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Cold nuclear matter effects in reactions with nuclei at a future electron-ioncollider (EIC) lead to a modification of semi-inclusive hadron production, jetcross sections, and jet substructure when compared to the vacuum. At leadingorder in the strong coupling, a jet produced at an EIC is initiated as anenergetic quark, and the process of this quark splitting into a quark-gluonsystem underlies experimental observables. The spectrum of gluons associatedwith the branching of this quark jet is heavily modified by multiple scatteringin a medium, allowing jet cross sections and jet substructure to be used as aprobe of the medium's properties. We present a formalism that allows us tocompute the gluon spectrum of a quark jet to an arbitrary order in opacity, theaverage number of scatterings in the medium. This calculation goes beyond thesimplifying limit in which the gluon radiation is soft and can be interpretedas energy loss of the quark, and it significantly extends previous work whichcomputes the full gluon spectrum only to first order in opacity. Thetheoretical framework demonstrated here applies equally well to light partonand heavy quark branching, and is easily generalizable to all in-mediumsplitting processes.

Quark branching in QCD matter to any order in opacity beyond the soft gluon emission limit