What do we know about the proton spin structure?

The proton spin puzzle has inspired a vast programme of experiments and theoretical work challenging our understanding of QCD and its role in the structure of hadrons.The proton's internal spin structure is connected to chiral symmetry and, through gluon degrees of freedom in the flavour singlet channel, to the physics of the $\eta'$ meson. Why do quarks contribute just about one third of the proton's spin? Why are $\eta'$ mesons and their interactions so sensitive to gluonic...

A complete, fundamental understanding of the proton must include knowledge of the underlying spin structure. The transversity distribution, $h_1\left(x\right)$, which describes the transverse spin structure of quarks inside of a transversely polarized proton, is only accessible through channels that couple $h_1 \left(x\right)$ to another chiral odd distribution, such as the Collins fragmentation function ($\Delta^N D_{\pi/q^\uparrow}\left(z,j_T\right)$). Significant Collins a...

It is shown that the proton "spin crisis'' or "spin puzzle" can be understood by the relativistic effect of quark transversal motions due to the Melosh-Wigner rotation. The quark helicity $\Delta q$ measured in polarized deep inelastic scattering is actually the quark spin in the infinite momentum frame or in the light-cone formalism, and it is different from the quark spin in the nucleon rest frame or in the quark model. The flavor asymmetry of the Melosh-Wigner effect for t...

Understanding the internal spin structure of the nucleon remains a challenge in strong interaction physics. The unique capability of RHIC opened new avenues in studying the internal structure of the proton with unprecedented depth and precision. Significant progress has been made in the last few years through various measurements at STAR. The longitudinal spin measurements have contributed significantly to our understanding of the quark and gluon helicity distributions inside...

In this talk we present the results of the investigation on the so called double parton distribution functions (dPDFs), accessible quantities in high energy proton-proton and proton nucleus collisions, in double parton scattering processes (DPS). These new and almost unknown distributions encode information on how partons inside a proton are correlated among each other and represent a new tool to explore the three dimensional partonic structure of hadrons. In the present cont...

The Relativistic Heavy Ion Collider (RHIC), as the world's first and only polarized proton collider, offers a unique environment in which to study the spin structure of the proton. In order to study the proton's transverse spin structure, the PHENIX experiment at RHIC took data with transversely polarized beams in 2001-02 and 2005, and it has plans for further running with transverse polarization in 2006 and beyond. Results from early running as well as prospective measuremen...

We present a detailed assessment of how well a future Electron-Ion Collider could constrain helicity parton distributions in the nucleon and, therefore, unveil the role of the intrinsic spin of quarks and gluons in the proton's spin budget. Any remaining deficit in this decomposition will provide the best indirect constraint on the contribution due to the total orbital angular momenta of quarks and gluons. Specifically, all our studies are performed in the context of global Q...

The Relativistic Heavy Ion Collider (RHIC) at Brookhaven National Laboratory is the first accelerator facility that can accelerate, store and collide spin polarized proton beams. This development enables a physics program aimed at understanding how the spin of the proton results from its quark and gluon substructures. Spin states that are either parallel (longitudinal) or perpendicular (transverse) to the proton momentum reveal important insight into the structure of the prot...

The exact decomposition of the proton spin has been a much debated topic, on the experimental as well as the theoretical side. In this talk we would like to report on recent non-perturbative results and ongoing efforts to explore the proton spin from lattice QCD. We present results for the relevant generalized form factors from gauge field ensembles that feature a physical value of the pion mass. These generalized form factors can be used to determine the total spin and angul...

We derive a new twist-3 partonic sum rule for the transverse spin of the proton, which involves the well-know quark spin structure function $g_T(x)=g_1(x)+g_2(x)$, the less-studied but known transverse gluon polarization density $\Delta G_T(x)$, and quark and gluon canonical orbital angular momentum densities associated with transverse polarization. This is the counter part of the sum rule for the longitudinal spin of the proton derived by Jaffe and Manohar previously. We rel...