A novel formulation of the unintegrated gluon distribution for DIS

TL;DR

This paper introduces a new semi-classical formulation of the unintegrated gluon distribution in DIS, bridging small and moderate x regimes, and proposes lattice computation for probing saturation effects.

Contribution

It presents a novel unintegrated gluon distribution that unifies dipole and gluonic PDF descriptions, enabling systematic analysis across different kinematic regimes.

Findings

New unintegrated gluon distribution with explicit x dependence

Framework for lattice computation of gluon operators

Systematic matching of small and moderate x regimes

Abstract

We provide a semi-classical description of the inclusive gluon induced Deep Inelastic Scattering cross section in a way that accounts for the leading powers in both the Regge and Bjorken limits. Our approach thus allows a systematic matching of small and moderate $x_{\rm Bj}$ regimes of gluon proton structure functions. We find a new unintegrated gluon distribution with an explicit dependence on the longitudinal momentum fraction $x$ which entirely spans both the dipole operator and the gluonic Parton Distribution Function. Computing this gauge invariant gluon operator on the lattice could allow to probe the energy dependence of the saturation scale from first principles.