Coulomb corrections to inclusive cross sections at the future Electron-Ion Collider

The experimental results of the future Electron-Ion ($eA$) Collider are expected to constrain the dynamics of the strong interactions at small values of the Bjorken $x$ variable and large nuclei. Recently it has been suggested that Coulomb corrections can be important in inclusive and diffractive $eA$ interactions. In this paper, we present a detailed investigation of the impact of the Coulomb corrections to some of the observables that will be measured in the future $eA$ collider. In particular, we estimate the magnitude of these corrections for the charm and longitudinal cross sections in inclusive and diffractive interactions. Our results demonstrate that the Coulomb corrections for these observables are negligible, which implies that they can be used to probe the QCD dynamics.

Figure 1

Dependence on the photon virtuality $Q^2$ for different atomic numbers and $x={10}^{-4}$ of the ratio between the electromagnetic and strong contributions for the inclusive (left panel) and diffractive (right panel) cross sections.

Figure 2

Ratio ${\sigma }_{\mathrm{diff}}/{\sigma }_{\mathrm{tot}}$ as a function of $Q^2$ for fixed $x$ (left panel) and as a function of $x$ for fixed $Q^2$ (right panel).

Figure 3

Flavor decomposition for the ratio between the electromagnetic and strong contributions for the inclusive (left panel) and diffractive (right panel) processes as a function of photon virtuality $Q^2$ and fixed $x={10}^{-4}$ for gold nucleus.

Figure 4

Dependence on $Q^2$ (left panel) and $x$ (right panel) of the ratios between the charm and total cross sections for inclusive and diffractive interactions.

Figure 5

Upper panels: Dependence on $Q^2$ of the ratio between the electromagnetic and strong longitudinal cross sections for the inclusive (left) and diffractive (right) interactions. Lower panels: Dependence on $Q^2$ of the ratio between the electromagnetic and strong transverse cross sections for inclusive (left) and diffractive (right) interactions.

Figure 6

Dependence on $Q^2$ (left panel) and $x$ (right panel) for the ratio between the longitudinal and total cross sections for inclusive and diffractive interactions.