Time resolution studies for the future LHCb Electromagnetic Calorimeter

During Runs 5 and 6 of the Large Hadron Collider (LHC), the LHCb experiment at CERN will operate at a luminosity up to $1.5\times10^{34}\text{cm}^{-2} \text{s}^{-1}$, requiring substantial upgrades to its Electromagnetic Calorimeter (ECAL). Specifically, the upgraded detector will have to withstand high radiation doses and achieve time resolutions of a few tens of picoseconds in order to mitigate pile-up effects. The inner and high-occupancy regions of the future detector — named PicoCal — will utilize a new Spaghetti-Calorimeter (SpaCal) technology composed of scintillating fibres (polystyrene or garnet crystals) in a dense absorber (lead or tungsten). Ongoing investigations are focused on the photodetectors (PMTs) selection and their impact on the overall timing performance. Simulation studies of a lead-polystyrene module with single-sided readout (PMTs coupled only to the downstream side) show that fast PMTs result in worse time resolutions due to the longitudinal showers' fluctuations, which introduce a bias in the timestamps determined by the Constant Fraction Discriminator (CFD) algorithm. This hypothesis was corroborated by observing that a significant improvement in time resolution would be achievable if the positions of the electromagnetic shower barycenters were known. Additionally, a correlation between signal rise time and depth of the electromagnetic showers has been observed. Data from a test beam campaign conducted at the CERN SPS in June 2024 have been analysed to measure the time resolution of a tungsten-polystyrene SpaCal prototype, comparing four PMT models and two fibre types. By exploiting a rise-time-based correction procedure, time resolutions below 20 ps at high energies have been reached, with the fastest PMTs undergoing larger corrections, as expected from simulations.