Coherent medium-induced gluon radiation in hard forward 1 → 1 partonic processes

We revisit the medium-induced coherent radiation associated to hard and forward (small angle) scattering of an energetic parton through a nuclear medium. We consider all 1→1 hard forward processes (g→g, q→q, q→g and g→q), and derive the energy spectrum of induced coherent radiation rigorously to all orders in the opacity expansion and for the specific case of a Coulomb scattering potential. We obtain a simple general formula for the induced coherent spectrum, which encompasses the results corresponding to previously known special cases.