Abstract

In this paper, we study the electroproduction of open heavy flavor and mesons in the kinematics of future colliders, such as the Electron Ion Collider (EIC), the Large Hadron electron Collider (LHeC), and the Future Circular Collider (FCC-he). We study in detail the dependence of the cross sections on multiplicity of coproduced hadrons, in view of its possible sensitivity to contributions from multi-Pomeron contributions, and discuss different observables which might be used for its study. According to our theoretical expectations, in collisions the multi-Pomeron contributions are small in the EIC kinematics, although they might be sizable at LHeC and FCC-he. We also provide theoretical predictions for the production cross sections of heavy mesons in the kinematics of all the above-mentioned colliders.