COMPASS is the longest-running experiment at CERN, with a record-breaking 20 years of data collection from 2002 to 2022. The experiment has a unique and diverse physics programme focused on nucleon structure and spectroscopy measurements.

The experimental results obtained by COMPASS during Phase I (2002-2011) and Phase II (2012-2022) for a wide range of nucleon spin structure-related DIS...

Understanding the 3D structure of visible matter in the universe while advancing the tomography of nucleons is one of the central goals of contemporary nuclear physics, pursued at the upgraded 12 GeV Jefferson Lab accelerator and at the planned Electron-Ion Collider (EIC). To fully capitalize on the data emerging from these experiments and to guide their extraction, the DOE-funded EXCLusives...

Hard exclusive meson production is one of the common approaches to constrain Generalised Parton Distributions. Such exclusive measurement and notably exclusive $\pi^{0}$ production were conducted at COMPASS in 2016 and 2017 at the M2 beamline from the CERN SPS using the 160 GeV/$c$ muon beam scattering off a 2.5~m long liquid hydrogen target inserted into a~barrel-shaped time-of-flight...

We will present preliminary results on Spin Density Matrix Elements (SDMEs) measured in hard exclusive $\phi$ meson muoproduction on protons at COMPASS using 160 GeV/$c$ polarised $\mu ^{+}$ and $\mu ^{-}$ beams scattering off a liquid hydrogen target. The measurements cover the range 6 GeV/$c^2$ < W < 17 GeV/$c^2$, 1.0 (GeV/$c$)$^2 <$ Q$^2 <$ 10.0 (GeV/$c$)$^2$ and 0.01 (GeV/$c$)$^2$ <...

We give an overview of recent developments in the computation of the anomalous dimension matrix of composite operators in non-forward kinematics. The elements of this matrix determine the scale dependence of non-perturbative parton distributions, such as GPDs, and hence constitute important input for phenomenological studies of exclusive processes like deeply-virtual Compton scattering....

We review our results on a new class of 2 -> 3 exclusive processes, as a probe of both chiral-even and chiral-odd quark GPDs. We consider the exclusive photoproduction of a photon-meson pair, in the kinematics where the pair has a large invariant mass, described in the collinear factorization framework. We cover the whole kinematical range from medium energies in fixed target experiments to...

We formulate a light-front spectator model for the proton incorporating the gluonic degree of freedom. We investigate the helicity distribution which is consistent with existing experimental data and satisfies the perturbative QCD constraints at small and large longitudinal momentum of gluon in this model. We present the transverse momentum dependent distributions (TMDs) for gluon in this...

We propose to extract quark orbital angular momentum (OAM) through exclusive $\pi^0$ production in electron-(longitudinally-polarized) proton collisions. Our analysis demonstrates that the $\rm sin(2\phi)$ azimuthal angular correlation between the transverse momentum of the scattered electron and the recoil proton serves as a sensitive probe of quark OAM. Additionally, we present a numerical...

Generalized Parton Distributions (GPD) are multidimensonal structure functions that encode the information about the internal structure of hadrons. Using privileged channels such as Deeply Virtual Compton Scattering (DVCS) or Timelike Compton Scattering (TCS), it is possible to make direct measurements at points where the momentum fraction of the parton equals the respective scaling...

Spin, a fundamental and subtle concept in nuclear physics, is deeply rooted in the symmetries and structure of space-time. The primary goal of the Spin Physics Program at the STAR experiment is to use spin as a probe to unravel the internal structure and the QCD dynamics of nucleons with unprecedented precision. This is made possible by the unique capability of RHIC to provide both...

Unraveling the proton spin composition, comprising intrinsic spins and angular momenta of quarks and gluons, stands as one of the most fundamental and challenging questions in QCD. Tremendous progress has been made since the first surprising result by the EMC experiment in the late 1980s, significantly contributing to our understanding of this question. However, the helicity distributions of...

The spin physics program of the PHENIX experiment at the Relativistic Heavy Ion Collider (RHIC) has a number of recent and ongoing analyses exploring the spin structure of the proton. Leveraging the unique capability of RHIC to collide polarized proton beams, transverse single spin asymmetry ($A_N$) measurements at PHENIX are performed on a variety of final states. These analyses are typically...

About 50 years ago, it was discovered that $\Lambda$ hyperons are produced polarized in collisions of unpolarized protons on beryllium. Since then, the $\Lambda$ polarization has been observed in various collision systems, including $e^+$+$e^-$ collisions. Majority of current results indicate the importance of final state effects, such as hadronization or fragmentation, in polarization of the...

I review the recent efforts in the NNPDF collaboration towards a new extraction of polarized parton distributions functions (pPDF) which will be highly relevant for the upcoming Electron-Ion-Collider (EIC) experiments. This includes a recent study on heavy quark effects in polarized DIS, where we apply the FONLL prescription for the first time in a polarized setup and demonstrate the...

