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Interference effects in medium-induced gluon radiation

As a step towards understanding the in-medium evolution of a hard jet, we consider the interference pattern for the medium induced gluon radiation produced by a color singlet quark-antiquark antenna embedded in a QCD medium with size L. We focus on the typical kinematics for medium-induced gluon radiation in the BDMPS-Z regime, that is, short formation times τ_f << L and relatively large emission angles θ>>θ_c = 2/\sqrt{\hat q L^3}, with \hat q the `jet quenching' parameter. We demonstrate that, for a dipole opening angle θ_{q\bar q} larger than θ_c, the interference between the medium-induced gluon emissions by the quark and the antiquark is parametrically suppressed with respect to the corresponding direct emissions. Physically, this is so since the direct emissions can be delocalized anywhere throughout the medium and thus yield contributions proportional to L. On the contrary, the interference occurs only between gluons emitted at very early times, within the characteristic time scales for quantum and color coherence between the two emitters, which in this regime are much smaller than L. This implies that, for θ_{q\bar q} >> θ_c, the medium-induced radiation by the dipole is simply the sum of the two BDMPS-Z spectra individually produced by the quark and the antiquark, without coherence effects like angular ordering. For θ_{q\bar q} << θ_c, the BDMPS-Z radiation by the dipole vanishes.