The probability density function of the arrival time of \v{C}erenkov light

TL;DR

This paper models the probability density function of Cherenkov light arrival times on photomultiplier tubes, considering production, transmission, and detection effects to improve understanding of light behavior in particle detection.

Contribution

It provides a comprehensive analysis of Cherenkov light arrival times, incorporating production, transmission, and detection factors for the first time.

Findings

Derived the probability density function considering multiple effects.

Quantified the impact of medium properties on light transmission.

Enhanced accuracy in timing measurements for Cherenkov detectors.

Abstract

The probability density function of the arrival time of \v{C}erenkov light on a photo-multiplier tube has been studied. This study covers light production, transmission and detection. The light production includes the light from a muon, the light from a shower and the light due to the energy loss of a muon. For the transmission of light, the effects of dispersion, absorption and scattering in the medium are considered. For the detection of light, the angular acceptance and the quantum efficiency of the photo-multiplier tube are taken into account.