Tracing the evolution of nuclear excitation at the future Electron-Ion Collider

The evolution of nuclear excitation in electron-gold ( <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"> <a:mrow> <a:mi>e</a:mi> <a:mspace width="0.16em"/> <a:mo>+</a:mo> <a:mspace width="0.16em"/> <a:mi>Au</a:mi> </a:mrow> </a:math> ) collisions at the forthcoming Electron-Ion Collider (EIC) is investigated using the event generator. The EIC's collider kinematics and detector-motivated rapidity selections enable a clear separation, in the laboratory frame, of the dominant reaction stages: hard scattering, intranuclear cascade (INC), and nuclear deexcitation. A systematic study of the event-by-event mean transverse momentum fluctuation observable <d:math xmlns:d="http://www.w3.org/1998/Math/MathML"> <d:mi>κ</d:mi> </d:math> reveals strong sensitivity to the intranuclear-cascade formation time and to nuclear geometry, with only weak dependence on the electron-beam energy. These findings indicate that <e:math xmlns:e="http://www.w3.org/1998/Math/MathML"> <e:mi>κ</e:mi> </e:math> can serve as an exploratory diagnostic for disentangling the cascade and deexcitation stages of nuclear excitation at the EIC. The pronounced sensitivity observed within the framework underscores the model dependence of the present results while at the same time motivating systematic cross-model investigations to establish the broader applicability of <f:math xmlns:f="http://www.w3.org/1998/Math/MathML"> <f:mi>κ</f:mi> </f:math> . The results yield stage-resolved, testable predictions for early EIC measurements.