From RHIC to EIC: Nuclear Structure Functions

We study the nuclear structure function $F_2^A$ and its logarithmic derivative in the high energy limit (small $x$ region) using the Color Glass Condensate formalism. In this limit the structure function $F_2$ depends on the quark anti-quark dipole-target scattering cross section $N_F (x_{bj}, r_t, b_t)$. The same dipole cross section appears in single hadron and hadron-photon production cross sections in the forward rapidity region in deuteron (proton)-nucleus collisions at high energy, i.e. at RHIC and LHC. We use a parameterization of the dipole cross section, which has successfully been used to describe the deuteron-gold data at RHIC, to compute the nuclear structure function $F_2^A$ and its log $Q^2$ derivative (which is related to gluon distribution function in the double log limit). We provide a quantitative estimate of the nuclear shadowing of $F_2^A$ and the gluon distribution function in the kinematic region relevant to a future Electron-Ion Collider.