Simulation study of lateral distribution properties of ultra-high energy cosmic ray air showers for the Telescope Array

Ultra-high energy cosmic rays (UHECRs) are extremely rare and of unknown origin. They are studied indirectly via air showers, but the reconstructed energy scale carries intrinsic uncertainties whose causes are not fully understood. We investigate the lateral distribution of particle densities in UHECR-induced showers simulated for the Telescope Array (TA) surface detectors using CORSIKA with QGSJET-II04, EPOS-LHC, and Sibyll 2.3e. Analyzing detector-level simulation outputs without reconstruction eliminates biases from the array layout and algorithms. The results show systematically steeper lateral distributions than the empirical function used in TA analysis. While 𝑆(800) remains a robust energy estimator, differences from the currently used look-up table are attributed to idealized versus realistic array assumptions. Hybrid events help calibrate this offset. Dependence on primary particle and interaction model is marginal. These findings support future efforts to derive average lateral distributions from data to constrain related uncertainties.