Spin-orbit correlations in QCD

• Yoshitaka Hatta

I present QCD analyses of the spin-orbit correlation of quarks and gluons inside hadrons. I discuss what we can learn from such correlations and how to access them in experiments at the EIC.

Phenomenology of transverse momentum dependent distributions of the pion and proton

• Patrick Barry

Recent works on pion structures through the JAM framework introduce both Drell-Yan (DY) and leading neutron (LN) electroproduction observables to constrain parton distribution functions (PDFs) in the pion. Extending to the transverse direction, we make use of low energy transverse momentum dependent DY data to extract pion transverse momentum dependent (TMD) PDFs. In these fixed target DY experiments, we additionally extract proton and nuclear TMDs. Using TMD factorization in the Collins, Soper, Sterman formalism, we also have access to dependence on the collinear PDF through the operator product expansion. Because of this, for the first time, we simultaneously analyzed TMD and collinear PDFs in the pion. Our results show a significant diRerence in the pion and proton TMDs, quantified by the first moment of the TMDs in transverse coordinate space. We indicate this diRerence comes from a nontrivial diRerence in the nonperturbative TMD structure.

Status of unpolarized TMD extractions from global fits

• Matteo Cerutti (Hampton University and Jefferson Lab)

In this talk, we discuss the latest results on the extraction of Transverse-Momentum-Dependent (TMD) distributions from global analyses of presently available experimental data. In particular, we focus on the simultaneous extraction of TMD Parton Distribution Functions (TMD PDFs) and Fragmentation Functions (TMD FFs) from global fits of semi-inclusive DIS and Drell-Yan data sets in the framework of the MAP Collaboration, and we discuss the differences from the results obtained by other groups.

Gluonic structure of proton from lattice QCD

• Raza Sufian

We present the first lattice QCD determination of the gluon helicity parton distribution function (PDF) toward ruling out the negative gluon polarization in the nucleon within the mid to large momentum fraction region. Additionally, we highlight the potential synergy between lattice QCD and generative machine learning applications, offering an avenue to explore the diverse systematic uncertainties linked to determining both unpolarized and polarized gluon distributions in the nucleon. We briefly outline preliminary findings concerning the gluon distribution in the pion using large-$N_c$ lattice gauge theory calculations and explore its potential implications.

Probing the gluon gravitational form factors of proton using near threshold J/ψ photoproduction

• Shivangi Prasad

Gravitational form factors (GFFs) encapsulate fundamental information about a hadron's internal structure including its mass distribution and mechanical quantities such as the pressure and shear forces. Recently, significant efforts have been made to access these GFFs experimentally and via ab initio lattice calculations. In this talk, I will focus on measurement of near-threshold $J/\psi$ photoproduction t-channel cross section which provides a unique tool to probe gluon GFFs of the nucleon. $J/\Psi$-007 experiment (E12-16-007) was conducted in Hall-C at the Thomas Jefferson National Accelerator Facility to measure near threshold 2-D $J/\psi$ exclusive photoproduction cross sections as a function of photon energy $E_{\gamma}$ and Mandelstam variable $t$. The experiment utilized a high intensity real photon beam produced by incidence of a 10.6 GeV incident electron beam on a copper radiator situated upstream of a hydrogen target. The produced $e^-e^+$ ($\mu^-\mu^+$) pair from decay of $J/\Psi$ was detected using two arm spectrometers in Hall C: the HMS and the SHMS. The bremsstrahlung photon energy range $E_{\gamma}$ and momentum transfer $|t|$, are between 9.1 GeV and 10.6 GeV and up to 4.5 GeV$^2$, respectively. I will focus on the recently published results on extracted gluon GFFs from the electron channel data. In addition, I will also present preliminary results from analysis of muon channel data and its impact on the uncertainties of the extracted form factors.

Proton GPD from lattice QCD

• Martha Constantinou

Most of the information from lattice QCD is on the Mellin moments of GPDs, namely form factors and their generalizations. Calculating the x-dependence of GPDs from lattice QCD has become feasible in the last few years due to novel approaches. In this work, we employ the approach of quasi-distributions, which relies on matrix elements of fast-moving hadrons coupled to non-local operators. The quasi-distributions are matched to the light-cone distributions using Large Momentum Effective Theory (LaMET). The approach has been extensively used for twist-2 PDFs, and is now extended to twist-2 GPDs. More recently, the feasibility of the approach for twist-3 PDFs and GPDs was . In this talk, we present an overview of selected results on x-dependent GPDs. This demonstrates the potential of lattice QCD calculations to complement other theoretical and experimental efforts toward the 3-D structure of hadrons.

