Propagation of muon induced Cherenkov photons through a diffusive medium

Analytic functions are derived that describe the arrival time distribution of photons (photoelectrons) induced by the passage of a high energy muon through a detector containing a Cherenkov medium that has scattering and absorptive properties. These functions, derived in the diffusive approximation, are as yet the best analytic descriptions of photon propagation from a moving point source of photons. As such, usage of these functions within the context of likelihood or other reconstruction algorithms will increase the pointing accuracy of neutrino telescopes that are embedded in ice or submerged in water.