Hardware Implementation of a Fast Algorithm for the Reconstruction of Muon Tracks in ATLAS Muon Drift-Tube Chambers for the First-Level Muon Trigger at the HL-LHC

The High-Luminosity LHC will provide the unique opportunity to explore the nature of physics beyond the Standard Model of strong and electroweak interactions. Highly selective first level triggers are essential for the physics programme of the ATLAS experiment at the HL-LHC where the instantaneous luminosity will exceed the LHC Run 1 instantaneous luminosity by almost an order of magnitude. The ATLAS first level muon trigger rate is dominated by low momentum muons, selected due to the moderate momentum resolution of the resistive plate and thin gap trigger chambers. This limitation can be overcome by including the data of the precision muon drift tube (MDT) chambers in the first level trigger decision. This requires the fast continuous transfer of the MDT hits to the off-detector trigger logic and a fast track reconstruction algorithm performed in the trigger logic. In order to demonstrate the feasibility of reconstructing tracks in MDT chambers within the short available first-level trigger latency of about 3~$\mu$s we implemented a seeded Hough transform on the ARM Cortex A9 microprocessor of a Xilinx Zynq FPGA and studied its performance with test-beam data recorded in CERN's Gamma Irradiation Facility. We could show that by using the ARM processor's Neon Single Instruction Multiple Data Engine to carry out 4 floating point operations in parallel the challenging latency requirement can be matched.