Non-perturbative Collins-Soper kernel from a Coulomb-gauge-fixed quasi-TMD with chiral fermions

• Xiang Gao

We present the first lattice QCD calculation of the rapidity anomalous dimension of transverse-momentum-dependent distributions (TMDs), i.e. the Collins-Soper (CS) kernel, employing the recently proposed Coulomb-gauge-fixed quasi-TMD formalism as well as a chiral-symmetry-preserving lattice discretization. This unitary lattice calculation is conducted using the domain wall fermion discretization scheme, a fine lattice spacing of approximately 0.08 fm, and physical values light and strange quark masses. The CS kernel is determined analyzing the ratios of pion quasi-TMD wave functions (quasi-TMDWFs) at next-to-leading logarithmic (NLL) perturbative accuracy. We observe significantly slower signal decay with increasing quark separations compared to the established gauge-invariant method with a staple-shaped Wilson line. This enables us to determine the CS kernel at large nonperturbative transverse separations and find its near-linear dependence on the latter. Our result is consistent with the recent lattice calculation using gauge-invariant quasi-TMDWFs, and agrees with various recent phenomenological parametrizations of experimental data.

Nucleon transversity and tensor charge from di-hadron production

• Andreas Metz

We first present a new quantum field-theoretic definition of dihadron fragmentation functions (DiFFs) that have a number density interpretation. We then discuss the first global QCD analysis of dihadron production for a comprehensive set of data in electron-positron annihilation, semi-inclusive deep-inelastic scattering, and proton-proton collisions, from which we extract simultaneously the transversity distributions of the nucleon and pi+pi- DiFFs. In our fits, we incorporate known theoretical constraints on transversity. We show that lattice-QCD results for the tensor charges can be successfully included in the analysis. We also find agreement with results for the transversity and tensor charges obtained from measurements on single-hadron production, demonstrating for the first time the universal nature of all available information for the transversity distributions and the tensor charges of the nucleon.

Femtoscopy of the matter distribution in the proton

• Gastão Krein

Femtoscopy measurements of $J/\psi$-proton correlation functions in high-energy hadron collisions can access information on the matter distribution in the proton. The QCD multipole expansion allows us to express the $J/\psi$-proton scattering amplitude in terms of the product of the $J/\psi$ chromopolarizability and a scalar gluon gravitational (GFF) form factor. The scalar gluon GFF gives the gluonic contribution to the nucleon mass and determines the corresponding matter radius. We show the Jpsi-proton correlation function displays clear sensitivity to the scalar gluon GFF for a wide range of the $J/\psi$ chromopolarizability.

Overview of TMD related measurements

• Ralf Seidl

Transverse momentum dependent distribution and fragmentation functions are relevant in many processes when transverse momenta of final-state particles are observed. They provide additional information on the transverse spin and momentum structure of partons inside the nucleon that can otherwise not be accessed. For example, the Sivers function provides information on the transverse nucleon spin - parton orbit correlations while the Collins function relates the transverse quark spin to an azimuthal asymmetry of final-state hadrons. The unpolarized TMDs are even relevant at the highest energies when e.g. observing differential heavy boson or Higgs cross sections. Many measurements related to TMDs have been obtained in semi-inclusive DIS, e+e- annihilation and hadron collisions. Their recent results will be summarized in this talk, together with an outlook of what to expect from the EIC.

A separable Bethe-Salpeter approach to deuteron structure

• Adam Freese

Motivated by the desire to maintain manifest Lorentz covariance in calculations of deuteron structure, I model the nucleon-nucleon interaction using a non-local separable interaction Lagrangian. The Bethe-Salpeter equation for the deuteron's bound state vertex is separable and solvable in this model. With the deuteron vertex in hand, I calculate the electromagnetic and mechanical structure of the deuteron, which both receive significant contributions from two-body currents. I also explore the deuteron wave function in the non-relativistic limit, finding that good physical behavior at the origin imposes several constraints on the model parameters.

