A method for luminosity determination based on real-time hit reconstruction with the LHCb silicon pixel detector

The data acquisition system of the upgraded LHCb experiment includes the fast reconstruction of all hits in the vertex locator (VELO) pixel detector at the beam-crossing rate of 40 MHz, implemented as on-the-fly clustering embedded in the firmware of the readout board FPGAs. The availability of a high rate of reconstructed clusters in real time enables a new fast approach for measuring luminosity and monitoring the LHCb luminous region, directly at the detector readout level. This methodology has been implemented as an array of real-time cluster counters in the VELO readout FPGAs and has been in operation since the start of the 2024 physics run of LHCb. This paper describes the methodology and its features and performance, both on proton-proton and lead-lead collision data. The method shows a statistical resolution better than the percent level, and a sensitivity to variable running conditions of the same level. This is achieved with an intrinsic time granularity better than 100 ms, undersampled to 3 s for analysis purposes. Nonlinear behaviour is compatible with zero in a luminosity range including the LHCb Run 3 operating point.