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.
Highlights
An important discovery of the electron-proton (e þ p) deep inelastic scattering (DIS) experiments at HERA was the rapid growth of the gluon distribution with decreasingBjorken x, for fixed large momentum transfer squared Q2 .This demonstrated that the proton wave function in the corresponding high energy Regge limit is dominated byFock state configurations containing large numbers of gluons
Paper I, we reported on a first color glass condensate (CGC) computation of the leading order differential cross section for inclusive prompt photon production in conjunction with two jets in electronnucleus (e þ A) DIS at small x
We demonstrate here the cancellation of collinear divergences between real and virtual processes resulting in an infrared safe differential cross section
Summary
An important discovery of the electron-proton (e þ p) deep inelastic scattering (DIS) experiments at HERA was the rapid growth of the gluon distribution with decreasing. Paper I, we reported on a first CGC computation of the leading order differential cross section for inclusive prompt photon production in conjunction with two jets in electronnucleus (e þ A) DIS at small x This process has clean initial and final states and is the simplest nontrivial process besides fully inclusive DIS to study the physics of gluon saturation in e þ A collisions. With all the divergences in the (NLO∶2) quantum fluctuations of the virtual photon projectile accounted for, one can write the infrared (IR) safe jet cross section as jet jet hdσ NLO∶2 i 1⁄4 hδσ NLO∶2 i þ 1⁄2DρA W Λ−0 1⁄2ρA dσjet;finite These NLO contributions (shown in Fig. 5) can be broken up into two pieces. Appendix J provides a short proof of the subdominance of noncollinearly divergent contributions to the cross section for real gluon emissions when we work in the limit of small jet cone radius
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