Towards factorization with emergent scales for jets in dense media

Employing the recently developed open quantum system Effective Field Theory framework, we investigate jet production and evolution in a dense nuclear medium in electron-ion/heavy-ion collisions. We confirm that the frequent monitoring of the jet by the medium leads to the emergence of a perturbative transverse momentum scale, often referred to as the saturation scale that necessitates further factorization to completely isolate the non-perturbative physics of the medium. A part of this goal is achieved in this paper by providing an operator definition for the broadening probability of a gluon in the medium within the Markovian approximations. We show that this distribution is (semi)universal; it depends on the angular measurement on the jet and probes both the large and small $x$ dynamics of the medium. We further elucidate all other contributions to non-perturbative physics suggesting that the parameterization of non-perturbative physics is more complex than previously assumed and outline steps required for a complete factorization of the jet production cross section.