Reconstruction of tracks in real time in the high luminosity environment at LHC

In modern experiments at high-energy hadron colliders, powerful real-time tracking systems are needed to reconstruct and quickly select potentially interesting events for higher level of processing, and finally permanent storage for subsequent analysis. The problem is particularly challenging at experiments like LHCb, at the Large Hadron Collider, that aim at flavor events where there are no easily identifiable event characteristics that can be used for preselection, like total $E$$_{T}$, missing $E$$_{T}$, or high-pT leptons. This means that all events need to be tracked at the full crossing rate of 40 MHz. In this thesis we study in detail for the first time, with fully developed application to a specific detector, the potential of a new tracking algorithm inspired from neurobiology aspects of the visual mechanism in mammals, the so called "artificial retina" algorithm. This algorithm is based on massively parallel calculation of the response of an array of cells (each of them representing a region in the track parameter space) of tracks stored in a pattern database, covering the entire parameter space in which tracks are defined. By interpolating the response of adjacent cells, it is possible to obtain good performances while keeping the number of cells within manageable limits. Programmable electronic devices (FPGA) characterized by high speed, high bandwidth, and low latency are now available with sufficient computing power to implement realistic systems of this kind. We describe the design of a specialized Track Processing Unit (TPU), a Level-0 tracker system, that implements the artificial retina algorithm on FPGA devices, applied to the 2020 Upgrade of the LHCb experiment. The TPU was designed to process events at the LHC bunch-crossing rate of 40 MHz, providing high-quality tracks to the rest of LHCb DAQ system simultaneously with the detector data flow, acting as an additional virtual sub-detector providing tracks, instead detector hits. This allows both a selection of interesting events at very early stage in the trigger chain (Level-0 rate reduction) and saving the computing time needed for the track finding task, the most expensive tracking job from what concerning the needed computing resources for the higher-level trigger systems. A software simulation in C++ language has been developed to study the TPU potential and performances for the LHCb tracking task. This software simulation describes the TPU system in full detail, with no parametrization or other approximations involved. We found that it is possible to reconstruct tracks in the Vertex Locator Pixel (VELOPIX) and Upstream silicon Tracker (UT) subdetectors, performing one of the most important tracking sequence of the LHCb Upgrade. We used a total of 16+2 layers, with a system based on just about 50,000 cells of the track parameter space. This system is implementable in a reasonably limited number (<100) of FPGA devices and can process online all events at the full LHCb bunch-crossing rate, at luminosity of L = 3 x 10$^{33}$ cm$^{-2}$ s$^{-1}$. An interface with the official realistic LHCb Upgrade simulation has been also developed, by which is possible to process realistic LHCb events trough the TPU. Measurements of the TPU tracking performance have been done and compared with the standard offline reconstruction. A few important physics processes are simulated as benchmark for our system: $B$$_{s}^{0}$ to $\phi$(1020)$\phi$(1020), $D$$^{0}$ to $K$$_{s}^{0}$$\pi$$^{+}$$\pi$$^{-}$, $B$$_{D}^{0}$ to $K$$^{*}$(892)$^{0}$$\mu$$^{+}$$\mu$$^{-}$. All of them are golden modes for studying CP violation in the charm and beauty sectors and represent an important benchmark for a tracker system because of low momenta of decay products. Collecting enriched high-purity samples of these decays necessitates offline quality level measurement of all track parameters at early stages in the trigger chain. The B to K mu^+ mu^- decays, unlike the fully hadronic modes, take advantage in the trigger chain by the presence of muons in the final states. Even in this case, the expected high level of occupancy of muon sub-detectors at the LHCb-Upgrade conditions means that we can benefit from a confirmation from the tracker system of the “muon track” already at Level-0 of the trigger system. For these reasons, the considered signal events are good representatives of the variety of decay processes that are the main goals of LHCb physics program. As a result of our work, we obtained TPU tracking performances closely comparable to the offline reconstruction, for all considered benchmark processes. In order to perform a test on real data from the past LHC run, we additionally have designed an alternative configuration that can be applied on current tracking detectors. We have performed some basic tests on the silicon Inner Tracker (IT) subdetectors, used by LHCb reconstruction algorithms for track momentum measurement. Applying our system to 2012 LHCb real data, we have found that it is capable to reconstruct tracks in real time with momentum resolution near to the offline reconstruction, resorting to significantly less information than the offline algorithm. In conclusion, with this thesis work we designed a device for real-time tracking, based on the artificial retina algorithm, implemented in a realistic detector environment. It provides high-quality tracks at the LHC bunch-crossing rate of 40 MHz, and it is capable to select at Level-0 stage high-purity signal samples for higher-level trigger systems.