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Theoretical formalism of radiative jet energy loss in a finite size dynamical QCD medium

The computation of radiative energy loss in a finite size QCD medium with dynamical constituents is a key ingredient for obtaining reliable predictions for jet quenching in ultra-relativistic heavy ion collisions. We here present a theoretical formalism for the calculation of the first order in opacity radiative energy loss of a quark jet traveling through a finite size dynamical QCD medium. We show that, while each individual contribution to the energy loss is infrared divergent, the divergence is naturally regulated once all diagrams are taken into account. Finite size effects are shown to induce a non-linear path length dependence of the energy loss, recovering both the incoherent Gunion-Bertsch limit, as well as destructive Landau-Pomeanchuk-Migdal limit. Finally, our results suggest a remarkably simple general mapping between energy loss expressions for static and dynamical QCD media.