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Color coherence in a heavy quark antenna radiating gluons inside a QCD medium

We compute the color coherence effects for soft gluon radiation off antennas containing heavy quarks in the presence of a QCD medium - in color singlet, triplet or octet global states. This work completes the studies of antenna radiation inside a medium which provide a useful picture of the relevance of interference effects in jet parton showers for the jet quenching phenomenon observed in high-energy nuclear collisions. The analysis is performed resumming the multiple scatterings of the partonic system with the medium. The main conclusion is that decorrelation due to color rotation is more effective in the case in which at least one of the emitters of the antenna is a heavy quark. This effect, present both for a heavy-quark-antiquark or a heavy-quark-gluon antenna is more relevant for the later or for the case in which the energies of the quark and antiquark are very different. The parameter controlling these effects involves the dead-cone angle. We find that interferences are cancelled, spoiling the color correlation of the pair, when $θ_{ DC}=M/E >>1/\sqrt{ωL}$ where E and ω are the energies of the heavy quark and the radiated gluon and L is the medium length. In the case of a heavy-quark-antiquark antenna $t_{form}$ appears instead of L if the original splitting is symmetric. The presence or absence of interferences modifies the energy loss pattern.