Analytical Method (AM) for DT Trigger Primitive Generation in Phase 2

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 5-7.5x10$^{34}$cm$^{-2}$s$^{-1}$. 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. In a final step, information from both DT and RPC systems can be merged to form the so-called super-primitives (SP). Initial performance studies of the AM method, with and without using RPC information, are shown here, using a variety of methods. Efficiency and resolutions are measured based on simulations of the Phase 2 detector and conditions. Studies have been done using the current readout chain to mimic the input to the DT Phase 2 electronics, due to their similar characteristics. These have been used to validate the DT-only TP software emulator to firmware comparisons using prototype boards of the new backend system. Initial results from cosmics data taking in the Slice Test, where a CMS DT sector has been instrumented with HL-LHC DT electronics prototypes running the AM firmware for trigger primitive generation, are presented as well.