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

Abstract

In JHEP 11 (2022) 169, we performed the first complete computation of the back-to-back inclusive di-jet cross-section in Deeply Inelastic Scattering (DIS) at small $x_{\mathrm{Bj}}$ to next-to-leading order (NLO) in the Color Glass Condensate effective field theory (CGC EFT). We demonstrate here that for di-jets with relative transverse momentum $P_{\perp }$ 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 nonperturbative 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.

Comments: 73 pages, 8 figures, 1 table, revised version with extended discussion of running coupling effect to CSS evolution at small x