Back-to-back inclusive dijets in DIS at small $x$: Gluon Weizs\"acker-Williams distribution at NLO

TL;DR

This paper presents a next-to-leading order calculation of back-to-back inclusive dijet production in DIS at small x, demonstrating factorization into a perturbative impact factor and a nonperturbative gluon distribution within the CGC EFT framework.

Contribution

It provides the first complete NLO computation of the dijet cross-section in DIS at small x, including a factorization formula involving the WW gluon distribution and resummation of Sudakov logs.

Findings

Factorization of the cross-section into impact factor and WW gluon distribution.

Derivation of a compact analytic expression for the impact factor.

Validation of the WW TMD's evolution via the kinematically constrained JIMWLK equation.

Abstract

In JHEP 11 (2022) 169, we performed the first complete computation of the back-to-back inclusive di-jet cross-section in Deeply Inelastic Scattering (DIS) at small $x_{\rm Bj}$ to next-to-leading order (NLO) in the Color Glass Condensate effective field theory (CGC EFT). We demonstrate here that for di-jets with relative transverse momentum $P_\perp$ and transverse momentum imbalance $q_\perp$, to leading power in $q_\perp/P_\perp$, the cross-section for longitudinally polarized photons can be fully factorized into the product of a perturbative impact factor and the nonperturbative Weizs\"{a}cker-Williams (WW) transverse momentum dependent (TMD) gluon distribution to NLO accuracy. The impact factor can further be expressed as the product of a universal soft factor which resums Sudakov double and single logs in $P_\perp/q_\perp$ and a coefficient function given by a remarkably compact analytic expression. We show that in the CGC EFT the WW TMD satisfies a kinematically constrained JIMWLK renormalization group evolution in rapidity. This factorization formula is valid to all orders in $Q_s/q_\perp$ for $q_\perp, Q_s \ll P_\perp$, where $Q_s$ is the semi-hard saturation scale that grows with rapidity.