• Artifical Retina
• Heavy Flavor Physics
• LHCb
• Realtime
• Tracking

The precise measurement of flavour-changing transitions in hadrons is a long established and powerful tool to precisely study the dynamics of the Standard Model, and simultaneously to seek out manifestations of new physics phenomena.
The mass scales that can be probed in loop-level processes are far higher than those that can be accessed in direct searches for on-shell particles. Furthermore, many of the open questions in fundamental physics reside in the flavour sector. The LHCb experiment has demonstrated that the LHC is an ideal laboratory for quark-flavour physics. The current LHCb detector, operating at a luminosity of 4 × 10^32 cm^−2 s^−1 , will continue data taking until the end of Run 2 of the LHC, in 2018. During Long Shutdown 2 (LS2) it will be replaced by an upgraded experiment, referred as the Phase-I Upgrade (LHC Run 3, 2021-2024 and LHC Run 4, 2027-2030). The Phase-I Upgrade, operating at a luminosity of L = 2 × 10^33 cm^−2 s^−1, will greatly improve the sensitivity of many flavour studies. However, the precision on a host of important, theoretically clean, measurements will still be limited by statistics, and other observables associated with highly suppressed processes will be poorly known. There is therefore a strong motivation for a consolidation of the the Phase-I Upgrade in view of the LHC Run 41, and for building a Phase-II Upgrade, which will fully realize the flavour potential of the HL-LHC during the LHC Run 5 (≥ 2031) at luminosity L > 10^34 cm^-2 s^−1.
Although the trigger strategy of both the Phase-I and Phase-II Upgrades is software based, studies are underway to learn what benefits could accrue by adding dedicated processors to help solve specific low-level tasks. One relevant example is to find tracks downstream of the magnet at the earliest trigger level. This capability is not part of the baseline trigger scheme on account of the significant CPU time required to execute the search. Not having access to this information greatly limits efficiency for decay modes with downstream tracks that cannot easily be triggered through another signature, for example channels containing a Ks and less than two prompt charged hadrons, for example B → KS KS , B → KS KS KS , B → ηKS , B → φKS , B → ωKS , D0 → KS KS , Ds → KS π , D+ → KS K , KS → μμ, etc. The same is true for decays involving Λ baryons (i.e. Λ0 b → 3Λ) and long-lived exotic particles (hidden sector WIMP Dark Matter and Majorana neutrinos).
The LHCb Pisa group has recently proposed an innovative tracking device, the so called Downstream Tracker, capable of reconstructing in real-time long-lived particles in the context of the envisioned Future Upgrades (beyond LHC Run 3) of the LHCb experiment, with the aim of recovering the reconstruction efficiency of the downstream tracks. Such a specialized processor is supposed to obtain a copy of data from the readout system, reconstruct downstream tracks, and insert them back in the readout chain before the event is assembled, in order to be sent to the high level trigger in parallel with the raw detector information. This approach, where tracks can be seen as the output of an additional “embedded track detector” is based on the artificial retina algorithm, which is a highly-parallel pattern-matching algorithm, whose architectural choices, inspired to the early stages of image processing in mammals, make it particularly suitable for implementing a track-finding system in present-day FPGAs. First small prototypes of track-processing unit, able to reconstruct two-dimensional straight-line tracks in a 6-layers realistic tracking detector, based on the artificial retina algorithm have been designed, simulated, and built using commercial boards, equipped with modern high-end FPGAs.
Throughputs in processing realistic LHCb-Upgrade2 events in the range of tens of MHz and latencies lesser than 1 μs have been achieved running at the nominal clock speed, demonstrating the feasibility of fast track-finding with a FPGA-based system.
This open the way for a full realistic application as the Downstream Tracker. In fact, the design can be scaled to larger area detectors and to higher input rates in a cost-effective way.
The aim of this thesis project is to assess the tracking performance, that such an approach could achieve to the Future Upgrades of the LHCb experiment, for the realization of the Downstream Tracker project. This will be evaluated within known budget constraints; an affordable size of such an envisioned device has to be of about 10^5 pattern cells, where each of them corresponds to about 1000 Logic Elements (LEs). A high-level simulation of the envisioned device, written in C++ programming language, has been therefore developed in order to determine the achievable tracking performances, given the above constraints on the size of the system and on the compliance with the future LHCb data acquisition system. The main task of thesis has been the precise determination of the tracking parameters in reconstructing LHCb-Upgrade downstream tracks, such as the reconstruction efficiency and the probability of reconstructing fake tracks (’ghosts’) as a function of track parameters, along the resolution in measuring three-dimensional momentum and space trajectory. Lastly, an exhaustive comparison between simulated tracks, reconstructed by the envisioned device, and tracks reconstructed with LHCb-Upgrade offline tracking program, running in the high level trigger sequence, has been carried out in order to assess tracking performance in absolute terms. In particular, the thesis project has faced the challenge of reconstructing the so-called T-tracks, i.e. the tracks reconstructed using hits from the Scintillating Fibre Tracker detector (SciFi detector) located downstream the dipole magnet. This is the first, and the most CPU-time consuming, stage of the reconstruction of downstream tracks.
The thesis presents the first results on the reconstruction of the three-dimensional T-tracks of a generic LHCb-Upgrade event. Using a number of 2 × 10^5 pattern cells, corresponding to about 1300 pattern cells in a single FPGA chip, it has been possibile to solve the pattern recognition both in the axial (10^5 pattern cells for 6-axial layers) and stereo (10^5 pattern cells for 6-stereo layers) views of the SciFi detector.
The SciFi detector has the highest hits occupancy amongst the LHCb-Upgrade sub-detectors with an average number of reconstructible tracks per event of about 140 tracks/event, where the long tail of the distribution reaches values up to 400 tracks/event. Both reconstruction efficiency and ghost rate5 are comparable to those obtained with the official offline tracking program; a generic T track is reconstructed with an efficiency of about 70% with a ghost rate of about 20%. Requiring a minimal momentum threshold, as three-dimensional momentum larger than 5 GeV, and that the track has to be a downstream track or it has to come from the interaction point, efficiencies in the range of 90% are achieved. Resolution on the measurement of track parameters are also comparable to those obtained with the official offline tracking program.
In conclusion, this thesis presents the first study of the performance of real-time reconstruction of tracks in the SciFi detector achievable with the artificial retina algorithm, using fully simulated events at the LHCb Upgrade (LHC Run 4) conditions.
This is a crucial milestone on the path of the realization of the Downstream Tracker processor for the Future Upgrades of the LHCb experiment. This thesis has shown that tracking performance obtainable with this approach is comparable with the offline software reconstruction performance.