We demonstrate that chiral-odd dimeson generalized distribution amplitudes (CO-GDAs)—nonperturbative objects encoding the transition of a quark-antiquark pair into two mesons—can be accessed in high-energy <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 into two meson pairs, each with a relatively low invariant mass. While chiral-even GDAs contribute to the leading one-photon amplitude, the chiral-odd sector enters via two-photon exchange. We show that the interference between these amplitudes leads to specific effects which may be measurable at BES III or future tau-charm factories. This work opens a direct path to experimentally probing the long-missing chiral-odd sector of meson structure—specifically, the spin-orbit correlation in a spin-0 meson, in some contexts referred to as anomalous tensorial magnetic moment.

United States

Shohini Bhattacharya

France

Renaud Boussarie

Bernard Pire

Poland

Lech Szymanowski

Revealing chiral-odd two-meson generalized distribution amplitudes in <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><mo stretchy="false">→</mo><mo stretchy="false">(</mo><mi>π</mi><mi>π</mi><mo stretchy="false">)</mo><mo stretchy="false">(</mo><mi>π</mi><mi>π</mi><mo stretchy="false">)</mo></math> reactions

In our previous work [S. Bhattacharya et al., <a href="http://dx.doi.org/10.1103/PhysRevLett.128.182002">Phys. Rev. Lett. 128, 182002 (2022)</a>], we introduced a pioneering observable aimed at experimentally detecting the orbital angular momentum (OAM) of gluons. Our focus was on the longitudinal double spin asymmetry observed in exclusive dijet production during electron-proton scattering. We demonstrated the sensitivity of the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>cos</mi><mi>ϕ</mi></math> angular correlation between the scattered electron and proton as a probe for gluon OAM at small <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>x</mi></math> and its intricate interplay with gluon helicity. This current work provides a comprehensive exposition, diving further into the aforementioned calculation with added elaboration and in-depth analysis. We reveal that, in addition to the gluon OAM, one also gains access to the spin-orbit correlation of gluons. We supplement our work with a detailed numerical analysis of our observables for the kinematics of the Electron-Ion Collider. In addition to dijet production, we also consider the recently proposed semi-inclusive diffractive deep inelastic scattering process, which potentially offers experimental advantages over dijet measurements. Finally, we investigate quark-channel contributions to these processes and find an unexpected breakdown of collinear factorization.

Yoshitaka Hatta

Exploring orbital angular momentum and spin-orbit correlations for gluons at the Electron-Ion Collider

Exclusive diffractive meson production represents a golden channel for investigating gluonic saturation inside nucleons and nuclei. In this Letter, we settle a systematic framework to deal with beyond leading power corrections at small <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>x</mi></math>, including the saturation regime, and obtain the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msup><mrow><mi>γ</mi></mrow><mrow><mo>*</mo></mrow></msup><mo stretchy="false">→</mo><mi>M</mi><mo stretchy="false">(</mo><mi>ρ</mi><mo>,</mo><mi>ϕ</mi><mo>,</mo><mi>ω</mi><mo stretchy="false">)</mo></mrow></math> impact factor with both incoming photon and outgoing meson carrying arbitrary polarizations. This is of particular interest since the saturation scale at modern colliders, although entering a perturbative regime, is not large enough to prevent higher-twist effects to be sizable.

Michael Fucilla

Samuel Wallon

Probing Gluonic Saturation in Deeply Virtual Meson Production beyond Leading Power

We develop a framework combining the higher-twist formalism of exclusive processes in the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>s</mi></math> channel with the semiclassical effective description of small-<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>x</mi></math> physics in the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>t</mi></math> channel. We apply it to transversely polarized light vector meson production, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msup><mrow><mi>γ</mi></mrow><mrow><mo>*</mo></mrow></msup><mi>p</mi><mo stretchy="false">→</mo><mi>V</mi><mo stretchy="false">(</mo><mi>ρ</mi><mo>,</mo><mi>φ</mi><mo>,</mo><mi>ω</mi><mo stretchy="false">)</mo><mi>p</mi></mrow></math>, which starts at the next-to-leading power and for which a purely collinear treatment leads to end-point singularities. The result is obtained in the most general kinematics, including both forward and nonforward cases by preserving the full impact parameter dependence in the nonperturbative correlators, in both momentum and coordinate space representations. A systematic expansion of the Wilson lines in terms of Reggeized gluon fields is performed in order to obtain the results in the weak-field BFKL approximation. These new results will allow for investigating the dilute-to-dense regime transition of quantum chromodynamics for a wide class of observables.

Twist corrections to exclusive vector meson production in a saturation framework

We compute the spin-orbit correlations of quarks and gluons at small-x and show that the helicity and the orbital angular momentum of individual partons are strongly anti-aligned even in unpolarized or spinless hadrons and nuclei. Combined with the fact that gluons in the Color Glass Condensate are linearly polarized, our finding indicates that the helicity and the orbital angular momentum of single gluons are maximally entangled in a quantum mechanical sense.

