Realistic arrival time distribution from an isotropic light source

TL;DR

This paper derives a realistic probability density function for photon arrival times in high energy neutrino telescopes, accounting for detector resolution and medium scattering, enhancing event reconstruction accuracy.

Contribution

It introduces a new expression for the photon time delay distribution considering finite detector resolution and medium scattering effects.

Findings

Derived an explicit probability density function for photon arrival times.

Analyzed the asymptotic behavior of the distribution.

Discussed implications for event reconstruction in neutrino telescopes.

Abstract

The event reconstruction in high energy neutrino telescopes is based on the expression of the time delay distribution of the detected photons propagating to some distance from their emission point through a uniform and scattering medium. Considering a realistic detector with a finite time resolution, we derive an expression for the probability density function of the time delay of detected photons. The asymptotic properties of this function as well as its corresponding cumulative probability distribution are calculated and discussed.