  The description of the modifications of the coherence pattern in a parton
shower, in the presence of a QGP, has been actively addressed in recent
studies. Among the several achievements, finite energy corrections, transverse
momentum broadening due to medium interactions and interference effects between
successive emissions have been extensively improved as they seem to be
essential features for a correct description of the results obtained in
heavy-ion collisions. In this work, based on the insights of our previous work
[1], we explore the physical interplay between broadening and decoherence, by
generalising previous studies of medium-modifications of the antenna spectrum
[2, 3, 4] - so far restricted to the case where transverse motion is neglected.
The result allow us to identify two quantities controlling the decoherence of a
medium modified shower that can be used as building blocks for a successful
future generation of jet quenching Monte Carlo simulators: a generalisation of
the $\Delta_{med}$ parameter of the works of [2, 4] - that controls the
interplay between the transverse scale of the hard probe and the transverse
resolution of the medium - and of the $\Delta_{coh}$ in [1] - that dictates the
interferences between two emitters as a function of the transverse momentum
broadening acquired by multiple scatterings with the medium.
