Energy Correlators Resolving Proton Spin

TL;DR

This work tackles the proton spin puzzle by proposing spin-dependent energy correlators (EECs) in polarized DIS as a principled observable to access spin–momentum dynamics of confined partons. It develops a SCET-based framework that yields a CFR description in terms of TMDs and a TFR description in terms of Nucleon Energy Correlators (NECs), with RG evolution reaching up to $N^3$LL/NNLL accuracy. The authors establish all-order factorization theorems in both regions, perform NNLO/N^3LO matching to standard collinear PDFs, and demonstrate that EECs provide a robust, collinear-safe pathway to probe confinement and spin at the upcoming Electron–Ion Collider. The approach offers a novel three-dimensional tomographic handle on nucleon structure with wide experimental applicability at the EIC, complementing existing spin studies via DIS and hadronic collisions.

Abstract

We investigate the partonic origin of the proton longitudinal spin using spin-dependent energy correlator measured in lepton-hadron collisions with longitudinally polarized proton beams. These observables encode angular correlations in energy flow and are sensitive to the spin-momentum structure of confined partons. Using soft-collinear effective theory (SCET), we analyze the correlation patterns in both nearly back-to-back and forward limits, which establishes a direct correspondence with longitudinally polarized transverse momentum dependent distributions (TMDs) and nucleon energy correlators (NECs). The TMDs and NECs allow consistent matching onto hard radiation region, and provide a comprehensive description of the transition from perturbative parton branching to nonperturbative confinement. Using renormalization group evolution, we obtain joint $\text{N}^{3}$LL/NNLL quantitative predictions for spin-dependent energy correlation patterns in the current and target fragmentation regions (CFR and TFR). The framework provides new theoretical insight into how the internal motion and spin of partons contribute to the formation of the proton longitudinal spin, and offers an experimental paradigm for probing the interplay between color confinement and spin dynamics at forthcoming Electron-Ion Collider (EIC).

Figures (8)

• Figure 1: Current Fragmentation.
• Figure 2: QCD fixed-order results versus SCET prediction in the large angle limit, using LHAPDF6Buckley:2014ana PDF datasets CT14nloDulat:2015mca and NNPDFpol1.1Nocera:2014gqa.
• Figure 3: The energy correlation spectrum parameterized by $\tau=\tan \theta/2$. Left (a, b): Bjorken weighted (N=5) Energy Correlators with $b_\ast$ prescription Collins:2014jpa. Right (c, d): Energy Correlators without $b_\ast$ prescription, (c,d) are subject to a $q_T$ cut to ensure the observable remains in the perturbative regime.
• Figure 4: Target Fragmentation.
• Figure 5: Unpolarized and polarized NEC singlets renormalized at a perturbative scale with struck parton energy $E_a=100$GeV. The scale band indicates the variation with respect to the boundary scale $\mu_0 \sim E_a \sin\theta$.