NLO impact factor for inclusive photon$+$dijet production in $e+A$ DIS at small $x$

TL;DR

This paper calculates the next-to-leading order impact factor for inclusive photon plus dijet production in electron-nucleus deep inelastic scattering at small x, advancing theoretical understanding of high-energy QCD processes.

Contribution

It provides the first explicit expressions for the NLO impact factor in this process within the CGC framework, including the resummation of power corrections and the derivation of the JIMWLK evolution.

Findings

Derived the NLO impact factor for photon+dijet production.

Connected the impact factor with JIMWLK evolution equations.

Produced the LO photon+3 jet cross-section as a byproduct.

Abstract

We compute the next-to-leading order (NLO) impact factor for inclusive photon $+$dijet production in electron-nucleus (e+A) deeply inelastic scattering (DIS) at small $x$. An important ingredient in our computation is the simple structure of ``shock wave" fermion and gluon propagators. This allows one to employ standard momentum space Feynman diagram techniques for higher order computations in the Regge limit of fixed $Q^2\gg \Lambda_{\rm QCD}^2$ and $x\rightarrow 0$. Our computations in the Color Glass Condensate (CGC) effective field theory include the resummation of all-twist power corrections $Q_s^2/Q^2$, where $Q_s$ is the saturation scale in the nucleus. We discuss the structure of ultraviolet, collinear and soft divergences in the CGC, and extract the leading logs in $x$; the structure of the corresponding rapidity divergences gives a nontrivial first principles derivation of the JIMWLK renormalization group evolution equation for multiparton lightlike Wilson line correlators. Explicit expressions are given for the $x$-independent $O(\alpha_s)$ contributions that constitute the NLO impact factor. These results, combined with extant results on NLO JIMWLK evolution, provide the ingredients to compute the inclusive photon $+$ dijet cross-section at small $x$ to $O(\alpha_s^3 \ln(x))$. First results for the NLO impact factor in inclusive dijet production are recovered in the soft photon limit. A byproduct of our computation is the LO photon+ 3 jet (quark-antiquark-gluon) cross-section.