Back-to-Back Inclusive Dijets in Deep Inelastic Scattering at Small x : Complete NLO Results and Predictions

We compute the back-to-back dijet cross section in deep inelastic scattering at small <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mi>x</a:mi></a:math> to next-to-leading order (NLO) in the color glass condensate effective field theory. Our result can be factorized into a convolution of the Weizsäcker-Williams gluon transverse-momentum-dependent distribution function (WW gluon TMD) with a universal soft factor and an NLO coefficient function. The soft factor includes both double and single logarithms in the ratio of the relative transverse momentum <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"><c:mrow><c:msub><c:mrow><c:mi>P</c:mi></c:mrow><c:mrow><c:mo>⊥</c:mo></c:mrow></c:msub></c:mrow></c:math> of the dijet pair to the dijet momentum imbalance <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"><e:msub><e:mi>q</e:mi><e:mo>⊥</e:mo></e:msub></e:math>; its renormalization group (RG) evolution is resummed into the Sudakov factor. Likewise, the WW TMD obeys a nonlinear RG equation in <g:math xmlns:g="http://www.w3.org/1998/Math/MathML" display="inline"><g:mi>x</g:mi></g:math> that is kinematically constrained to satisfy both the lifetime and rapidity ordering of the projectile. Exact analytical expressions are obtained for the NLO coefficient function of transversely and longitudinally polarized photons. Our results allow for the first quantitative separation of the dynamics of Sudakov suppression from that of gluon saturation. They can be extended to other final states and provide a framework for precision tests of novel QCD many-body dynamics at the Electron-Ion Collider.