The MIP Timing Detector will provide additional timing capabilities for detection of minimum ionizing particles (MIPs) at CMS during the High Luminosity LHC era, improving event reconstruction and pileup rejection. The central portion of the detector, the Barrel Timing Layer (BTL), will be instrumented with LYSO:Ce crystals and Silicon Photomultipliers (SiPMs) providing a time resolution of about 30 ps at the beginning of operation, and degrading to 50-60 ps at the end of the detector lifetime as a result of radiation damage. In this work, we present the results obtained using a 120 GeV proton beam at the Fermilab Test Beam Facility to measure the time resolution of unirradiated sensors. A proof-of-concept of the sensor layout proposed for the barrel region of the MTD, consisting of elongated crystal bars with dimensions of about 3 x 3 x 57 mm$^3$ and with double-ended SiPM readout, is demonstrated. This design provides a robust time measurement independent of the impact point of the MIP along the crystal bar. We tested LYSO:Ce bars of different thickness (2, 3, 4 mm) with a geometry close to the reference design and coupled to SiPMs manufactured by Hamamatsu and Fondazione Bruno Kessler. The various aspects influencing the timing performance such as the crystal thickness, properties of the SiPMs (e.g. photon detection efficiency), and impact angle of the MIP are studied. A time resolution of about 28 ps is measured for MIPs crossing a 3 mm thick crystal bar, corresponding to an MPV energy deposition of 2.6 MeV, and of 22 ps for the 4.2 MeV MPV energy deposition expected in the BTL, matching the detector performance target for unirradiated devices.
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