New physical processes for extracting generalized parton distributions with a better sensitivity to partonic structure

• Zhite Yu

Generalized parton distributions (GPDs) encode important non-perturbative information of hadron structures including the tomographic parton images. We introduce a type of exclusive processes for a better study of GPDs, which we refer to as single diffractive hard exclusive processes (SDHEPs), and give a general argument for their factorization into GPDs. We advocate a two-stage framework for picturing SDHEPs, which not only gives a clear view of factorization properties but also provides a unified description of the kinematics including various polarization asymmetries. We demonstrate that the SDHEP is not only sufficiently generic to cover all known processes but also well motivated for searching for new processes for extracting GPDs. Importantly, we also examine the sensitivity of the SDHEP to the parton momentum fraction x-dependence of GPDs, and demonstrate it quantitatively with two specific processes that can be readily measured at J-PARC/AMBER using a pion beam and at JLab using a photon beam, respectively. Both processes are capable of providing enhanced sensitivity to the $x$-dependence, overcoming the problem of shadow GPDs, and disentangling different types of GPDs with various spin asymmetries.

Experimental search for saturation physics at STAR

• Xiaoxuan Chu

Nucleons (protons and neutrons), composed of quarks held together by gluons, exhibit rapid growth in gluon density towards small momentum fractions (x). It is expected that this growth is controlled by nonlinear Quantum Chromodynamics (QCD) effects leading to the effect of gluon saturation. Understanding the role of saturated strong gluon fields has motivated tremendous theoretical efforts. Gluon saturation in heavy nuclei is predicted to result in suppressed and broader two-particle angular correlation in heavy nuclei involved collisions. Finding definitive evidence for a novel universal regime of nonlinear gluon dynamics is a primary objective of the RHIC Cold QCD Program and the EIC project. During 2015 and 2016, the STAR experiment collected high luminosity p+p, p+A, and d+A data. In this talk, we will present the recent results of forward di-hadron correlations from those datasets using STAR detectors. Simulation studies on the predicted broadening phenomena will also be discussed.

Small-x TMD factorization at NLO: semi-inclusive dijets and dihadrons in DIS

• Farid Salazar

Two-particle azimuthal correlations are an excellent window to access the dynamics of gluon saturation in collider experiments. In the kinematic regime where the two particles are produced sufficiently forward rapidities but back-to-back in the transverse plane, the differential cross-section computed in the Color Glass Condensate (CGC) admits a small-x TMD-like factorization. In this talk, I will report on recent advances in the joint resummation of small-x and Sudakov logarithms in semi-inclusive dijet and di-hadron production in nuclear deep inelastic scattering.

QCD spectroscopy and scattering theory on the lattice

• Raúl Briceño

To gain general principles of QCD from the spectrum and structure of hadrons, it is necessary to look across a broad range of states and see if patterns emerge. This is no small task due to two major obstacles. First, of course QCD is non-perturbative, which can in-principle be overcome with the use of lattice QCD. Second, the vast majority of states are unstable resonances that decay rapidly to multi-hadron states, and their existence can only be deduce from the dynamical properties of the scattering amplitudes of their byproducts. This has motivated an increasingly sophisticated program to study resonant scattering processes via lattice QCD. In this talk, I will review this rich ongoing program, and discuss how this may be one-day be used to access structural information of even resonant states.

Exploring Meson Structures from Lattice QCD

• Qi Shi

We present a comprehensive study of the electromagnetic form factors (EMFFs) of the pion and kaon, as well as the generalized parton distributions (GPDs) of the pion, using lattice QCD. For the pion and kaon form factors, we compute the pion and kaon EMFFs at high momentum transfers, -t, up to 10 and 28 GeV², respectively, achieving good agreement with experimental results up to -t ≲ 4$ GeV² and providing benchmarks for forthcoming experiments. We also test the QCD collinear factorization framework, relating form factors to meson distribution amplitudes, at next-to-next-to-leading order (NNLO) in perturbation theory. Additionally, we report a lattice calculation of x-dependent pion GPDs at zero skewness with multiple values of momentum transfers. We compare the Lorentz-invariant amplitudes derived from the symmetric and non-symmetric frames, and renormalize the bare matrix elements in the hybrid scheme. The quasi-GPDs can be obtained through the Fourier transform and then matched to the light-cone GPDs utilizing the large momentum effective theory (LaMET) with improved matching, which includes NNLO perturbative corrections, leading renormalon resummation (LRR) as well as renormalization group resummation (RGR). Our results also offer a 3D imaging of the pion in impact-parameter space, providing insights into the internal structure of these fundamental particles.

