We study the QCD scaling behavior of the small-angle energy-energy correlator (EEC), focusing on the transition between its perturbative preconfinement and nonperturbative postconfinement regimes. Applying the light-ray operator product expansion (OPE), we develop a formalism that describes the scaling of the EEC with the input energy <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>Q</mi></mrow></math> in the transition and the postconfinement region, where the latter quantum scaling is determined by the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>J</mi><mo>=</mo><mn>5</mn></mrow></math> DGLAP anomalous dimension. A key result of our Letter is a novel connection between the light-ray OPE and the dihadron fragmentation function (DFF), where we show that the nonperturbative OPE coefficients correspond to moments of the DFF. This finding establishes a new paradigm for studying hadronization. Our theoretical predictions are validated against Monte Carlo simulations for both <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msup><mrow><mi>e</mi></mrow><mrow><mo>+</mo></mrow></msup><msup><mrow><mi>e</mi></mrow><mrow><mo>−</mo></mrow></msup></mrow></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>p</mi><mi>p</mi></math> collisions, showing excellent agreement. The potential role of the quantum scaling in the precision determination of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msub><mrow><mi>α</mi></mrow><mrow><mi>s</mi></mrow></msub></mrow></math> is also discussed.

United States

Cyuan-Han Chang

Hao Chen

China

Xiaohui Liu

David Simmons-Duffin

Feng Yuan

Hua Xing Zhu

Quantum Scaling in Energy Correlators beyond the Confinement Transition

By utilizing the dihadron fragmentation formalism, we extend the previous factorization of near-side energy-energy correlators (EECs) in the collinear limit and derive an all order resummation in the Fourier transform <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msub><mrow><mi>b</mi></mrow><mrow><mi>T</mi></mrow></msub></mrow></math>-space. A perfect matching is obtained when we compare to the fixed-order results. We further demonstrate the resummation effects for the EECs in <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msup><mrow><mi>e</mi></mrow><mrow><mo>+</mo></mrow></msup><msup><mrow><mi>e</mi></mrow><mrow><mo>−</mo></mrow></msup></mrow></math> annihilation and show that they will significantly improve the theoretical predictions at small angles.

Yuxun Guo

Wenbin Zhao

Factorization and Resummation for the Near-Side Energy-Energy Correlators

Within the Colour Glass Condensate effective theory, we demonstrate that back-to-back dijet correlations in dilute-dense collisions involving a small- <italic>x</italic> quark from the nuclear target can be factorised in terms of universal transverse momentum dependent distributions (TMDs) for the sea quarks. Two building blocks are needed to construct all these TMDs at the operator level: the sea quark TMD operator which appears in semi-inclusive Deep-Inelastic Scattering (SIDIS) or in the Drell-Yan process and the elastic <italic>S</italic>-matrix for a quark-antiquark dipole. Compared to SIDIS, the saturation effects are stronger for dijet production in forward proton-nucleus collisions, due to additional scattering in the initial and final state, effectively resulting in a larger value for the nuclear saturation momentum.

France

Paul Caucal

Marcos Guerrero Morales

Edmond Iancu

Farid Salazar

Unveiling the sea: universality of the transverse momentum dependent quark distributions at small <italic>x</italic>

With Bayesian inference, we investigate the impact of recent near-threshold <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>J</mi><mo>/</mo><mi>ψ</mi></mrow></math> production measurements by the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>J</mi><mo>/</mo><mi>ψ</mi><mn>007</mn></mrow></math> experiment and GlueX Collaboration on the extraction of proton gravitational form factors. We apply the generalized parton distribution framework at the next to leading order and demonstrate a stable expansion for the near-threshold kinematics. We find that the experimental constraints are in good agreement with the state-of-the-art lattice simulations, where negative <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>C</mi><mi>q</mi></msub><mo stretchy="false">(</mo><mi>t</mi><mo stretchy="false">)</mo></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msub><mrow><mi>C</mi></mrow><mrow><mi>g</mi></mrow></msub><mo stretchy="false">(</mo><mi>t</mi><mo stretchy="false">)</mo></mrow></math> are strongly preferred. This highlights a great potential to extract them from future high-precision experiments.

Bayesian Inferring Nucleon Gravitational Form Factors via Near-Threshold <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>J</mi><mo>/</mo><mi>ψ</mi></mrow></math> Photoproduction

We study the forward-backward azimuthal angular correlations of hadrons in association with multiparticle production in the central rapidity region in proton-proton collisions at the LHC. We apply the nucleon energy-energy correlator framework, where the spinning gluon distribution introduces a nontrivial <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>cos</mi><mo stretchy="false">(</mo><mn>2</mn><mi>ϕ</mi><mo stretchy="false">)</mo></math> asymmetries. We will demonstrate that the fundamental helicity structure of quantym chromodynamics (QCD) amplitudes predicts a unique power counting rule: <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>cos</mi><mo stretchy="false">(</mo><mn>2</mn><mi>ϕ</mi><mo stretchy="false">)</mo></math> asymmetry starts at <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="script">O</mi><mo stretchy="false">(</mo><msubsup><mi>α</mi><mi>s</mi><mn>2</mn></msubsup><mo stretchy="false">)</mo></math> order for dijet, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="script">O</mi><mo stretchy="false">(</mo><msub><mi>α</mi><mi>s</mi></msub><mo stretchy="false">)</mo></math> for three jet and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="script">O</mi><mo stretchy="false">(</mo><mn>1</mn><mo stretchy="false">)</mo></math> for four (and more) jet productions. Our results will help us to understand the longstanding puzzle of nearside ridge behavior observed in high multiplicity events of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>p</mi><mi>p</mi></math> collisions at the LHC.

