10 cells at a time, containing all physical trajectories in the given super layer. For cases with 4 hits (one per layer), time is computed from each triplet and then combined in an arithmetic mean. Once the collision time is known, the track parameters are computed using exact formulas from least squares method (chi2-minimisation). For 3 hits all hit laterality assumptions providing physical solutions are considered as candidates. For 4 hits select a unique final candidate, the one with minimum chi2. For muons with fits of 4 hits or 3 hits both in super-layer 1 (SL1) and and super-layer 3 (SL3), the information from both fits can be correlated if the corresponding segment times are within a window of +/- 25 ns. If a match is found the candidate trigger primitive parameters are re-defined as follows: the new time is the mean of the per super layer fits times, the new position is the mean of the superlayer fits positions, and the new slope is computed from the difference in fit positions in SL3 and SL1 divided by distance between the two r-phi super layers. If no match found, all per-superlayer candidates are kept. In a final step information from RPCs can be added to define ‘super-primitives’, with corrected time measurement. This algorithm has been implemented in CMS software (CMSSW) as an emulator for the firmware implementation in FPGA.

Efficiency and resolution studies

Trigger Primitives efficiencies and resolutions are evaluated in simulation samples with Phase-2 conditions. Results are produced out of a particle-gun sample (flat pT [2,100] GeV) with a <pile-up> of 200 collisions/BX superimposed to the signal in a [-3,+3] BX range. The GEANT simulation configuration is the one typically used for standard CMS Monte Carlo Productions, in particular regarding the modelling of background. Moreover they are processed with and without assuming the “end of phase-2 (3 ab^-1)” ageing/failure scenario presented in this Twiki

Figure	Caption
	Efficiency: Muon barrel trigger primitive efficiency computed in rings defined by DT chambers with same wheel and station (MB). Efficiency is computed with respect to local reconstructed segments geometrically matched with generator-level muons. Segments are required to have at least 4 hits in r-phi, to have a theta component (in MB1/2/3) and their crossing time (t0seg) is requested to be in the [-15,15] ns range. No ageing is ever applied to segments for the efficiency computation.
	Position Resolution: Angular resolution σ for position azimuthal coordinate, for muon barrel TPs computed in rings defined by DT chambers with same wheel and station (MB). The innermost and outermost simulated hits matched within each chamber to the parent muon are used to obtain the simulation-level position, which is used to compute the residual respect to the position from the local trigger. Two gaussians are used to fit the resolution distribution. The width of the narrower gaussian (σ) is reported in the plot.
	Direction Resolution: Angular bending (direction) resolution σ for muon barrel TPs computed in rings defined by DT chambers with same wheel and station (MB). The innermost and outermost simulated hits matched within each chamber to the parent muon are used to obtain the simulation-level direction, which is used to compute the residual respect to the direction from the local trigger. Two gaussians are used to fit the resolution distribution. The width of the narrower gaussian (σ) is reported in the plot.
	Time Distribution: Muon Barrel Sub-BX timing distribution for the station1 (MB1) wheel+1 (W+1) ring, computed for TPs computed with the AM method and associated to a generated muon with pT> 20 GeV. The time distribution becomes narrower when applying sub-BX “correction” based on RPC information. The time distribution becomes broader when applying the DT ageing scenario for 3000 fb-1, while the inclusion of the considered RPC failures has a very mild effect.

Firmware-Emulator comparisons

A test stand at CIEMAT allows to perform dedicated tests of the AM algorithm for DT chambers (phi view, only DT not RPC) as implemented in firmware (v146) in an AB7 board. Input DT hits, coming from all chambers in the CMS detector, are stored in a file and injected at the input buffers of the AB7 board, modifying according the corresponding parameters for each chamber. At present we are using real reconstructed Z->mu mu events from 2016 proton-proton collision data, but any type of hits can be used. These hits have Phase 2 data format but also, they are injected at a predefined time, emulating OBDT behavior. Hits go through all the Chamber trigger chain inside the Virtex 7 FPGA -Trigger primitives are generated in the board and readout. Plots presented here show a comparison of firmware and emulator results for Analytical Method (AM) for DT Trigger Primitive Generation in Phase 2, taking as input DT hits from 10000 reconstructed Z-> mumu events in the 2016 collision data sample. The emulator is run on the RAW data, and in parallel the DT hits are input to the AB7 board in CIEMAT as previously described. Comparison is made of the fitted parameters (time, local position and local direction) for TPs coming from emulator and from firmware, in the cases when TPs have fitted the same hits with same laterality. All plots at ‘chamber level’, including all qualities, for all chambers.

