Development and validation of the signal simulation for the underground muon detector of the Pierre Auger Observatory

The underground muon detector of the Pierre Auger Observatory is aimed at attaining direct measurements muonic component extensive air showers produced by cosmic rays with energy from $10^{16.5}$ eV up to region ankle (around $10^{18.7}$ eV). It consists two nested triangular grids scintillators 433 m, and 750 m spacings a total 71 positions, each 192 scintillator strips (30 m$^2$) deployed 2.3 underground. light impinging muons in propagated optical fibers towards an array silicon photomultipliers. In this work, we present development, validation, performance end-to-end tool for simulating response single-muon signals, which constitutes basis further simulations whole array. Laboratory data simulation outcomes are found consistent, showing that can measure single muons, efficiency 99 %, about 1050 particles arriving exactly same time 30 m$^2$ scintillator.