Quark fracture function at small $x$ from the Color Glass Condensate

Abstract

The target-fragmentation region in deeply inelastic electron-nucleus scattering provides insight into the partonic structure of the target, as hadrons measured in the final state retain information about the nonperturbative dynamics of spectator partons inside the nucleus. In QCD factorization theorems, this nonperturbative dynamics is encoded in objects known as fracture functions. In this paper, we study the extended quark fracture function in the limit where the struck (anti)quark carries a very small longitudinal momentum fraction, $x$. We first present an elementary derivation within the Color Glass Condensate effective field theory of the quark fracture function in terms of the dipole operator at small $x$. At the parton level, the quark extended fracture function is sensitive to gluon saturation when the transverse momentum $P_\perp$ of the outgoing parton produced in the target-fragmentation region is smaller than the nuclear saturation scale $Q_s$, in which regime the $P_\perp$ distribution becomes approximately flat. We then show, through a numerical study that incorporates the convolution of this parton-level result with a collinear fragmentation function, that hadronization largely washes out these saturation effects, as the convolution predominantly probes partonic transverse momenta that are typically larger than $Q_s$.