The radiation pattern of a QCD antenna in a dense medium

A bstract We calculate the radiation spectrum off a $ q\overline{q} $ pair of a fixed opening angle $ {\theta_{{q\overline{q}}}} $ traversing a medium of length L . Multiple interactions with the medium are handled in the harmonic oscillator approximation, valid for soft gluon emissions. We discuss the time-scales relevant to the decoherence of correlated partons traversing the medium and demonstrate how this relates to the hard scale that govern medium-induced radiation. For large angle radiation, the hard scale is given by $ {Q_{\mathrm{hard}}}=\max \left( {r_{\bot}^{-1 },{Q_s}} \right) $ , where $ {r_{\bot }}={\theta_{{q\overline{q}}}}L $ is the probed transverse size and Q s is the maximal transverse momentum accumulated by the emitted gluon in the medium. These situations define in turn two distinct regimes, which we call “dipole” and “decoherence” regimes, respectively, which are discussed in detail. A feature common to both cases is that coherence of the radiation is restored at large transverse momenta, k ⊥ > Q hard .