Small-$x$ factorisation in the target fragmentation region

TL;DR

This paper derives a factorised expression for jet production in the target fragmentation region of DIS at small x, highlighting the role of extended fracture functions and their sensitivity to saturation effects.

Contribution

It introduces a novel factorisation formula for target fragmentation jet production at small x, extending the concept of fracture functions to this kinematic regime.

Findings

The cross-section is not power suppressed in P_/Q for longitudinal photons.

The extended quark jet fracture function is highly sensitive to saturation effects.

The derived formula is valid at next-to-leading order in _s at small x.

Abstract

We consider the differential cross-section for single-inclusive jet production with transverse momentum $P_\perp$ in Deep Inelastic Scattering (DIS) at small Bjorken $x_{\rm Bj}$, mediated by a virtual photon with virtuality $Q^2$. Unlike most studies at small $x$, which focus on particle production in the current fragmentation region, we investigate the kinematic regime where the jet is produced in the target fragmentation hemisphere of the Breit frame, and with $P_\perp \ll Q$. For a longitudinally polarised photon, we demonstrate that this cross-section is not power suppressed in $P_\perp/Q$ and we derive a factorised expression in terms of extended quark and gluon jet fracture functions. Our formula, valid at next-to-leading order in $\alpha_s$ at small $x$, is akin to the Altarelli-Martinelli identity for the longitudinal DIS structure function. Numerical estimates show that the extended quark jet fracture function is the most sensitive to saturation effects in large nuclei.