Spin-orbit entanglement in the Color Glass Condensate

The goal of this white paper is to give a comprehensive overview of the rich field of forward physics. We discuss the occurrences of BFKL re-summation effects in special final states, such as Mueller–Navelet jets, jet–gap–jets, and heavy quarkonium production. It further addresses TMD factorization at low \(x\) and the manifestation of a semi-hard saturation scale in (generalized) TMD PDFs. More theoretical aspects of low-\(x\) physics, probes of the quark–gluon plasma, as well as the possibility to use photon–hadron collisions at the LHC to constrain hadronic structure at low \(x\), and the resulting complementarity between LHC and the EIC are also presented. We also briefly discuss diffraction at colliders as well as the possibility to explore further the electroweak theory in central exclusive events using the LHC as a photon–photon collider.

Mexico

Martin Hentschinski

Christophe Royon

Marco Alcazar Peredo

Cristian Baldenegro

Italy

Andrea Bellora

Francesco Giovanni Celiberto

Türkiye

Salim Cerci

Portugal

Grigorios Chachamis

Czechia

J.G. Contreras

Brazil

Sylvain Fichet

Gero von Gersdorff

Germany

Pablo González

Andreas van Hameren

Jamal Jalilian-Marian

Mats Kampshoff

United Kingdom

Valery Khoze

Michael Klasen

Spencer Robert Klein

Georgios Krintiras

Piotr Kotko

Krzysztof Kutak

Jean-Philippe Lansberg

Emilie Li

Constanin Loizides

Mohammed M.A. Mohammed

Maxim Nefedov

Melih A. Ozcelik

Alessandro Papa

CERN

Michael Pitt

Spain

Agustin Sabio Vera

Jens Salomon

Sebastian Sapeta

Gustavo Gil da Silveira

Victor Paulo Gonçalves

Mark Strikman

Deniz Sunar Cerci

Daniel Tapia Takaki

Marek Taševský

White Paper on Forward Physics, BFKL, Saturation Physics and Diffraction

We revisit high energy factorization for gluon mediated inclusive Deep Inelastic Scattering (DIS) for which we propose a new semi-classical approach that accounts systematically for the longitudinal extent of the target in contrast with the shockwave limit. In this framework, based on a partial twist expansion, we derive a factorization formula that involves a new gauge invariant unintegrated gluon distribution which depends explicitly on the Feynman x variable. It is shown that both the Regge and Bjorken limits are recovered in this approach. We reproduce in particular the full one loop inclusive DIS cross-section in the leading twist approximation and the all-twist dipole factorization formula in the strict x = 0 limit. Although quantum evolution is not discussed explicitly in this work, we argue that the proper treatment of the x dependence of the gluon distribution encompasses the kinematic constraint that must be imposed on the phase-space of gluon fluctuations in the target to ensure stability of small-x evolution.

Yacine Mehtar-Tani

Gluon-mediated inclusive Deep Inelastic Scattering from Regge to Bjorken kinematics

We propose a novel observable for the experimental detection of the gluon orbital angular momentum (OAM) that constitutes the proton spin sum rule. We consider longitudinal double spin asymmetry in exclusive dijet production in electron-proton scattering and demonstrate that the <math><mi>cos</mi><mi>ϕ</mi></math> azimuthal angle correlation between the scattered electron and proton is a sensitive probe of the gluon OAM at small <math><mi>x</mi></math> and its interplay with the gluon helicity. We also present a numerical estimate of the cross section for the kinematics of the Electron-Ion Collider.

Signature of the Gluon Orbital Angular Momentum

We provide a semi-classical description of the inclusive gluon mediated Deep Inelastic Scattering cross section in a way that accounts for the leading powers in both the Regge and Bjorken limits. Our approach thus allows a systematic matching of small and moderate <math><msub><mrow><mi>x</mi></mrow><mrow><mi>Bj</mi></mrow></msub></math> regimes of gluon proton structure functions. We find a new unintegrated gluon distribution with an explicit dependence on the longitudinal momentum fraction x which entirely spans both the dipole operator and the gluonic Parton Distribution Function. Computing this gauge invariant gluon operator on the lattice could allow to probe the energy dependence of the saturation scale from first principles.

A novel formulation of the unintegrated gluon distribution for DIS

We compute the differential yield for quark anti-quark dijet production in high-energy electron-proton and electron-nucleus collisions at small x as a function of the relative momentum P ⊥ and momentum imbalance k ⊥ of the dijet system for different photon virtualities Q 2, and study the elliptic and quadrangular anisotropies in the relative angle between P ⊥ and k ⊥. We review and extend the analysis in [1], which compared the results of the Color Glass Condensate (CGC) with those obtained using the transverse momentum dependent (TMD) framework. In particular, we include in our comparison the improved TMD (ITMD) framework, which resums kinematic power corrections of the ratio k ⊥ over the hard scale Q ⊥. By comparing ITMD and CGC results we are able to isolate genuine higher saturation contributions in the ratio Q  s  /Q ⊥ which are resummed only in the CGC. These saturation contributions are in addition to those in the Weizsäcker-Williams gluon TMD that appear in powers of Q  s  /k ⊥. We provide numerical estimates of these contributions for inclusive dijet production at the future Electron-Ion Collider, and identify kinematic windows where they can become relevant in the measurement of dijet and dihadron azimuthal correlations. We argue that such measurements will allow the detailed experimental study of both kinematic power corrections and genuine gluon saturation effects.

Finland

Heikki Mäntysaari

Farid Salazar

Björn Schenke

The importance of kinematic twists and genuine saturation effects in dijet production at the Electron-Ion Collider