	Difference between trigger primitive’s BX as obtained by the software emulator and event BX (blue) and difference between trigger primitive’s BX obtained by the firmware and event BX (red) when running on DT hits from reconstructed Z-> mumu events in the 2016 collision data sample, for pairs of primitives fitting same hits with same laterality (67066 entries) Agreement is achieved for all trigger primitive qualities
	Difference between trigger primitive’s BX as obtained by the software emulator and event BX (blue) and difference between trigger primitive’s BX obtained by the firmware and event BX (red) when running on DT hits from reconstructed Z-> mumu events in the 2016 collision data sample, for pairs of primitives fitting same hits with same laterality (67066 entries) As shown in the insert, agreement in time is at the level of Least Significant Bit for all trigger primitive qualities
	Trigger primitive’s time minus Event BX*25, as obtained by the software emulator (blue) and obtained by the firmware (dashed red) when running on DT hits from reconstructed Z-> mumu events in the 2016 collision data sample, for pairs of primitives fitting same hits with same laterality. Agreement between time obtained by emulator and firmware is at < 1ns level for all trigger primitive qualities
	Trigger primitive’s time minus Event BX*25, as obtained by the software emulator (blue) and obtained by the firmware (dashed red) when running on DT hits from reconstructed Z-> mumu events in the 2016 collision data sample, for pairs of primitives fitting same hits with same laterality. As shown in the insert, agreement is at the level of Least Significant Bit for all trigger primitive qualities
	Trigger primitive’s local position, as obtained by the software emulator (blue) and obtained by the firmware (dashed red) when running on DT hits from reconstructed Z-> mumu events in the 2016 collision data sample, for pairs of primitives fitting same hits with same laterality. Agreement is achieved for all trigger primitive qualities
	Trigger primitive’s local position, as obtained by the software emulator (blue) and obtained by the firmware (dashed red) when running on DT hits from reconstructed Z-> mumu events in the 2016 collision data sample, for pairs of primitives fitting same hits with same laterality. As shown in the insert, agreement is at the level of Least Significant Bit for all trigger primitive qualities
	Trigger primitive’s local direction (slope defined as tangent of local angle ψ), as obtained by the software emulator (blue) and obtained by the firmware (dashed red) when running on DT hits from reconstructed Z-> mumu events in the 2016 collision data sample, for pairs of primitives fitting same hits with same laterality. Agreement is achieved for all trigger primitive qualities
	Trigger primitive’s local direction (slope defined as tangent of local angle ψ), as obtained by the software emulator (blue) and obtained by the firmware (dashed red) when running on DT hits from reconstructed Z-> mumu events in the 2016 collision data sample, for pairs of primitives fitting same hits with same laterality. As shown in the insert, agreement is at the level of Least Significant Bit for all trigger primitive qualities
	Trigger primitive’s local position as obtained by the software emulator versus trigger primitive’s local position obtained by the firmware, when running on DT hits from reconstructed Z-> mumu events in the 2016 collision data sample, for pairs of primitives fitting same hits with same laterality (67066 entries). Agreement is achieved for all trigger primitive qualities
	Trigger primitive’s local position as obtained by the software emulator versus trigger primitive’s local position obtained by the firmware, when running on DT hits from reconstructed Z-> mumu events in the 2016 collision data sample, for pairs of primitives fitting same hits with same laterality (67066 entries). As seen from the insert, agreement is at the level of Least Significant Bit for all trigger primitive qualities
	Trigger primitive’s local direction (slope tanpsi) as obtained by the software emulator versus trigger primitive’s local direction obtained by the firmware, when running on DT hits from reconstructed Z-> mumu events in the 2016 collision data sample, for pairs of primitives fitting same hits with same laterality (67066 entries). Agreement is achieved for all trigger primitive qualities
	Trigger primitive’s local direction (slope tanpsi) as obtained by the software emulator versus trigger primitive’s local direction obtained by the firmware, when running on DT hits from reconstructed Z-> mumu events in the 2016 collision data sample, for pairs of primitives fitting same hits with same laterality (67066 entries). As seen in the insert, agreement is at the level of Least Significant Bit for all trigger primitive qualities

First Slice Test results

During Long Shutdown 2 a complete exercise has been made to instrument one sector (wheel +2 sector 12) of the CMS detector with the HL-LHC DT electronics frontend and backend prototypes. One of these backend boards (the so-called AB7) runs the AM firmware. This way, both Phase 1 and Phase 2 electronics can be run inside the CMS infrastructure, and the AM firmware can be validated using real cosmic muons. Plots show results of difference between trigger primitive time (online time) for either phase-2 and/or legacy system primitives and offline reconstructed phase1-segment time, for a cosmic muon sample collected in MB4/YB+2/Se12 with the slice test set up, and triggered by MB3. Phase1-segments are reconstructed offline from legacy hits, and selected to have a |local dir|< 30°, at least 4 hits, and t0 < 50 ns Note that no time calibration correction has been implemented in the TDC data used to produce the phase-2 trigger primitives

Difference between trigger primitive’s time and the offline reconstructed segment time, for phase-2 in blue and for Legacy trigger (red) in a cosmic muon sample collected in the Slice Test set up. For phase-2 only primitives fitting at least 4-hits are considered (denoted as Q>=4/8 in the legend), in order to be compared with the Legacy system (requesting minimal H quality). For the Legacy system the trigger output time is in BX units (25 ns step) The red line shows the convolution of a flat distribution within the BX time interval of 25 ns with a 3 -4 ns time resolution of the reconstructed segment. For phase-2, the inherent online time resolution is of few ns. The improved online time resolution in phase 2 reflects in this particular sample (unbuched cosmic muons) as a lower (half) fraction of triggers at a wrong bx, i.e. 12.5 ns away from the time the muon crossed the chamber

Difference between trigger primitive’s fitted time and the offline reconstructed segment time, for phase-2 trigger primitives in a cosmic muons sample collected in the Slice Test set up. Considering every quality (3-hit primitives included). Note that while for the Legacy system the trigger output time is in BX units (25 ns step), for phase-2, the inherent online time resolution is of few ns. The core sigma of this distribution is ~3ns

-- SilviaGoyLopez - 2020-05-28