Signatures of the Yang-Mills deconfinement transition from the gluon two-point correlator

• Duifje van Egmond

The breaking of center symmetry in pure Yang-Mills theories has been connected to the confinement/deconfinement transition on the lattice, but continuum results did not show the same signatures. I will discuss the longitudinal or (chromo-)electric Yang-Mills gluon propagator in the recently proposed center-symmetric Landau gauge at finite temperature. We use the Curci-Ferrari model which accounts for lattice data in the deep infrared, showing massive behaviour of the gluons. This model allows us to rely on perturbative calculations. At one-loop order in the SU(2) case, the so-obtained longitudinal gluon propagator provides a clear signature for Z2 center-symmetry breaking with a singular behavior, characteristic of a continuous phase transition. This is in sharp contrast with what is found within the standard Landau gauge. We also identify various signatures for Z3 center-symmetry breaking in the SU(3) case in the form of genuine order parameters. Our results open new ways of identifying the transition from correlation functions both within continuum approaches and on the lattice.

TMD factorization unifying large and small x

• Andrey Tarasov

Hadron structure from the lattice Compton amplitude

• Gerrit Schierholz

Experimentally, hadron structure functions are extracted from the forward and off-forward Compton amplitudes. On the other hand, theoretical calculations are limited to Euclidean space-time. The closest one can come to exploiting the full potential of the EIC is to compute the Compton amplitude on the lattice in full diversity. In this talk I will discuss the challenges and the potential of this approach and present some recent highlights of the calculations.

Transverse Momentum Distributions from Lattice QCD without Wilson Lines

• Yong Zhao

The transverse-momentum-dependent distributions (TMDs), which are defined by gauge-invariant 3D parton correlators with staple-shaped lightlike Wilson lines, can be calculated from quark and gluon correlators fixed in the Coulomb gauge on a Euclidean lattice. These quantities can be expressed gauge-invariantly as the correlators of dressed fields in the Coulomb gauge, which reduce to the standard TMD correlators in the infinite boost limit. In the framework of Large-Momentum Effective Theory, a quasi-TMD defined from such correlators in a large-momentum hadron state can be matched to the TMD via a factorization formula, whose exact form is derived using Soft Collinear Effective Theory and verified at one-loop order. Compared to the currently used gauge-invariant quasi-TMDs, this new method can substantially improve statistical precision and simplify renormalization, thus providing a more efficient way to calculate TMDs in lattice QCD.

Lattice QCD calculation of the pion distribution amplitude with domain wall fermions at physical pion mass

• Rui Zhang

Pion distribution amplitude (DA) describes the wave function of pion as a quark-antiquark pair in the infinite-momentum frame. It has rich phenomenology due to its universality as inputs to exclusive processes and form factors at large momentum transfer. In this talk, I will present our recent lattice QCD calculation of pion DA on a chiral-symmetric domain-wall fermion ensemble at physical pion mass through the large momentum effective theory (LaMET) approach. I will discuss the theoretical improvements within the LaMET framework, especially the first application of threshold resummation in the perturbative matching onto the light-cone DA, which resums the large logarithms in the soft gluon limit at next-to-next-to-leading order. Applying the same analysis to data from a similar ensemble but with explicit chiral-breaking term, we find with 2σ confidence level that the DA obtained from chiral fermions is flatter and lower near x=0.5, with a larger second Mellin moment extracted through operator product expansion.

Insights into the cold QCD medium

• Charles-Joseph Naïm

Abstract: Understanding the effects of cold nuclear matter (CNM) is still a puzzle, especially in terms of their magnitude. These effects vary depending on the hard process, impacting the rapidity and transverse momentum distributions of the dilepton. Deciphering CNM effects is crucial for comprehending suppressions observed in hA collisions from fixed targets to LHC energies, but also in heavy-ion collisions. To address this challenge, we propose a global study of Drell-Yan and quarkonium production in pA and \piA collisions. Our goal is to establish a complete,coherent, and universal formalism for characterizing the impact of CNM effects. Additionally, the upcoming Electron-Ion-Collider (EIC) will play a crucial role in providing strong additional constraints on these effects. We will explore the extent to which the EIC can enhance our understanding of these effects.