Germany

Long range energy-energy correlator at the LHC

We analyzed two-loop planar contributions to a three-body form factor at next-to-leading power in the high-energy limit, where the masses of the external particles are much smaller than their energies. Calculations were performed by exploiting differential equations for the expansion coefficients, both to facilitate linear relations among them and to derive their analytic expressions. The results are expressed in terms of generalized polylogarithms involving a few simple symbol letters. Our method can readily be applied to calculations of non-planar contributions as well. Our results provide crucial information for establishing sub-leading factorization theorems for massive scattering amplitudes in the high-energy limit.

Yishuai Guo

Zhi-Feng Liu

Mingming Lu

Tianya Xia

Li-Lin Yang

A three-body form factor at sub-leading power in the high-energy limit: planar contributions * Supported in part by the National Natural Science Foundation of China Sunder (12375097, 12347103) and the Fundamental Research Funds for the Central Universities. Zhi-Feng Liu was supported by the China Postdoctoral Science Foundation (2023M733123, 2023TQ0282) and the Postdoctoral Fellowship Program of China Postdoctoral Science Foundation

We investigate the energy-energy correlator (EEC) of hadrons produced on the same side in <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msup><mrow><mi>e</mi></mrow><mrow><mo>+</mo></mrow></msup><msup><mrow><mi>e</mi></mrow><mrow><mo>−</mo></mrow></msup></mrow></math> annihilation or in leading jets in <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>p</mi><mi>p</mi></mrow></math> collisions. We observe a remarkable universality of the correlator. Using a nonperturbative transverse momentum dependent (TMD) fragmentation function to model the transition from the “free-hadron” region to the perturbative collinear region, we are able to describe the near-side shapes and peaks over a wide range of energy for both the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>e</mi><mo>+</mo></msup><msup><mi>e</mi><mo>−</mo></msup></math> annihilation and the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>p</mi><mi>p</mi></math> jet substructure measurements in terms of just two parameters. We present further predictions for the ratio of the projected three-point energy correlator to the EEC. The excellent agreement between our calculations and the experimental data may provide new insights into the role of nonperturbative physics for EECs, and suggests the possibility of exploring nonperturbative TMDs using theoretical tools developed for the energy correlators.

Werner Vogelsang

Universality in the Near-Side Energy-Energy Correlator

Using the color dipole picture of deep inelastic scattering (DIS) and the color glass condensate effective theory, we study semi-inclusive jet production in DIS at small <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>x</mi></mrow></math> in the limit where the photon virtuality <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msup><mrow><mi>Q</mi></mrow><mrow><mn>2</mn></mrow></msup></mrow></math> is much larger than the transverse momentum squared <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msubsup><mrow><mi>P</mi></mrow><mrow><mo>⊥</mo></mrow><mrow><mn>2</mn></mrow></msubsup></mrow></math> of the produced jet. In this limit, the cross section is dominated by aligned jet configurations, that is, quark–antiquark pairs in which one of the fermions—the would-be struck quark in the Breit frame—carries most of the longitudinal momentum of the virtual photon. We show that physically meaningful jet definitions in DIS are such that the effective axis of the jet sourced by the struck quark is controlled by its virtuality rather than by its transverse momentum. For such jet definitions, we show that the next-to-leading order cross section admits factorization in terms of the (sea) quark transverse momentum dependent distribution, which in turn satisfies a universal Dokshitzer-Gribov-Lipatov-Altarelli-Parisi and Sudakov evolution.

A.H. Mueller

Jet Definition and Transverse-Momentum–Dependent Factorization in Semi-inclusive Deep-Inelastic Scattering

By investigating the soft gluon radiation in the <math><mi>J</mi><mo>/</mo><mi>ψ</mi></math> plus jet photoproduction at the electron-ion collider (EIC), we demonstrate that the azimuthal angular correlations between the leading jet and heavy quarkonium provide a unique probe to the production mechanism of the latter. In particular, a significant <math><mi>cos</mi><mo>(</mo><mi>ϕ</mi><mo>)</mo></math> asymmetry is found for the color-singlet channel, whereas it vanishes or has an opposite sign for color-octet production, depending on the jet transverse momentum. Numerical results of <math><mi>cos</mi><mo>(</mo><mi>ϕ</mi><mo>)</mo></math> and <math><mi>cos</mi><mo>(</mo><mn>2</mn><mi>ϕ</mi><mo>)</mo></math> asymmetries employing both the color-singlet model and the nonrelativistic QCD approach are presented for typical kinematics at the future EIC.

Netherlands

Luca Maxia

Azimuthal angular correlation of <math><mi>J</mi><mo>/</mo><mi>ψ</mi></math> plus jet production at the electron-ion collider

We discuss the angular dependence of the recently proposed transverse momentum dependent quark and gluon diffractive parton distributions at small-x. We introduce the diffractive versions of the Sivers function and the elliptic gluon Wigner distribution and evaluate them in simple models with gluon saturation and study their geometric scaling properties. We also show that the diffractive version of the linearly polarized gluon distribution identically vanishes to leading order. These distributions enrich the physics opportunities for measuring semi-inclusive diffractive DIS processes at the future electron-ion colliders.