Real-time monitoring of LHCb interaction region with a fast trackless methodology

The increasing computing power and bandwidth of FPGAs opens new possibilities in the field of real-time processing of high-energy physics data. The LHCb experiment has implemented a cluster-finder FPGA architecture aimed at reconstructing hits in its innermost silicon-pixel detector on-the-fly during readout. In addition to accelerating the event reconstruction procedure by providing it with higher-level primitives, this system enables further opportunities. LHCb triggerless readout architecture makes these reconstructed hit positions available for every collision, amounting to a flow of $10^{11}$ hits per second, that can be used for further analysis. In this work, we have implemented a set of programmable counters, counting the hit rate at many locations in the detector volume simultaneously. We use these data to continuously track the motion of the beams overlap region and the relative position of the detector elements, with precisions of $\mathcal{O}\left(\mu m\right)$ and time granularity of $\mathcal{O}\left(ms\right)$. We show that this can be achieved by simple linear combination of data, that can be executed in real time with minimal computational effort. This novel approach allows a fast and precise determination of the beamline position without the need to reconstruct more complex quantities like tracks and vertices. We report results obtained with $pp$ collision data collected in 2024 at LHCb.