{"paper":{"title":"Transverse momentum dependent parton distributions at small $x$","arxiv_id":"2610.26004","primary_cat":"hep-ph","submitted_at":"2026-10-19T08:30:31+00:00","version_compiled":"v1"},"notice":"Every quoted sentence is the authors' text from the arXiv listing abstract. Labels and probabilities are the outputs of classifier-1.13.0 on the question bank abstract-p1-20260923, exactly as returned. No sentence in this record was written by a language model.","schema":"pith.compiled-record/v0","status":"compiled","abstract":{"source":"arXiv listing abstract v1","sentences":[{"i":0,"p":1.0,"id":"s0","own":false,"role":"background","text":"Transverse-momentum-dependent (TMD) parton distributions provide a three-dimensional description of the momentum structure of hadrons.","hedge":{"p":1.0,"label":"asserted"},"own_p":0.04,"main_claim_p":0.04,"quantitative":false,"quantitative_p":0.14,"role_probabilities":{"gap":0.0,"method":0.0,"result":0.0,"background":1.0,"limitation":0.0,"future_work":0.0,"contribution":0.0,"interpretation":0.0}},{"i":1,"p":1.0,"id":"s1","own":false,"role":"background","text":"They are probed in proton-proton and proton-nucleus collisions at the LHC and RHIC, and are a central part of the physics program of the future Electron-Ion Collider (EIC).","hedge":{"p":1.0,"label":"asserted"},"own_p":0.05,"main_claim_p":0.03,"quantitative":false,"quantitative_p":0.06,"role_probabilities":{"gap":0.0,"method":0.0,"result":0.0,"background":1.0,"limitation":0.0,"future_work":0.0,"contribution":0.0,"interpretation":0.0}},{"i":2,"p":0.75,"id":"s2","own":false,"role":"background","text":"While TMD factorization is well established at moderate Bjorken $x$, the small-$x$ regime requires a different treatment, since large logarithms of $1/x$ must be resummed and non-linear effects due to high gluon densities become important.","hedge":{"p":1.0,"label":"asserted"},"own_p":0.05,"main_claim_p":0.08,"quantitative":false,"quantitative_p":0.36,"role_probabilities":{"gap":0.25,"method":0.0,"result":0.0,"background":0.75,"limitation":0.0,"future_work":0.0,"contribution":0.0,"interpretation":0.0}},{"i":3,"p":0.7,"id":"s3","own":false,"role":"background","text":"The Color Glass Condensate (CGC) effective theory provides a natural framework to describe TMDs in this saturation regime and to connect them with standard TMD factorization.","hedge":{"p":0.99,"label":"asserted"},"own_p":0.08,"main_claim_p":0.15,"quantitative":false,"quantitative_p":0.05,"role_probabilities":{"gap":0.0,"method":0.27,"result":0.0,"background":0.7,"limitation":0.0,"future_work":0.0,"contribution":0.03,"interpretation":0.0}},{"i":4,"p":0.96,"id":"s4","own":false,"role":"contribution","text":"This chapter reviews quark and gluon TMDs at small $x$, covering operator definitions, gauge-link structures, and Wilson-line correlators in the CGC for unpolarized and polarized distributions.","hedge":{"p":0.92,"label":"asserted"},"own_p":0.27,"main_claim_p":0.07,"quantitative":false,"quantitative_p":0.06,"role_probabilities":{"gap":0.0,"method":0.02,"result":0.0,"background":0.02,"limitation":0.0,"future_work":0.0,"contribution":0.96,"interpretation":0.0}},{"i":5,"p":0.97,"id":"s5","own":true,"role":"contribution","text":"We discuss factorization for inclusive and diffractive observables, highlighting the role of process dependence and the emergence of a limited set of Wilson-line operators.","hedge":{"p":0.89,"label":"asserted"},"own_p":0.56,"main_claim_p":0.09,"quantitative":false,"quantitative_p":0.1,"role_probabilities":{"gap":0.0,"method":0.03,"result":0.0,"background":0.0,"limitation":0.0,"future_work":0.0,"contribution":0.97,"interpretation":0.0}},{"i":6,"p":0.72,"id":"s6","own":false,"role":"contribution","text":"We then summarize the evolution of these distributions, namely the resummation of logarithms of $1/x$ by the Balitsky-Kovchegov and JIMWLK equations, and of Sudakov logarithms of the hard scale through Collins-Soper-Sterman evolution.","hedge":{"p":0.97,"label":"asserted"},"own_p":0.17,"main_claim_p":0.07,"quantitative":false,"quantitative_p":0.1,"role_probabilities":{"gap":0.0,"method":0.25,"result":0.0,"background":0.03,"limitation":0.0,"future_work":0.0,"contribution":0.72,"interpretation":0.0}},{"i":7,"p":0.93,"id":"s7","own":false,"role":"contribution","text":"We also review TMDs beyond the eikonal approximation, including the sub-eikonal Wilson-line operators that give access to helicity and other spin-dependent distributions, their double-logarithmic small-$x$ evolution and the resulting asymptotics, and the sub-eikonal corrections to the eikonal distributions, which provide a first step toward the moderate-$x$ regime.","hedge":{"p":0.98,"label":"asserted"},"own_p":0.31,"main_claim_p":0.11,"quantitative":false,"quantitative_p":0.3,"role_probabilities":{"gap":0.0,"method":0.05,"result":0.01,"background":0.01,"limitation":0.0,"future_work":0.0,"contribution":0.93,"interpretation":0.0}},{"i":8,"p":0.58,"id":"s8","own":false,"role":"future_work","text":"Finally, we discuss phenomenological implications for present and future experiments, with emphasis on the EIC, and outline the theoretical challenges toward a unified description of TMDs.","hedge":{"p":0.64,"label":"asserted"},"own_p":0.47,"main_claim_p":0.17,"quantitative":false,"quantitative_p":0.04,"role_probabilities":{"gap":0.0,"method":0.0,"result":0.0,"background":0.0,"limitation":0.0,"future_work":0.58,"contribution":0.34,"interpretation":0.08}}]},"compiled":{"main_claim":{"p":0.86,"text":"The Color Glass Condensate (CGC) effective theory provides a natural framework to describe TMDs in this saturation regime and to connect them with 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