[Paper Review] Dijet impact factor in DIS at next-to-leading order in the Color Glass Condensate

Paul Caucal, Farid Salazar+1 more|arXiv (Cornell University)|Aug 13, 2021

High-Energy Particle Collisions Research128 references75 citations

TL;DR

This paper computes the next-to-leading order (NLO) impact factor for inclusive dijet production in deep-inelastic scattering (DIS) off nuclei within the Color Glass Condensate (CGC) effective field theory. Using covariant perturbation theory and lightlike Wilson line correlators, it demonstrates that rapidity evolution at NLO is governed by the JIMWLK Hamiltonian, achieving O(α²ₛ ln(xf/xBj)) accuracy for the dijet cross-section. This result enables precision studies of gluon saturation at the Electron-Ion Collider (EIC).

ABSTRACT

We compute the next-to-leading order impact factor for inclusive dijet production in deeply inelastic electron-nucleus scattering at small $x_{ m Bj}$. Our computation, performed in the framework of the Color Glass Condensate effective field theory, includes all real and virtual contributions in the gluon shock wave background of all-twist lightlike Wilson line correlators. We demonstrate explicitly that the rapidity evolution of these correlators, to leading logarithmic accuracy, is described by the JIMWLK Hamiltonian. When combined with the next-to-leading order JIMWLK Hamiltonian, our results for the impact factor improve the accuracy of the inclusive dijet cross section to $\mathcal{O}(\alpha_s^2 \ln(x_f/x_{ m Bj}))$, where $x_f$ is a rapidity factorization scale. These results are an essential ingredient in assessing the discovery potential of inclusive dijets to uncover the physics of gluon saturation at the Electron-Ion Collider.

Motivation & Objective

• To compute the next-to-leading order (NLO) impact factor for inclusive dijet production in electron-nucleus deep-inelastic scattering (DIS) at small xBj.
• To extend the accuracy of inclusive dijet cross-section calculations in the Color Glass Condensate (CGC) framework to O(α²ₛ ln(xf/xBj)) by combining NLO impact factors with NLL JIMWLK evolution.
• To establish JIMWLK factorization of the NLO dijet amplitude in the slow gluon limit, isolating the impact factor for future numerical applications.
• To provide a foundational tool for probing gluon saturation and the quadrupole correlator in high-energy QCD at the Electron-Ion Collider (EIC).

Proposed method

• Performs a systematic NLO computation in the CGC effective field theory using covariant perturbation theory and momentum-space Feynman rules with CGC vertices.
• Computes all real and virtual corrections involving gluon emission before and after the shock wave, including self-energy and vertex diagrams with dressed and free gluon propagators.
• Applies contour integration techniques and Schwinger parametrization to evaluate loop integrals, particularly focusing on soft and collinear divergences.
• Demonstrates that divergences (soft, collinear, ultraviolet) cancel at one-loop order, ensuring renormalizability of the amplitude.
• Identifies the slow gluon limit (small longitudinal momentum fraction) to extract the impact factor and prove JIMWLK factorization via the JIMWLK Hamiltonian.
• Derives explicit expressions for the NLO impact factor in both transverse and longitudinal photon polarization states, including regular and instantaneous gluon contributions.

Experimental results

Research questions

• RQ1 How can the NLO impact factor for inclusive dijet production in DIS be computed in the CGC framework at small xBj?
• RQ2 To what extent do real and virtual corrections in the CGC framework cancel divergences, and how is renormalization achieved at NLO?
• RQ3 Does the NLO amplitude factorize in the slow gluon limit, and if so, does it reproduce the JIMWLK Hamiltonian for rapidity evolution?
• RQ4 What is the structure of the NLO impact factor for transversely and longitudinally polarized virtual photons, and how does it depend on jet kinematics?
• RQ5 How does combining the NLO impact factor with the NLL JIMWLK evolution improve the accuracy of the inclusive dijet cross-section?

Key findings

• The NLO dijet impact factor is computed in the CGC EFT, including all real and virtual corrections in the gluon shock wave background, with full control over divergences.
• All soft, collinear, and ultraviolet divergences cancel at one-loop order, confirming the consistency of the NLO amplitude in the CGC framework.
• In the slow gluon limit, the NLO amplitude factorizes into a process-dependent impact factor and a universal evolution kernel, proving JIMWLK factorization at NLO.
• The rapidity evolution of Wilson line correlators is shown to be governed by the JIMWLK Hamiltonian at leading logarithmic accuracy, with the NLO kernel now fully incorporated.
• The inclusive dijet cross-section achieves O(α²ₛ ln(xf/xBj)) accuracy when the NLO impact factor is combined with NLL JIMWLK evolution, enabling precision phenomenology at the EIC.
• Explicit analytical expressions are derived for the NLO impact factor in both transverse and longitudinal photon polarization states, including contributions from regular and instantaneous gluon vertices.