Back-to-back inclusive dijets in DIS at small x: gluon Weizsäcker-Williams distribution at NLO

In [1], we performed the first complete computation of the back-to-back inclusive dijet cross-section in Deeply Inelastic Scattering (DIS) at small x _Bj to next-to-leading order (NLO) in the Color Glass Condensate effective field theory (CGC EFT). We demonstrate here that for dijets with relative transverse momentum P _⊥ and transverse momentum imbalance q _⊥, to leading power in q _⊥/P _⊥, the cross-section for longitudinally polarized photons can be fully factorized into the product of a perturbative impact factor and the non-perturbative Weizsäcker-Williams (WW) transverse momentum dependent (TMD) gluon distribution to NLO accuracy. The impact factor can further be expressed as the product of a universal soft factor which resums Sudakov double and single logs in P _⊥/q _⊥ and a coefficient function given by a remarkably compact analytic expression. We show that in the CGC EFT the WW TMD satisfies a kinematically constrained JIMWLK renormalization group evolution in rapidity. This factorization formula is valid to all orders in Q_s/q _⊥ for q _⊥, Q_s ≪ P _⊥, where Q_s is the semi-hard saturation scale that grows with rapidity.