Unraveling the internal structure of hadrons: from form factors to generalized parton distributions and future directions

• Melany Higuera Angulo

We present our extensive investigation into the internal structure of hadrons, particularly pseudo-scalar mesons, utilizing a unified algebraic model based on Schwinger-Dyson equations (SDEs). We showcase calculations of various non-perturbative objects, including electromagnetic (EFFs), transition form factors (TFFs), parton distribution functions (PDFs), generalized parton distributions (GPDs), and impact parameter space GPDs, which guide our future research directions in JLab. For this endeavor, we employed two approaches: the overlap approximation in the light front formalism and the impulse approximation. The overlap approximation offers insights into the 3D image of mesons through GPDs, leading to the derivation of PDFs, EFFs, and impact parameter space GPDs. Concurrently, the impulse approximation simplifies the construction of EFFs and TFFs. This study enhances our understanding of the algebraic model's capabilities and limitations regarding pseudo-scalar mesons. It also underscores the importance of focusing on more realistic techniques for future investigations.

Nuclear-modified transverse momentum distribution functions

• John Terry

For more than 50 years, bound hadrons have been known to undergo non-trivial modifications due to the presence of the cold nuclear medium."During this time, experimental measurements at collider facilities have focused on how the one-dimensional structure of hadrons is modified, with global QCD analyses proving extremely successful in extracting these distributions. More recently, we have used experimental data from Jefferson Lab to constrain the nuclear-modified fragmentation functions. Our methodology incorporates the global set of experimental data from both Drell-Yan production and Semi-Inclusive Deep Inelastic Scattering. Through a comprehensive global extraction of these distributions, we demonstrate the effectiveness of this extension by strongly describing the entire global dataset. A focal point of this paper is the impact of recent Jefferson Lab measurements. Most notably, to simultaneously describe experimental data at Jefferson Lab and HERMES we find that it is necessary to introduce a parameter which accounts for the non-perturbative scale evolution of the nTMDs. Additionally, we assess the kinematic coverage of the experimental data and provide insights into experimental opportunities at Jefferson Lab, future Electron-Ion Colliders, RHIC, and the LHC. These opportunities have the potential to significantly enhance and refine global analyses of nuclear-modified TMDs, contributing to a deeper understanding of the structure of cold nuclear matter.

Hadronization dynamics from the spectral representation of the gauge invariant quark propagator

• Caroline Costa

It is well known that a gauge dependent two-point correlation function can be made gauge invariant by introducing a gauge link connecting the fields. This stringy ansatz is widely used to build gauge invariant observables in DIS, as for instance, parton distribution functions (PDFs) and transverse-momentum-dependent functions (TMDs). In this talk, I will discuss recent results connecting the gauge invariant quark propagator to hadronization dynamics using the spectral representation of the (gauge dependent) quark propagator.

Gravitational form factors from lattice QCD

• Dimitra Pefkou

Multi-dimensional analyses of spin asymmetries

• Gunnar Schnell

One of the challenges faced in the analysis of semi-inclusive processes, like semi-inclusive deep-inelastic scattering, is the richness of the cross section with multi-dimensional dependence on various kinematic variables. The fully differential cross section of even just unpolarized lepton-nucleon scattering already requires at least five dimensions (single-hadron production) and even more so for more involved processes. Spin degrees of freedom often add further dependences. This requires special attention in experiment to have either a very good acceptance or at least control of it. In this talk I will briefly discuss some of the methods employed at HERMES and present some of the later highlights resulting from such HERMES analyses.

Novel reactions to access Generalized Parton Distributions in dilepton pairs

• Marie Boër

Threshold resummation for the virtual Compton process

• Jakob Schoenleber

I explain how to resum the threshold x -> +-xB logarithms in the hard coefficient function for the virtual Compton process in momentum space. This is the off-forward generalization of the threshold resummation in DIS in the endpoint xB -> 1 region. The interesting case is that of an outgoing real photon, i.e. DVCS, where the threshold limit corresponds to the limit of zero parton momenta x -> +-xi. I discuss why the logs are generally not large and hence the resummation does is not expected to give a sizable correction to DVCS observables.