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.

United States

Yuxun Guo

Feng Yuan

Wenbin Zhao

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.

China

Xiaohui Liu

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

Hua Xing Zhu

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.

France

Paul Caucal

Edmond Iancu

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.

Yoshitaka Hatta

Angular dependence in transverse momentum dependent diffractive parton distributions at small-

We study the exclusive near threshold photoproduction of heavy quarkonium in the framework of the generalized parton distribution (GPD) factorization, taking the <math><mi>J</mi><mo>/</mo><mi>ψ</mi></math> production as an example. Because of the threshold kinematics, the Compton-like amplitudes are related to gluon GPDs at large skewness <math><mi>ξ</mi></math>, distinct from the common kinematics in asymptotic high energy where the skewness is typically small. We discuss the nature of large-<math><mi>ξ</mi></math> expansion of these amplitudes in terms of the moments of gluon GPDs in the large-<math><mi>ξ</mi></math> limit. Based on that, we propose several ways to extract the first few moments of the gluon GPDs from these amplitudes, with the leading ones corresponding to the gluonic gravitational or energy-momentum tensor form factors (GFFs). We apply these methods to analyze the recent near threshold <math><mi>J</mi><mo>/</mo><mi>ψ</mi></math> production measurements by the <math><mrow><mi>J</mi><mo>/</mo><mi>ψ</mi></mrow></math> 007 experiment and GlueX Collaboration and find that the <math><mi>ξ</mi></math> scaling of the measured differential cross sections is consistent with the asymptotic behavior. However, the current data are not accurate enough yet for a complete determination of the gluonic GFFs, and therefore we consider some prospects for better extractions in the future.

Xiangdong Ji

Proton’s gluon GPDs at large skewness and gravitational form factors from near threshold heavy quarkonium photoproduction

