The STAR Collaboration at RHIC is exploring the partonic origin of the proton spin with a broad range of measurements in polarized pp collisions. STAR measurements of the transverse single-spin asymmetry, A_N, for W boson production provide the first experimental investigation of the non-universality of the Sivers function. Precise follow-up measurements of A_N for direct photon production,...

COMPASS is a fixed target experiment located at the M2 beamline of the SPS accelerator at CERN. One of the most important objectives of the experiment is the study of the spin structure of the nucleon. Within the QCD parton model approach, the quark structure of the nucleon spin can be parametrized in terms of quark transverse momentum dependent (TMD) parton distribution functions (PDFs) while...

In this contribution we investigate the transverse single spin asymmetry in the inelastic $J/\Psi$ photoproduction in $p^\uparrow p$ and $p^\uparrow A$ collisions at RHIC energies. At leading order this process probes the gluon Sivers function. We predict large values for the cross sections, which indicates that its experimental analysis is, in principle, feasible. The rapidity dependence of...

First we perform a phenomenological analysis of the cos 2φ azimuthal asymmetry in virtual photon plus jet production induced by the linear polarization of gluons in unpolarized pA collisions. Employing a small-x model input distribution, the asymmetry is found to be strongly suppressed under TMD evolution, but still remains sufficiently large to be measurable in the typical kinematical region...

The talk will present the complete twist-4 result for the semi-inclusive deeply inelastic scattering $e^- N \to e^-qX$ with polarized electron and proton beams at the tree level of pQCD. The calculations have been carried out using the formulism obtained after collinear expansion where the multiple gluon scattering are taken into account and gauge links are obtained automatically in a...

In this talk, I will discuss the relevance of using quarkonium-hadroproduction data in order to study the gluon TMDs in unpolarised protons. I will discuss the case of single $\eta_c$ production as well as that of $J/\psi(\Upsilon)+\gamma$ and $J/\psi$ pairs. In particular, I will discuss our first extraction of $f_1^g$ using the di-$J/\psi$ LHCb data and argue that $h_1^{\perp g}$ can be...

The first measurement of transverse-spin-dependent azimuthal

asymmetries in the pion-induced Drell-Yan (DY) process will be

presented, which was reported in PRL 119, 112002. We use the CERN SPS

190 GeV/c pi- beam and a transversely polarized ammonia target.

Three azimuthal asymmetries giving access to different

transverse-momentum-dependent (TMD) parton distribution functions

(PDFs) are...

Transverse single-spin asymmetries (TSSA) of light hadron production from $p^{\uparrow}+p$ collisions provide valuable information on the spin structure of the nucleon. TSSA in the process $p^\uparrow + p \rightarrow h+X$ has been described in terms of twist-3 spin-dependent three-parton correlation functions, or twist-3 fragmentation functions in the QCD collinear factorization approach. In...

We study the orbital angular momentum (OAM) of quarks and gluons in the nucleon in the small-x region. We argue, in two different ways, that the gluon OAM significantly cancels the gluon helicity distribution at small-x. A similar cancellation occurs also in the quark sector.

The STAR experiment has been studying the spin structure of the proton, using the unique high-energy polarized proton collider, the Relativistic Heavy Ion Collider (RHIC). The kinematic coverage at STAR allows accessing gluons because quark-gluon and gluon-gluon scatterings dominate particle production at low and medium transverse momentum. The polarized gluon distribution function can be...

Jet production in high energy proton-proton ($pp$) collisions is dominated by hard QCD scatterings such as gluon-gluon ($gg$) and quark-gluon ($qg$) scatterings, and therefore an effective tool to probe the internal distribution of gluons in the proton. The STAR Collaboration at Relativistic Heavy Ion Collider (RHIC) is using longitudinally polarized $pp$ collisions at center of mass energies,...

The longitudinal double-spin asymmetry $A_{LL}$ in spin-polarized $p+p$ collisions provides insight into the gluon contribution to the proton's spin by accessing the gluon helicity distribution $\Delta$g. Prior RHIC 200 GeV measurements show non-zero asymmetries and hence indicate a nonzero contribution of gluon helicity to the proton spin $\Delta$G for the Bjorken-$x$ range $x > 0.05$ in the...

A new collinear factorization analysis of inclusive DIS scattering with suitable non-perturbative “jet correlators” shows that a novel, non perturbative spin-flip term associated with the invariant mass of the produced hadrons couples to the target's transversity distribution function. In inclusive cross sections, this provides an hitherto neglected and large contribution to the twist-3...

We study the double-spin asymmetry $A^{\cos\phi_S}_{LT}$ in semi-inclusive DIS for charged and neutral pions production by scattering a longitudinal polarized beam off a transversely polarized proton target. Within the collinear framework, in which the transverse momentum of the final state hadron is integrated out, we predict the asymmetries for three pion productions at the kinematics of...

The transverse spin transfer from polarized proton to $\Lambda$ and $\bar{\Lambda}$ hyperons is expected to be sensitive to the transversity distribution of the nucleon, and to the transversely polarized fragmentation function. We report the first measurement of the transverse spin transfer of $\Lambda$ and $\bar{\Lambda}$ along the polarization direction of the fragmenting quark, $D_{TT}$, in...