We present a new determination of the helicity-dependent parton distribution functions (PDFs) of the proton from a set of longitudinally polarised inclusive deep-inelastic scattering 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...

Calculations at NNLO in QCD require an analytic understanding of the infrared singular structure involving up to two unresolved partons, which was achieved up to now only for unpolarized matrix elements. We derive the full set of splitting amplitudes arising in longitudinally polarised tree-level QCD matrix elements at NNLO in the Larin $\gamma_5$ scheme. They are extracted from DIS-like...

We investigate the different decompositions of the angular momentum in QCD for a relativistic spin $1/2$ composite state, namely a quark dressed with a gluon. We use light-front Hamiltonian perturbation theory, and in the light-front gauge, use the two-component framework by eliminating the constrained degrees of freedom. We also investigate the different decompositions of the angular momentum...

Inclusive top quark pair production at the LHC proceeds primarily via gluon fusion. Decays of the polarized top pairs through various particle and jet channels have strong angular dependences reflecting the top and anti-top polarizations that produce a variety of correlations among the decay products - particles and jets. Those correlations are determined by the spin dependent gluon...

The origin of the large single transverse-spin asymmetries(SSAs) has been a long-standing problem since they were first observed in the pion production and the transversely polarized hyperon production about a half century ago. We currently know two successful pQCD based frameworks in the description of the SSA. One of them is transverse-momentum-dependent(TMD) factorization which is valid...

The longitudinal spin transfer of the fragmentation function, $G_{1L}$, represents the probability density of producing longitudinally polarized hadrons from longitudinally polarized quarks or circularly polarized gluons. It thus was usually measured in polarized reactions or high-energy collisions where weak interaction dominates. In our work, we propose the dihadron polarization correlation...

We study the longitudinal spin transfer of $\Lambda$-hyperon production in semi-inclusive deep inelastic scattering with both current and target fragmentation mechanisms. For existing fixed-target experiments, such as JLab, COMPASS and HERMES, the events from the current region and those from the target fragmentation region are not clearly separated. However the study of target fragmentation...

An overview of the JLab program on nucleon spin and 3-d structure will be given. Highlights from recent experimental results will be presented with measurements focusing in the high-x (valence quark) region and/or in the low to intermediate Q2 region. Future perspective will be discussed.

Measurements of semi-inclusive deep inelastic scattering (SIDIS) are an important constraint on the description of the parton structure functions. Both the intrinsic $k_\perp$ of the quarks as well as the $p_\perp$ dependence of the hadronization process affect the dependence of the SIDIS cross section on transverse momentum ($P_T$). Experimental determination of the transverse momentum...

We explore the azimuthal angle decorrelation of lepton-jet pairs in e-p and e-A collisions as a means for precision measurements of the three-dimensional structure of bound and free nucleons. Utilizing soft-collinear effective theory, we perform the first-ever resummation of this process in e-p collisions at NNLL accuracy using a recoil-free jet axis. Our results are validated against Pythia...

Deeply Virtual Compton Scattering is the most direct channel to access

Generalized Partons Distributions (GPDs) and understand more about the 3D

structure of the nucleon, the origin of its spin and the forces at play

within it. The complete extraction of GPDs requires the use of polarized

electron beams and polarized nucleon targets in DVCS measurements.

The first polarized target...

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...

Generalized parton distributions (GPDs) are off-forward matrix elements of quark and gluon operators that work as a window to the total angular momentum of partons and their transverse imaging (nucleon tomography). To access GPDs one needs to look into exclusive processes, out of which double deeply virtual Compton scattering (DDVCS) is a promising mechanism to measure GPDs outside the lines...

In this talk, I will discuss our work in 2311.09146, regarding the breakdown of collinear factorisation in the exclusive photoproduction of a $\pi^0 \gamma$ pair. Such a process is sensitive to both quark and gluon GPD channels. In the latter case, the amplitude fails to factorise, due to the presence of a Glauber pinch, which has the same power counting as the collinear pinch. The Glauber...

We present a further step toward a global extraction of generalized parton distributions (GPDs) in the Generalized parton distributions through universal moment parameterization (GUMP) framework. We include HERA measurements of Deeply Virtual Meson Production (DVMP) in order to study gluon GPDs at non-zero skewness using the same moment parameterization ansatz as the previous global fit which...

In this talk I will describe a Lattice QCD calculation of parton structure from off-forward matrix elements. Similar to DVCS cross sections, these matrix elements are convolutions of Generalized Parton Distributions (GPDs), or equivalently Double Distributions (DDs). In our methodology, the computational cost of many different momenta combinations can be ameliorated allowing for a plethera of...

After two decades of RHIC running as a polarized proton collider, we summarize recent achievements of the PHENIX spin program and their impact on our understanding of the nucleon’s spin structure on partonic level (e.g. quark and gluon spin contribution to the spin of the proton), and transverse spin phenomena giving access to parton dynamics within the nucleon. Of particular interest are...

