Abstract

In this paper, we study the electroproduction of open heavy flavor D and B mesons in the kinematics of future ep 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 ep 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 ep colliders.