Finite Formation Time Antenna Radiation: Color Spectators Break Single-Emitter BDMPS-Z

We compute the direct contribution to the squared matrix element for the in-medium soft gluon emission off a color-singlet quark-antiquark pair. To do this, we incorporate medium interactions that take place during the finite formation time of the antenna, thereby accounting for a largely neglected source of modifications with respect to the vacuum baseline. As a consequence, non-trivial correlations with the spectator (i.e.\ non-emitting) leg of the antenna emerge, greatly increasing the complexity of the result even at leading-$N_c$ order. The observed modifications entail a significant departure from the limit of instantaneous antenna formation, where the calculation effectively reduces to the well-known BDMPS-Z spectrum.