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

Abstract

Cold nuclear matter effects in reactions with nuclei at a future electron-ion collider (EIC) lead to a modification of semi-inclusive hadron production, jet cross sections, and jet substructure when compared to the vacuum. At leading order in the strong coupling, a jet produced at an EIC is initiated as an energetic quark, and the process of this quark splitting into a quark-gluon system underlies experimental observables. The spectrum of gluons associated with the branching of this quark jet is heavily modified by multiple scattering in a medium, allowing jet cross sections and jet substructure to be used as a probe of the medium's properties. We present a formalism that allows us to compute the gluon spectrum of a quark jet to an arbitrary order in opacity, the average number of scatterings in the medium. This calculation goes beyond the simplifying limit in which the gluon radiation is soft and can be interpreted as energy loss of the quark, and it significantly extends previous work which computes the full gluon spectrum only to first order in opacity. The theoretical framework demonstrated here applies equally well to light parton and heavy quark branching, and is easily generalizable to all in-medium splitting processes. *

A complete set of in-medium splitting functions to any order in opacity

“…As was shown for the q → qg branching in Ref. [17], the splitting functions can be expressed in terms of the following quantities: the light-front wave function (LFWF) of the branching ψ [37,38], the corresponding energy denominator ∆E − , the cross-section dσ el d 2 q to interact with a scattering center in the medium, and the scattering length λ of a parton. These features are universal to all partonic branching channels a → bc and to any QCD medium; the LFWF themselves will differ for different channels, but the way in which they are dressed by the medium is the same.…”

“…The basis of the opacity expansion and the current state of the field are reviewed in Ref. [17] and the references therein.…”

“…In Ref. [17] we constructed a new framework to compute these splitting functions to higher orders in the opacity expansion, which was previously limited to either the soft-gluon approximation x 1 or to first order in opacity. With the derivation of the full in-medium splitting functions and theoretical formalisms that bridge the gap between high energy and heavy ion physics, the question of corrections from higher orders in opacity must now be revisited.…”

Jet charge modification in finite QCD matter

“…Relation of this technique to other approaches to evaluate inelastic processes in matter is discussed in Ref. [55]. The opacity expansion was first developed in the soft-gluon emission parton energy loss limit.…”

“…At LHC energies early works [66,67] found that the first order in opacity is a good approximation for jet quenching applications. Recently, the full splitting functions have been calculated analytically to higher orders in opacity [55,56], but their numerical evaluation remains computationally intensive. For these reasons we will use the medium-induced splitting functions up to first order in opacity and focus on light flavor jets.…”