Abstract: Studies of the transverse-spin dependent azimuthal asymmetries in the Drell-Yan process permit to access the spin-dependent structure of the nucleon and especially to test the limited universality of its transverse-momentum dependent parton distributions. In 2015 and 2018 the COMPASS Collaboration at CERN performed measurements of the $\pi^-$p $\rightarrow \mu^+\mu^-$X reaction at...

Transverse Momentum Dependent (TMD) factorization leads to well established theorems for a restricted class of processes. In such cases, some of the effects produced by the soft radiation cancel out and the physics associated to them cannot be accessed. Extension of the factorization to non-standard processes inevitably leads to deal with the non trivial structure of the soft sector, revealing...

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 compare and contrast general features of our methodology with other common practices and emphasize the improvements derived from our approach that...

The transversity distribution function, $h_1^q(x)$, describes the transverse quark polarization within a transversely-polarized nucleon, where $x$ is the longitudinal momentum fraction carried by quark $q$. Being chiral-odd, $h_1^q(x)$ can be accessed only when coupled with another chiral-odd function, such as the spin-dependent interference fragmentation function (IFF) via the di-hadron...

In recent decades, there have been numerous efforts to unravel the origin of the unexpectedly significant transverse single spin asymmetry ($A_{N}$) observed in inclusive hadron productions at forward rapidities in $p^{\uparrow}$+$p$ collisions at various center-of-mass energies ($\sqrt{s}$). Several theories have been proposed to explain this phenomenon, including the twist-3 contributions...

Studies on the origin of transverse single-spin asymmetries have triggered the development of the twist-3 formalism and transverse-momentum-dependent parton distribution functions (TMDs). Measurement of the azimuthal distribution of identified hadrons within a jet in transversely polarized hadronic interactions provides an opportunity to study TMD physics, such as the Collins effect, which...

The transverse single spin asymmetries (TSSAs) in semi-inclusive deep inelastic scattering (SIDIS) have been intensively investigated over the last two decades. The TSSAs of $\rho^{0}$ are recently measured by COMPASS. Among these, the Sivers asymmetry can be expressed within the transverse momentum dependent (TMD) factorization framework, as the convolution of the Sivers function of the...

COMPASS is a fixed target high energy physics experiment that has been collecting data for 20 years (2002 to 2022) at the M2 beamline (SPS, North Area) at CERN. One of the goals of the experiment's broad physics program was to perform semi-inclusive measurements of target-spin dependent asymmetries in (di-)hadron production in DIS with high-energy muons colliding with polarised targets. The...

Pion-induced Drell-Yan muon-pair production is one of the key processes providing information on the structure of the $\pi$ meson. In this channel, the world data set is limitted to the cross-section measurements performed by the NA10 and E615 experiments more than 30 years ago. In 2015 and 2018, the COMPASS experiment at CERN collected data sensitive to the Drell-Yan process using a 190 GeV...

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.

The understanding of the gluon Sivers effect is one of the main objectives of current and future experiments as a possible solution to the large single transverse-spin asymmetry(SSA) which has been a mystery in high energy QCD over 40 years. The collinear twist-3 framework has been a successful perturbative QCD framework for the description of the SSA in the high transverse momentum region of...

A series of completed, ongoing, and proposed Semi Inclusive Deep Inelastic Scattering (SIDIS) experiments using the CLAS12 spectrometer in Hall B at Jefferson Lab are reviewed. These studies consist of scattering data from a highly polarized 11 GeV electron beam incident on a fixed proton/deuteron target which, in the case of the recently completed Run Group C experiment, were longitudinally...

The azimuthal angle distribution ($\phi_h$) of hadrons produced in deep inelastic scattering serves as a powerful tool for probing nucleon structure in terms of the transverse momentum-dependent parton distribution functions, and the fragmentation functions. For an unpolarized nucleon, three azimuthal modulations arise: $\cos \phi_h$ related to the Cahn effect, $\cos 2\phi_h$ linked to the...

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...

The Large Hadron Collider beauty (LHCb) experiment provides an opportunity to study hadronization processes, how particular hadrons are formed from scattered quarks and gluons (partons), in the forward region, 2 < η < 5. Going beyond traditional collinear non-perturbative fragmentation functions (FFs), transverse-momentum-dependent (TMD) FFs provide multidimensional information on the...

We describe a novel procedure to determine moments of parton distribution functions of any order with lattice QCD computations. The procedure is based on the gradient flow for fermion and gauge fields. The flowed matrix elements of twist-2 operators renormalize multiplicatively, and the matching with physical matrix elements is obtained making use of continuum symmetries. We calculate the...

Inclusive event shape distributions, as well as event shapes as a function of charge particle multiplicity are extracted from CMS low-pileup and compared with predictions from various generators. Multi-dimensional unfolded distributions are provided, along with their correlations, using state-of-the-art machine-learning unfolding methods.