We investigate the spin-dependent (naive) T-odd fragmentation function $D^\perp_{1T}$, which can provide an explanation on the transverse polarization of the $\Lambda^0$ hyperon produced in an unpolarized process. We calculate $D^\perp_{1T}$ for light flavors in the spectator diquark model, with a Gaussian form factor at the hyperon-quark-diquark vertex. We include in the calculation both the...

Precision data taken in e+e- annihilation at or near the Υ(4S) by the Belle experiment has been instrumental in the extraction of spin dependent and integrated fragmentation functions. In this talk, we report our measurement on the invariant-mass and fractional-energy dependence of inclusive production of di-hardons. We also report on the production rate of hyperons and charmed baryons, the...

The correlation between the longitudinal polarization of a fragmenting quark and the transverse momenta of the produced hadrons was predicted over two decades ago. Nevertheless, experimental searches in the electron-positron annihilation process, both through the so-called jet handedness measurement by the SLD collaboration and more recently via the helicity-dependent dihadron fragmentation...

We present our recent calculations of the complete set of the leading-twist quark-polarization-dependent dihadron fragmentation functions (DiFFs) to pion pairs. The quark-jet framework is used to model the sequential hadronization of a polarized quark into hadrons, where the polarization transfer to the remnant quark in each hadron emission step is calculated using the spin density matrix...

In perturbative QCD, the masses of the hadrons involved in high energy reactions can usually be neglected. In this talk, I will discuss one case in which this may not be a good approximation, namely production of Kaons in electron-proton collisions at low (and not so low) beam energies. In particular, I will present a recent proposal to include hadron masses in theoretical calculations,...

Jefferson Laboratory has an extensive program of Deep Virtual Exclusive Scattering (DVES). I will review salient results from the 6 GeV era, and present the status and goals of both Deep Virtual Compton Scattering (DVCS) and Deep Virtual Meson Production (DVMP). A set of DVCS and exclusive $\pi^0$ measurements from 7 to 11 GeV have been completed in Hall A. A first JLab observation of...

Generalized parton distributions embody information on both the longitudinal momentum of the quarks as well as their transverse position and thus allow determining a 3-dimensional image of the nucleon. For transversely polarized quarks and or nucleons, the resulting transverse deformation of these images provides new insight on nucleon spin structure and spin-orbit correlations. Twist-3 GPDs...

Being the "mother distributions" of all types of two-parton correlation functions, generalized TMDs (GTMDs) have garnered a lot of attention. We address the important question of how to access GTMDs in physical processes. Recently, we have shown that quark GTMDs can in principle be probed through the exclusive pion-nucleon double Drell-Yan process, where the focus was on two particular GTMDs...

Generalized parton distributions (GPDs) have been investigated in the deeply virtual Compton scattering (DVCS) to solve the proton spin puzzle. On the other hand, the generalized distribution amplitudes (GDAs) can be studied in the two-photon process $\gamma^*\gamma→h \bar{h}$ which is accessible at KEKB. Namely, the GDAs are the s-t crossed quantities of the GPDs. In 2016, the differential...

Generalized Parton Distributions (GPDs) encode the correlations between longitudinal momentum and transverse position of partons inside hadrons and can give access to a picture of the nucleon structure in 2+1 dimensions. They have been studied theoretically and experimentally for almost two decades and a new experimental era is starting (at JLab and COMPASS currently, and in the future at an...

The contribution of the quark and gluon helicity distributions to the proton spin requires integrating these helicity PDFs over the entire range of x. This necessarily involves an extrapolation of the measured PDFs at finite values of x into their small-x asymptotics. As is well-known in the case of the unpolarized quark and gluon distributions, the small-x asymptotics are governed by...

We will present results on the nucleon spin decomposition and the momentum distribution among quarks in the nucleon. Techniques for lattice QCD simulations at the physical pion mass applied for the computation of sea-quark and gluon contributions will be presented. We will discuss several challenges and perspectives for future developments.

We provide a first calculation of the complete next-to-leading order QCD corrections for heavy flavor contributions to the inclusive structure function $g_1$ in longitudinally polarized deep-inelastic scattering. The results are derived with largely analytical methods and retain the full dependence on the heavy quark’s mass. We discuss all relevant technical details of the calculation and...

The phenomenological study of the spin dependent ($g_1^{p,n}$) structure functions of the nucleon has been carried out using the polarized distribution functions of the quarks $\Delta q(x)$. In light of the improved precision of the world data, the $p$ and $n$ longitudinal spin asymmetries ($A_1^p(x)$ and $A_1^n(x)$) have been calculated. The ratio of the $n$ and $p$ structure functions...

We investigate the spin-spin correlations of logitudinally-polarized quark in a longitudinally-polarized proton $\rho_{\Lambda \lambda}$, transversely-polarized quark in transversely-polarized proton $\rho^i_{\Lambda_{T} \lambda_{T}}$, transversely-polarized quark in longitudinally-polarized proton $\rho^{i}_{\Lambda \lambda_T}$ and longitudinally-polarized quark in transversely-polarized...

In this talk, I will argue that sea quark Sivers function can be dynamically generated through spin dependent odderon. Due to the C-odd nature of odderon, the derived quark Sivers function and anti-quark Sivers function at small x are the same in size, but differ by a minus sign. We further show that sea quark Sivers function computed in CGC is reduced to that obtained in collinear twist-3...