Factorization and virtuality evolution of jet functions in heavy-ion collisions

Abstract

We develop a new framework to perform a virtuality-resolved description of jet propagation in heavy-ion collisions using perturbative techniques. The role of virtuality is rigorously identified by first deriving a factorized jet cross section that defines an in-medium jet function. This new definition allows to extend the usual BDMPS-Z formalism to include the virtuality-differential transverse momentum broadening distribution and medium-induced soft gluon spectrum. We study both the cases of a medium which is created with some delay time $τ_0$ after the hard collision as well as the case in which $τ_0\to 0$. Integration over the complete virtuality range recovers the standard BDMPS-Z results, while finite virtuality reveals the interplay between vacuum-like evolution and medium-induced dynamics. We identify the ratio between the medium formation time and the jet formation time as the variable controlling which initial virtualities contribute appreciably to the jet function.