Progresses related to lattice QCD calculations of the rapidity anomalous dimension of quark transverse-momentum-dependent distributions, i.e., the Collins-Soper (CS) kernel, will be presented. Methodological and numerical advances over the last year will be reviewed. Results from the state-of-the-art lattice QCD calculations will be presented and compared with the those from the...

Gravitational Form Factors (GFFs) provide an important portal for probing the energy-momentum and mass distribution of nucleons and nuclei. This work presents the study of photon and gluon momentum GFFs using the Weizsäcker-Williams method of relativistic hadrons.

First, we express the photon A-GFFs in terms of charge form factors and discuss the corresponding photon radius. Furthermore, we...

High-order behavior of the perturbative expansion for short-distance observables in QCD is intimately related to the contributions of small momenta in the corresponding Feynman diagrams and this correspondence provides one with a useful tool to investigate power-suppressed nonperturbative corrections. We use this technique to study the structure of power corrections to parton quasi- and...

I discuss the constraints that positivity of physical cross-sections impose on unpolarized and polarized collinear parton distribution functions. I explain why in a generic factorizations scheme leading-twist PDFs may turn negative beyond leading order, and show that however in the commonly used MSbar scheme this cannot happen in the perturbative regime. I then discuss the implications of this...

Semi-inclusive hadron production processes in deep-inelastic lepton-nucleon scattering (SIDIS) are important probes of the fragmentation dynamics of quarks into hadrons. Moreover, longitudinally polarized SIDIS is a powerful tool for resolving the quark flavor decomposition of the proton's spin structure. In this talk, I will present the recent calculation of the full next-to-next-to-leading...

We present an exact analytic solution of the revised large-$N_c$ small-$x$ helicity evolution equations derived recently. We find the corresponding small-$x$ asymptotics of the flavor-singlet helicity PDFs to be

\begin{align}

\Delta \Sigma (x, Q^2) \sim \Delta G (x, Q^2) \sim \left( \frac{1}{x} \right)^{\alpha_h}

\end{align}

with the intercept given by an exact analytic expression which...

I describe recent developments in Drell Yan transverse-momentum resummation, and their implications on the definition of a new observable for W-boson mass extraction from charge-current Drell Yan data.

We perform the first complete one-loop study of exclusive photoproduction of vector quarkonia off a proton, including full generalised-parton-distribution (GPD) evolution. We confirm the perturbative instability of the cross section at high photon-proton-collision energies at Next-to-Leading Order (NLO) using collinear factorisation. Such an instability is known since 20 years and has been...

I discuss ongoing progress in the understanding of heavy-quark transverse momentum-dependent (TMD) fragmentation functions (FFs). These advances include their explicit next-to-leading order calculation in massive QCD and boosted Heavy-Quark Effective Theory (bHQET), exposing a rich singularity structure that is also relevant for the extension of fixed-order subtraction schemes to...

In this presentation, I explore the connection between Transverse Momentum Dependent distributions (TMDs) and collinear distributions through the introduction and analysis of Transverse Momentum Moments (TMMs). These moments are defined as weighted integrals of TMDs over their transverse momentum with a cut-off scale. I illustrate that TMMs can be understood as equivalent to collinear...

Pseudo and quasi-PDFs are key tools to compute parton distribution functions (PDFs) directly on the lattice.

However, using the lattice to make these calculations has its challenges. To get the Bjorken-x dependence from the bi-local operator, one needs to know the behavior of these operators for large values of the momentum hadronic target.

Lattice calculation, on the other hand, can provide...

We calculate the next to leading order corrections to SIDIS at small Bjorken x using the color glass condensate formalism. We first show that all UV and soft divergences cancel. We then show that collinear divergences are absorbed into DGLAP evolution of quark-hadron fragmentation function while the rapidity divergences are absorbed into BK/JIMWLK evolution of dipoles. We finally show that...

I present the full list of ${1\over Q^2}$ power corrections to unpolarized Drell-Yan hadronic tensor for electromagnetic (EM) current at large $N_c$ and demonstrate EM gauge invariance at this level.

QCD factorization takes on different forms in the large-x and the small-x regimes. In the large-x motivated collinear factorization, one gets the DGLAP evolution equation, whereas, in the small-x motivated rapidity factorization, the BFKL equation is the major player. To unify different regimes, a new TMD factorization based on the background field method is proposed, which not only reduces to...

We consider the Energy-Energy Correlation function in electron-positron annihilation to hadrons. We concentrate on the back-to-back region, performing all-order resummation of the logarithmically enhanced contributions in QCD perturbation theory, up to next-to-next-to-next-to-leading logarithmic (N3LL) accuracy. Away from the back-to-back region, we consistently combine resummed predictions...

