Gluon-mediated inclusive Deep Inelastic Scattering from Regge to Bjorken kinematics

TL;DR

This paper introduces a new semi-classical approach to high energy gluon-mediated Deep Inelastic Scattering that systematically incorporates the target's longitudinal extent, unifying Regge and Bjorken kinematic limits.

Contribution

It proposes a novel factorization formula involving a gauge invariant unintegrated gluon distribution dependent on Feynman x, bridging Regge and Bjorken regimes.

Findings

Derives a new factorization formula with a gluon distribution depending on x.

Recovers both Regge and Bjorken limits within the framework.

Reproduces the full one-loop inclusive DIS cross-section in leading twist.

Abstract

We revisit high energy factorization for gluon mediated inclusive Deep Inelastic Scattering (DIS) for which we propose a new semi-classical approach that accounts systematically for the longitudinal extent of the target in contrast with the shockwave limit. In this framework, based on a partial twist expansion, we derive a factorization formula that involves a new gauge invariant unintegrated gluon distribution which depends explicitly on the Feynman $x$ variable. It is shown that both the Regge and Bjorken limits are recovered in this approach. We reproduce in particular the full one loop inclusive DIS cross-section in the leading twist approximation and the all-twist dipole factorization formula in the strict $x=0$ limit. Although quantum evolution is not discussed explicitly in this work, we argue that the proper treatment of the $x$ dependence of the gluon distribution encompasses the kinematic constraint that must be imposed on the phase-space of gluon fluctuations in the target to ensure stability of small-$x$ evolution.