Quantum Chromodynamics, the theory of quarks and gluons, whose interactions can be described by a local SU(3) gauge symmetry with charges called “color quantum numbers”, is reviewed; the goal of this review is to provide advanced Ph.D. students a comprehensive handbook, helpful for their research. When QCD was “discovered” 50 years ago, the idea that quarks could exist, but not be observed, left most physicists unconvinced. Then, with the discovery of charmonium in 1974 and the explanation of its excited states using the Cornell potential, consisting of the sum of a Coulomb-like attraction and a long range linear confining potential, the theory was suddenly widely accepted. This paradigm shift is now referred to as the November revolution. It had been anticipated by the observation of scaling in deep inelastic scattering, and was followed by the discovery of gluons in three-jet events. The parameters of QCD include the running coupling constant, $$\alpha _s(Q^2)$$ <math> <mrow> <msub> <mi>α</mi> <mi>s</mi> </msub> <mrow> <mo>(</mo> <msup> <mi>Q</mi> <mn>2</mn> </msup> <mo>)</mo> </mrow> </mrow> </math> , that varies with the energy scale $$Q^2$$ <math> <msup> <mi>Q</mi> <mn>2</mn> </msup> </math> characterising the interaction, and six quark masses. QCD cannot be solved analytically, at least not yet, and the large value of $$\alpha _s$$ <math> <msub> <mi>α</mi> <mi>s</mi> </msub> </math> at low momentum transfers limits perturbative calculations to the high-energy region where $$Q^2\gg \varLambda _{{\textrm{QCD}}} ^2\simeq $$ <math> <mrow> <msup> <mi>Q</mi> <mn>2</mn> </msup> <mo>≫</mo> <msubsup> <mi>Λ</mi> <mrow> <mtext>QCD</mtext> </mrow> <mn>2</mn> </msubsup> <mo>≃</mo> </mrow> </math> (250 MeV) $$^2$$ <math> <msup> <mrow></mrow> <mn>2</mn> </msup> </math> . Lattice QCD (LQCD), numerical calculations on a discretized space-time lattice, is discussed in detail, the dynamics of the QCD vacuum is visualized, and the expected spectra of mesons and baryons are displayed. Progress in lattice calculations of the structure of nucleons and of quantities related to the phase diagram of dense and hot (or cold) hadronic matter are reviewed. Methods and examples of how to calculate hadronic corrections to weak matrix elements on a lattice are outlined. The wide variety of analytical approximations currently in use, and the accuracy of these approximations, are reviewed. These methods range from the Bethe–Salpeter, Dyson–Schwinger coupled relativistic equations, which are formulated in both Minkowski or Euclidean spaces, to expansions of multi-quark states in a set of basis functions using light-front coordinates, to the AdS/QCD method that imbeds 4-dimensional QCD in a 5-dimensional deSitter space, allowing confinement and spontaneous chiral symmetry breaking to be described in a novel way. Models that assume the number of colors is very large, i.e. make use of the large $$N_c$$ <math> <msub> <mi>N</mi> <mi>c</mi> </msub> </math> -limit, give unique insights. Many other techniques that are tailored to specific problems, such as perturbative expansions for high energy scattering or approximate calculations using the operator product expansion are discussed. The very powerful effective field theory techniques that are successful for low energy nuclear systems (chiral effective theory), or for non-relativistic systems involving heavy quarks, or the treatment of gluon exchanges between energetic, collinear partons encountered in jets, are discussed. The spectroscopy of mesons and baryons has played an important historical role in the development of QCD. The famous X,Y,Z states – and the discovery of pentaquarks – have revolutionized hadron spectroscopy; their status and interpretation are reviewed as well as recent progress in the identification of glueballs and hybrids in light-meson spectroscopy. These exotic states add to the spectrum of expected $$q{{\bar{q}}}$$ <math> <mrow> <mi>q</mi> <mover> <mrow> <mi>q</mi> </mrow> <mrow> <mo>¯</mo> </mrow> </mover> </mrow> </math> mesons and qqq baryons. The progress in understanding excitations of light and heavy baryons is discussed. The nucleon as the lightest baryon is discussed extensively, its form factors, its partonic structure and the status of the attempt to determine a three-dimensional picture of the parton distribution. An experimental program to study the phase diagram of QCD at high temperature and density started with fixed target experiments in various laboratories in the second half of the 1980s, and then, in this century, with colliders. QCD thermodynamics at high temperature became accessible to LQCD, and numerical results on chiral and deconfinement transitions and properties of the deconfined and chirally restored form of strongly interacting matter, called the Quark–Gluon Plasma (QGP), have become very precise by now. These results can now be confronted with experimental data that are sensitive to the nature of the phase transition. There is clear evidence that the QGP phase is created. This phase of QCD matter can already be characterized by some properties that indicate, within a temperature range of a few times the pseudocritical temperature, the medium behaves like a near ideal liquid. Experimental observables are presented that demonstrate deconfinement. High and ultrahigh density QCD matter at moderate and low temperatures shows interesting features and new phases that are of astrophysical relevance. They are reviewed here and some of the astrophysical implications are discussed. Perturbative QCD and methods to describe the different aspects of scattering processes are discussed. The primary parton–parton scattering in a collision is calculated in perturbative QCD with increasing complexity. The radiation of soft gluons can spoil the perturbative convergence, this can be cured by resummation techniques, which are also described here. Realistic descriptions of QCD scattering events need to model the cascade of quark and gluon splittings until hadron formation sets in, which is done by parton showers. The full event simulation can be performed with Monte Carlo event generators, which simulate the full chain from the hard interaction to the hadronic final states, including the modelling of non-perturbative components. The contribution of the LEP experiments (and of earlier collider experiments) to the study of jets is reviewed. Correlations between jets and the shape of jets had allowed the collaborations to determine the “color factors” – invariants of the SU(3) color group governing the strength of quark–gluon and gluon–gluon interactions. The calculated jet production rates (using perturbative QCD) are shown to agree precisely with data, for jet energies spanning more than five orders of magnitude. The production of jets recoiling against a vector boson, $$W^\pm $$ <math> <msup> <mi>W</mi> <mo>±</mo> </msup> </math> or Z, is shown to be well understood. The discovery of the Higgs boson was certainly an important milestone in the development of high-energy physics. The couplings of the Higgs boson to massive vector bosons and fermions that have been measured so far support its interpretation as mass-generating boson as predicted by the Standard Model. The study of the Higgs boson recoiling against hadronic jets (without or with heavy flavors) or against vector bosons is also highlighted. Apart from the description of hard interactions taking place at high energies, the understanding of “soft QCD” is also very important. In this respect, Pomeron – and Odderon – exchange, soft and hard diffraction are discussed. Weak decays of quarks and leptons, the quark mixing matrix and the anomalous magnetic moment of the muon are processes which are governed by weak interactions. However, corrections by strong interactions are important, and these are reviewed. As the measured values are incompatible with (most of) the predictions, the question arises: are these discrepancies first hints for New Physics beyond the Standard Model? This volume concludes with a description of future facilities or important upgrades of existing facilities which improve their luminosity by orders of magnitude. The best is yet to come!