The calculation of parton distributions of the nucleon is a requisite for understanding hadronic cross sections in terms of quarks and gluons. Over the last decade many calculations from first principles lattice QCD have begun through matrix elements which can be factorized similarly to cross sections. In this talk, I will highlight our calculations using the pseudo-PDF approach and its...

Correlation measurements in DIS and pp collisions provide unique opportunity to explore nucleon structure, including TMDs, GPDs, and more recently Wigner distributions. In this talk, I will review some of recent studies, which can be explored at the current and future facilities, such as JLab 12 GeV, EIC and LHC.

Lattice QCD simulations are nowadays being done with physical values of the light, strange and charm quark masses. These state-of-the-art gauge ensembles are enabling precision hadron structure studies. Mellin moments are extracted at the physical point providing information of the momentum fraction and angular momentum carried by quarks and gluons in hadrons. In parallel, new theoretical...

We present exploratory studies of the 3D gluon content of the proton, as a result of analyses on leading-twist transverse-momentum-dependent (TMD) gluon distribution functions, calculated in a spectator model for the parent proton. Our formalism embodies a fit-based parameterization for the spectator-mass density, suited to describe both the small-x and the moderate-*x* regime. Particular...

We study the small-$x$ asymptotics of the flavor singlet, leading-twist quark transverse-momentum-dependent parton distribution functions (TMDs) via the eikonal expansion of quark propagator and the gauge link, expressing the TMD operator definitions at small-$x$ in terms of polarized dipole amplitudes, which involve an insertion of appropriate spin-dependent parton-exchange vertices into the...

I discuss MAPPDFpol1.0, a new determination of the helicity-dependent parton distribution functions (PDFs) of the proton from a set of longitudinally polarised inclusive and semi-inclusive deep-inelastic scattering data. The determination includes, for the first time, next-to-next-to-leading order QCD corrections to both processes, and is carried out in a framework that combines a...

It is well known that the axial current exhibits the so-called chiral anomaly. The role of this anomaly in the context of the spin sum rule of the nucleon has been intensely discussed soon after the experimental discovery of the spin crisis in the late 1980s. While this field was largely dormant over the last decades, recent work has revived interest in this area. We will discuss...

Recently, new results on the extraction of gluon helicity PDFs have been presented. These new results provide a comprehensive global analysis involving double spin asymmetries from high-energy polarized jet data, large-x polarized DIS, and recent calculations from LQCD. In this talk, I will provide a summary of the recent findings.

When quarkonium is produced in the low-transverse momentum region, the contribution of soft and ultra-soft radiation between the heavy-quark pair becomes relevant. At this region, non-relativistic QCD (NRQCD) breaks down and we need to promote the long-distance matrix elements to the TMD shape functions (TMDShFs) in the NRQCD factorization procedure. In this talk, I discuss the cross section...

Quarkonia are very "handy" objects for the spin-physics community because they can be used to fill up the lack of information on gluon transverse momentum dependent distributions (TMDs) at energies $Q \lesssim 100$ GeV. In particular, among the different kinds of quarkonia, the $J/\psi$ is definitely the one that attracts the most attention. Nonetheless, its theoretical description is still...

Within the framework of transverse momentum dependent factorization in combination with nonrelativistic QCD, we study charmonium and bottomonium production in hadronic collisions. We focus on quarkonium states with even charge conjugation, for which the color-singlet production mechanism is expected to be dominant in the small transverse momentum region, $q^2_T \ll 4M^2_{c,b}$. It is shown...

We present a calculation of the single-spin asymmetry (SSA) for the single-inclusive production of hadrons in collisions of transversely polarized protons

and unpolarized electrons, ep↑ → hX. We compute this transverse spin observable

within the collinear twist-3 factorization approach in perturbative QCD to next-to-leading order (NLO) accuracy. Several production channels contribute at NLO...

A back-to-back semi-inclusive $J/\psi + jet$ production is a promising process to study gluon transverse momentum distribution (TMDs) at the future electron-ion collider (EIC). A back-to-back configuration allows a higher transverse momentum for $J/\psi$. We present an extension of a previous work where we studied $cos2\phi$ azimuthal asymmetry within the TMD factorization framework. We...

Double spin asymmetries for particle and jet productions in longitudinally polarized proton-proton collisions have been the flagship measurements at RHIC to study proton’s spin content originating from gluons. Conventional theoretical framework used to extract gluons’ helicity distribution relies on the collinear factorization framework which is applicable primarily when there exists a large...

