Two-gluon emission and interference in a thin QCD medium: insights into jet formation

In heavy-ion collisions, an abundant production of high-energy QCD jets allows to study how these multiparticle sprays are modified as they pass through the quark-gluon plasma. In order to shed new light on this process, we compute the inclusive two-gluon rate off a hard quark propagating through a color deconfined medium at first order in medium opacity. We explicitly impose an energy ordering of the two emitted gluons, such that the "hard" gluon can be thought of as belonging to the jet substructure while the other is a "soft" emission (which can be collinear or medium-induced). Our analysis focusses on two specific limits that clarify the modification of the additional angle- and formation time-ordering of splittings. In one limit, the formation time of the "hard" gluon is short compared to the "soft" gluon formation time, leading to a probabilistic formula for production of and subsequent radiation off a quark-gluon antenna. In the other limit, the ordering of formation is reverted, which automatically leads to the fact that the jet substructure is resolved by the medium. We observe in this case a characteristic delay: the jet radiates as one color current (quark) up to the formation of the "hard" gluon, at which point we observe the onset of radiation of the new color current (gluon). Within our kinematic constraints, our computation supports a picture in which the in-medium jet dynamics are described as a collection of subsequent antennas which are resolved by the medium according to their transverse extent