Revisiting scaling properties of medium-induced gluon radiation

Discussing the general case of a hard partonic production process, we show that the notion of parton energy loss is not always sufficient to fully address medium-induced gluon radiation. The broader notion of gluon radiation associated with a hard process has to be used, in particular, when initial and final-state radiation amplitudes interfere, making the medium-induced radiated energy different from the energy loss of any well-identified parton. Our arguments are first presented in an Abelian QED model, and then applied to large-x(F) quarkonium hadroproduction. In this case, we show that the medium-induced radiated energy is qualitatively similar (but not identical) to the radiative energy loss of an asymptotic massive parton undergoing transverse momentum broadening when travelling through the nucleus. In particular, it scales as the incoming parton energy, which suggests that gluon radiation should be reconsidered as a possible explanation of large x(F) quarkonium suppression in p-A collisions. We expect a similar effect in open heavy-flavor and possibly light-hadron hadroproduction at large x(F).