Multiple parton radiation in hadroproduction at lepton-hadron colliders

I discuss the impact of the the coherent parton radiation on semi-inclusive production of hadrons in deep inelastic scattering at lepton-proton colliders. Such radiation can be consistently described in the $b$-space resummation formalism, which was originally developed to improve theoretical description of production of hadrons at $e^+e^-$ colliders and electroweak vector bosons at hadron-hadron colliders. I present the detailed derivation of the resummed cross section and the energy flow at the next-to-leading order of perturbative QCD. The theoretical results are compared to the experimental data measured at the $ep$ collider HERA. I argue that semi-inclusive deep inelastic scattering (SIDIS) at lepton-hadron colliders offers exceptional opportunities to study coherent parton radiation, which are not available yet at colliders of other types.