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$_{\perp}$, to leading power in q$_{\perp}$/P$_{\perp}$, 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$_{\perp}$/q$_{\perp}$ 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$_{\perp}$ for q$_{\perp}$, Q$_{s} \ll $ P$_{\perp}$, where Q$_{s}$ is the semi-hard saturation scale that grows with rapidity.