In this talk, I will revisit the evolution of generalised parton distributions (GPDs) at leading order in the strong coupling constant $\alpha_s$ for all of the twist-2 quark and gluon operators. I will present a rederivation of the one-loop evolution kernels, expressing them in a form suitable for implementation, and check analytically that some basic properties, such as DGLAP/ERBL limits and...

I will present the limits and complementarity of GPD phenomenology using simultaneously lattice QCD, experimental data and theoretical models. I will point out how none of the three can convey a satisfactory picture alone as of now, but explore collectively complementary information. I will stress the crucial role of evolution in the uncertainties on the lattice, the modeling of GPDs at small...

In this presentation, we provide an overview of Generalized Transverse Momentum Dependent Distributions (GTMDs) of hadrons, recognized as the most comprehensive two-parton correlation functions. We discuss recent advancements in this field, emphasizing the state-of-the-art observables for these quantities and their significant implications for the field of spin physics.

In this talk, we present the latest results by the MAP Collaboration about the extraction of unpolarized quark Transverse-Momentum-Dependent Distributions (TMD PDFs) and Fragmentation Functions (TMD FFs) from global fits of Drell-Yan and Semi-Inclusive Deep-Inelastic Scattering (SIDIS) data sets. In particular, we discuss the impact of the introduction of flavour dependence in the...

Pions and kaons play an important role in QCD, as they are the pseudo-Goldstone bosons of chiral symmetry breaking while also being confined systems of quarks and gluons. 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. By making use of...

We present a first practical implementation of a recently proposed hadron structure oriented (HSO) approach to TMD phenomenology applied to Drell-Yan like processes, including lepton pair production at moderate $Q^2$ and $Z^0$ boson production. We emphasize the HSO's preservation of a basic TMD parton-model-like framework even while accounting for full TMD factorization and evolution. We argue...

After recalling the latest extractions of the $\Lambda$ polarizing fragmentation functions within a TMD approach from fits to $e^+e^-$ data, I will present theoretical estimates for the spontaneous transverse polarization of $\Lambda$ hyperons produced in unpolarized $pp$ collisions inside a jet. For the latter, transverse momentum effects are included only in the fragmentation mechanism....

I will report on recent QCD global analyses of transverse single-spin asymmetries involving two different approaches: transverse momentum dependent (TMD)/collinear twist-3 (CT3) observables involving single-hadron FFs, and twist-2 collinear observables involving dihadron fragmentation functions (DiFFs). A byproduct of these studies is the extraction of the transversity PDFs and calculation of...

The string+3P0 model of hadronization has been recently applied to the fragmentation of a string stretched between a quark-antiquark pair with correlated spin states. The pair is assumed to be created in e+e- annihilation via the exchange of a virtual photon. To perform simulations of e+e- events, the model has been implemented in the Pythia Monte Carlo event generator by extending the...

The Drell-Yan process is essential for the determination of the collinear and transverse momentum dependent (TMD) parton distribution function. For a nuclear target, in addition to the non-perturbative parton structure that is intrinsically different from that of a free nucleon, there are dynamical nuclear matter effects that modify the TMD cross section in proton-nucleus ($pA$) collisions....

I will present a calculation of perturbative $T$-odd contributions to the lepton angular distribution in the Drell-Yan process. The talk is based on work done with Valery Lyubovitskij, Werner Vogelsang, and Alexey Zhevlakov; the corresponding pre-print is available under $\texttt{arXiv:2403.18741}$.

Using collinear factorization, we worked at the first order in QCD perturbation theory...

I will present a novel semi-analytical method for parton evolution. The talk is based on work done with co-authors Oliver Schüle and Fabian Wunder, the corresponding preprint is $\texttt{arXiv:2404.18667}$.

The presented method is based on constructing a family of analytic functions spanning $x$-space which is closed under the considered evolution equation. Using these functions as a basis,...

We present an extension of the Bayesian reweighting procedure to the case of multiple independent extractions of TMDs from SIDIS and $e^+e^-$ data, namely the quark Sivers, transversity and Collins TMD functions. The reweighting is performed using $A_N$ data measured in $p^\uparrow p \to \pi X$ collisions at RHIC. The agreement with $A_N$ data at large-$x_F$ values, a kinematical region...

We introduce a string-based parametrization for nucleon quark and gluon generalized parton distributions (GPDs) that effectively handles all skewness values. Our approach leverages conformal moments, representing them as the sum of spin-j nucleon A-form and skewness-dependent spin-j nucleon D-form factor, derived from t-channel string exchange in AdS spaces. This model-independent framework,...

Particular gluon transverse momentum dependent distributions (TMDs and GTMDs) become Wilson loop correlators in the limit of small x. In this talk I will discuss the consequences of this and what happens under evolution.