A Firmware-oriented Trigger Algorithm for CMS Drift Tubes in HL-LHC

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 information from the DT detector. This algorithm has to reconstruct muon segments from single wire DT hits which contain a time uncertainty of 400 ns due to the drift time in the cell. This algorithm provides the maximum resolution achievable by the DT chambers, bringing closer to the hardware system the offline performance capabilities. The results of the simulation and of the first implementations in the new electronics test bench will be shown.

Description of the algorithm

The input information is the wire position of the hit cell and the hit time from the start of the 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 (straight line), using information from 3 cells allows to solve for the collision time BX, as the dependence on track slope is factored out. 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 are correlated if the corresponding segment times are within a window of +/- 25 ns. If a match is found the trigger primitive parameters are re-defined as follows: the new time is the mean of the per super layer fits time, the new position as 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.

Description of the INTRINSIC performance, and of the EMULATOR performance

Evaluate difference (“resolution”) of obtained parameters (time and slope) with respect to the offline reconstructed segment for two workflows Studies of INTRINSIC PERFORMANCE: As first step, evaluate performance for obtaining the track parameters with a least square fitting method (chi2 minimisation) for all variables (including time for fits with 4 hits) in clean conditions. Take as input calibrated times of hits associated to offline segments (substitutes parts 1. and 2. of described workflow) This allows evaluation of intrinsic performance of a ‘exact solution’ for obtaining all the track parameters Studies of EMULATOR PERFORMANCE: The trigger primitive is reconstructed with the Analytical Method as implemented in the Emulator (including full grouping and pattern recognition) In case more than one trigger primitive generated, select the one closest to offline segment in x coordinate for performance studies

List of Plots

Figure	Caption
	INTRINSIC performance: Difference between trigger primitive reconstructed time and offline segment reconstructed time (“time resolution”), fitted to a gaussian, for primitives with 4 hits in super layer 1.The trigger primitive is reconstructed from hits associated to the offline segment in muons decays of Z bosons in a 2017 sample. All track parameters, including time, are obtained from a least square fitting method. All DT chambers are included. The sigma of the gaussian fit is ~3 ns. Note: here offline segment reconstructed from hits in more than one superlayer: good proxy for ‘true’ value of considered variables, small correlation expected
	INTRINSIC performance: Difference between trigger primitive reconstructed slope and offline segment reconstructed slope (“slope resolution”), fitted to two gaussians, for primitives with 4 hits in super layer 1. The trigger primitive is reconstructed from hits associated to the offline segment in muons decays of Z bosons in a 2017 sample. All track parameters, including time, are obtained from a least square fitting method. All DT chambers are included. The sigma of the narrow gaussian fit is ~7 mrad. Note: here offline segment reconstructed from hits in more than one SL: good proxy for ‘true’ value of considered variables, small correlation expected
	INTRINSIC performance: Difference between trigger primitive reconstructed time and offline segment reconstructed time (“time resolution”), fitted to a gaussian, for correlated primitives with 4 hits in super layer 1 and 4 hits in super layer 3. The trigger primitive is reconstructed from hits associated to offline segment in muons decays of Z bosons in a 2017 sample. All track parameters, including time, are obtained from a least square fitting method. All DT chambers are included. The sigma of the gaussian fit is <3 ns. Note: relevant correlations between fit results and variables obtained from offline segment possible
	INTRINSIC performance: Difference between trigger primitive reconstructed slope and offline segment reconstructed slope (“slope resolution”), fitted to a gaussian, for correlated primitives with 4 hits in super layer 1 and 4 hits in super layer 3. The trigger primitive is reconstructed from hits associated to offline segment in muons decays of Z bosons in a 2017 sample. All track parameters, including time, are obtained from a least square fitting method. All DT chambers are included. The sigma of the narrow gaussian fit is < 1 mrad. The big improvement with respect to fits in a given super layer comes from the increased lever arm given by the distance between SL1 and SL3. Note: relevant correlations between fit results and variables obtained from offline segment possible

-- SilviaGoyLopez - 2019-04-08