Centrality definition in e + A collisions at the electron-ion collider

In this work, we investigate the feasibility of defining centrality in electron-ion collisions at the electron-ion collider (EIC) by examining the correlation between the impact parameter and several observables, including total energy, total transverse momentum, and total number of particles. Using the BeAGLE Monte Carlo generator, we simulate e + Au and e + Ru collisions at different energies and analyze the correlation between the impact parameter and these observables across different kinematic regions. Our findings indicate that the correlation is weak in the central rapidity region but becomes stronger in the forward and far-forward rapidity regions. However, the correlation is not sufficiently robust to allow for precise centrality determination. We conclude that defining centrality in electron-ion collisions is more challenging than in ion-ion collisions, necessitating further studies to develop a robust centrality definition for the EIC.