Fluctuation of TeV to EeV Energy Muons and Induced Muon Showers in Water

TL;DR

This paper presents a precise Monte Carlo method to analyze the fluctuations in the range and behavior of ultra-high-energy muons in water, including their induced cascade showers, validated by analytical comparisons.

Contribution

It introduces an exact stochastic Monte Carlo approach for muon propagation in water that avoids the traditional continuous approximation, improving accuracy in modeling high-energy muon behavior.

Findings

Calculated muon range fluctuations and survival probabilities.

Generated cascade showers from various radiative processes.

Validated Monte Carlo results with analytical methods.

Abstract

By using the integral method in the muon propagation through water, we calculate the range fluctuation of high and ultra high energy muons. Many authors divide all radiative processes into two parts, namely, the continuous part and radiative part in their Monte Carlo simulation in order to consider the fluctuation in the both ranges and energies of the muons, while we treat all stochastic processes as exactly as possible, without the introduction of the continuous parts in all stochastic processes. The validity of our Monte Carlo method is checked by the corresponding analytical method which is methodologically independent on the Monte Carlo procedure. Accompanied cascade showers are generated by the direct electron pair production, bremsstrahlung and photo-nuclear interaction. These showers are calculated by the exact Monte Carlo Method in one dimensional way. We report survival probabilities, range distributions and examples of individual muon behavior.