Abstract

Cosmic rays that strike the top of the Earth’s atmosphere generate a shower of secondary particles that move toward the surface with relativistic speeds. Water Cherenkov detectors (WCDs) on the ground can detect charged muons, which are one of the many particles generated in the shower, with the Cherenkov imaging technique. A large number of these muons travel in WCD tanks near the speed of light in a vacuum, faster than the speed of light in water, and so trigger isotropic Cherenkov radiation, which is detected by the photomultiplier tubes (PMTs) placed inside the tanks. When the radial component of the speed of the muon toward a PMT drops from superluminal to subluminal, the PMT records Cherenkov light from an optical phenomenon known as relativistic image doubling (RID), which causes two Cherenkov images of the same muon to appear suddenly, with both images moving in geometrically opposite directions on the original muon track. The quantities associated with the RID effect can be measured experimentally with a variety of detector types and can be used to find various points on the original trajectory of the muon. In this paper, a detailed study of reconstructing the trajectory of a muon entering a WCD using the RID technique has been presented. It is found that the measurements of standard RID observables enables a complete reconstruction of the trajectory of the muon to a high degree of accuracy with less than 1% error.