NLO impact factor for inclusive <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mi>photon</mml:mi><mml:mo>+</mml:mo><mml:mi>dijet</mml:mi></mml:mrow></mml:math> production in <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>e</mml:mi><mml:mo>+</mml:mo><mml:mi>A</mml:mi></mml:math> DIS at small <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>x</mml:mi></mml:math>
Kaushik Roy, Raju Venugopalan
Abstract
We compute the next-to-leading order (NLO) impact factor for inclusive $\mathrm{photon}+\mathrm{dijet}$ production in electron-nucleus ($\mathrm{e}+\mathrm{A}$) 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 ${Q}^{2}\ensuremath{\gg}{\mathrm{\ensuremath{\Lambda}}}_{\mathrm{QCD}}^{2}$ and $x\ensuremath{\rightarrow}0$. 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 $O({\ensuremath{\alpha}}_{s})$ 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 $O({\ensuremath{\alpha}}_{s}^{3}\mathrm{ln}(x))$. 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 $\text{photon}+3$ jet (quark-antiquark-gluon) cross section.