Prospects for early heavy-quark measurements at the EIC
We assess the prospects for inclusive heavy-quark-pair electroproduction in electron-proton ($ep$) and electron-nucleus ($e$A) collisions, alongside double-charm-pair ($D^0 \bar{D}^0$ and $D^0D^0$) electroproduction in $ep$ collisions, during the early operational phase of the Electron-Ion Collider (EIC). Based on the anticipated beam energies and luminosities of the EIC, we estimate the total cross sections and differential distributions for photon virtuality $Q^2$, heavy-quark transverse momentum, and rapidity. This analysis evaluates different Bjorken-$x$ ($x_{\rm Bj}$) intervals across a range of $Q^2$ values. Expected event yields are estimated from the projected integrated luminosities of the early science programme, demonstrating the substantial improvement in statistical precision over previous HERA measurements at moderate and large $x_{{\rm Bj}}$. For electron--nucleus collisions, we compute the nuclear modification ratio $R^{e\text{A}}$ within collinear factorisation using nuclear parton distribution functions, and identify the kinematic regimes in which shadowing, anti-shadowing, and EMC-like suppression are accessible with early EIC data. These results are intended to serve as a parton-level baseline to support feasibility studies and to provide a reference for future higher-order theoretical and experimental investigations at the EIC.