Low $x$ physics as an infinite twist (G)TMD framework: unravelling the origins of saturation

Abstract

We show how the formulations of low $x$ physics involving Wilson line operators can be fully rewritten into an infinite twist TMD or GTMD framework, respectively for inclusive and exclusive observables. This leads to a perfect match between low $x$ physics and moderate $x$ formulations of QCD in terms of GTMDs, TMDs, GPDs or PDFs. We derive the BFKL limit as a kinematic limit and argue that beyond the Wandzura-Wilczek approximation, 3-body and 4-body unintegrated PDFs should be taken into account even in this regime. Finally, we analyze how saturation should be understood as three distinct effects: saturation through non-linearities in the evolution equations at small $x$, saturation through multiple interactions with slow gluons as TMD gauge links, and saturation as the enhancement of genuine twist corrections.

25 pages, 7 figures

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Cited by in corpus (30)

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• 50 Years of Quantum Chromodynamics
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• Back-to-back inclusive dijets in DIS at small $x$: Sudakov suppression and gluon saturation at NLO
• The importance of kinematic twists and genuine saturation effects in dijet production at the Electron-Ion Collider
• Quarks at next-to-eikonal accuracy in the CGC I: Forward quark-nucleus scattering
• Sub-femtometer scale color charge fluctuations in a proton made of three quarks and a gluon
• Probing the Sivers function with an unpolarized target: GTMD distributions and the Odderons
• T-odd Leading-Twist Quark TMDs at Small $x$
• Comparison of improved TMD and CGC frameworks in forward quark dijet production
• Low-$x$ improved TMD approach to the lepto- and hadroproduction of a heavy-quark pair
• On gauge invariance of transverse momentum dependent distributions at small x
• Sudakov resummation from the BFKL evolution
• Gluon-mediated inclusive Deep Inelastic Scattering from Regge to Bjorken kinematics
• Sub-femtometer scale color charge correlations in the proton
• Particle correlations from the initial state
• Probing gluon number density with electron-dijet correlations at EIC
• On systematic effects in the numerical solutions of the JIMWLK equation
• Forward Inclusive Jet Productions in pA Collisions
• Rapidity-only TMD factorization at one loop
• Incoherent diffractive dijet production in electron DIS off nuclei at high energy
• Forward trijet production in p-p and p-Pb collisions at LHC
• Quark TMDs from back-to-back dijet production at forward rapidities in pA collisions beyond eikonal accuracy in the CGC
• Transverse Momentum Dependent Gluon Distribution within High Energy Factorization at Next-to-Leading Order
• Dijet impact factor in DIS at next-to-leading order in the Color Glass Condensate
• Parton model contributions as next-to-eikonal corrections to the dipole factorization of DIS and SIDIS at low $x_{Bj}$
• Nucleon Tomography with 0-jettiness
• Dijet photoproduction at low $x$ at next-to-leading order and its back-to-back limit