Franz Gross

Eberhard Klempt

Stanley Brodsky

Andrzej Buras

Volker Burkert

Gudrun Heinrich

Karl Jakobs

Curtis Meyer

Kostas Orginos

Michael Strickland

Johanna Stachel

Giulia Zanderighi

Nora Brambilla

Peter Braun-Munzinger

Daniel Britzger

Simon Capstick

Tom Cohen

Volker Crede

Martha Constantinou

United Kingdom

Christine Davies

Luigi Debbio

Achim Denig

Carleton DeTar

Alexandre Deur

Russia

Latvia

Yuri Dokshitzer

Hans Dosch

Jozef Dudek

Monica Dunford

Evgeny Epelbaum

Spain

Miguel Escobedo

Harald Fritzsch

Japan

Kenji Fukushima

Italy

Paolo Gambino

Canada

Sweden

Dag Gillberg

Steven Gottlieb

CERN

Per Grafstrom

Switzerland

Massimiliano Grazzini

Boris Grube

JINR

Alexey Guskov

Toru Iijima

Frithjof Karsch

Stefan Kluth

John Kogut

Frank Krauss

Shunzo Kumano

Australia

Derek Leinweber

Heinrich Leutwyler

Hai-Bo Li

Yang Li

Bogdan Malaescu

Chiara Mariotti

Pieter Maris

Simone Marzani

Wally Melnitchouk

Johan Messchendorp

Harvey Meyer

Ryan Mitchell

Chandan Mondal

Frank Nerling

Sebastian Neubert

Marco Pappagallo

Saori Pastore

José Peláez

Andrew Puckett

Jianwei Qiu

Klaus Rabbertz

Alberto Ramos

Patrizia Rossi

Azerbaijan

Anar Rustamov

Andreas Schäfer

Stefan Scherer

Matthias Schindler

Steven Schramm

Mikhail Shifman

Edward Shuryak

Torbjörn Sjöstrand

George Sterman

Iain Stewart

Joachim Stroth

Eric Swanson

Costa Rica

Guy Téramond

Ulrike Thoma

Antonio Vairo

Danny Dyk

James Vary

Javier Virto

Marcel Vos

Christian Weiss

Markus Wobisch

Sau Wu

Christopher Young

Xingbo Zhao

Xiaorong Zhou

50 Years of quantum chromodynamics

We present an innovative approach to the linearly polarized gluons confined inside the unpolarized nucleon in lepton-nucleon scattering. Our method analyzes the correlation of energy flows at azimuthal separations <math><mi>ϕ</mi></math>. The interference of the spinning gluon with both positive and negative helicities translates into a <math><mi>cos</mi><mo>(</mo><mn>2</mn><mi>ϕ</mi><mo>)</mo></math> asymmetry imprinted on the detector. Unlike the conventional transverse momentum dependent probes, the <math><mi>cos</mi><mo>(</mo><mn>2</mn><mi>ϕ</mi><mo>)</mo></math> asymmetry in this approach is preserved by rotational symmetry, holds to all orders, and is free of radiation contamination and is thus expected to provide the exquisite signature of the nucleon linearly polarized gluons.

Xiao Lin Li

Illuminating nucleon-gluon interference via calorimetric asymmetry