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A new high-granular compact time-of-flight neutron detector for theidentification and energy measurement of neutrons produced in nucleus-nucleusinteractions at the BM@N experiment, Dubna, Russia, at energies up to 4 AGeV isunder development. The detector consists of approximately 2000 fast plasticscintillators, each with dimensions of 40$\times$40$\times$25 mm$^3$, equipedwith SiPM (Silicon Photomultiplier) with an active area of 6$\times$6 mm$^2$.The signal readout from these scintillators will employ a single-thresholdmultichannel Time-to-Digital Converter (TDC) to measure their response time andamplitude using the time-over-threshold (ToT) method. This article focuses onthe analytical description of the signals from the plastic scintillatordetectors equipped with silicon photomultipliers. This description is crucialfor establishing the ToT-amplitude relationship and implementing slewingcorrection techniques to improve the time resolution of the detector. Themethodology presented in this paper demonstrates that a time resolution at the70 ps level can be achieved for the fast plastic scintillator coupled withsilicon photomultiplier with epitaxial quenching resistors.

Analytical description of the time-over-threshold method based on the  time properties of plastic scintillators equipped with silicon  photomultipliers