BeAGLE: Benchmark $e$A Generator for LEptoproduction in high energy lepton-nucleus collisions

The upcoming Electron-Ion Collider (EIC) will address several outstanding puzzles in modern nuclear physics. Topics such as the partonic structure of nucleons and nuclei, the origin of their mass and spin, among others, can be understood via the study of high energy electron-proton ($ep$) and electron-nucleus ($e$A) collisions. Achieving the scientific goals of the EIC will require a novel electron-hadron collider and detectors capable to perform high-precision measurements, but also dedicated tools to model and interpret the data. To aid in the latter, we present a general-purpose $e$A Monte Carlo (MC) generator - BeAGLE. In this paper, we provide a general description of the models integrated into BeAGLE, applications of BeAGLE in $e$A physics, implications for detector requirements at the EIC, and the tuning of the parameters in BeAGLE based on available experimental data. Specifically, we focus on a selection of model and data comparisons in particle production in both $ep$ and $e$A collisions, where baseline particle distributions provide essential information to characterize the event. In addition, we investigate the collision geometry determination in $e$A collisions, which could be used as an experimental tool for varying the nuclear density.