This article reviews our present understanding of QCD spin physics: the proton spin puzzle and new developments aimed at understanding the transverse structure of the nucleon. Present experimental investigations of the nucleon's internal spin structure, the theoretical interpretation of the different measurements, and the open questions and challenges for future investigation are discussed.

/pdf/the-spin-structure-of-the-nucleon-4938rrpltt.pdf

The Spin Structure of the Nucleon

In the framework of quantum chromodynamics (QCD), parton distribution functions (PDFs) quantify how the momentum and spin of a hadron are divided among its quark and gluon constituents. Two main approaches exist to determine PDFs. The first approach, based on QCD factorization theorems, realizes a QCD analysis of a suitable set of hard-scattering measurements, often using a variety of hadronic observables. The second approach, based on first-principle operator definitions of PDFs, uses lattice QCD to compute directly some PDF-related quantities, such as their moments. Motivated by recent progress in both approaches, in this document we present an overview of lattice-QCD and global-analysis techniques used to determine unpolarized and polarized proton PDFs and their moments. We provide benchmark numbers to validate present and future lattice-QCD calculations and we illustrate how they could be used to reduce the PDF uncertainties in current unpolarized and polarized global analyses. This document represents a first step towards establishing a common language between the two communities, to foster dialogue and to further improve our knowledge of PDFs.

/pdf/parton-distributions-and-lattice-qcd-calculations-a-4rjavyd9do.pdf

Parton distributions and lattice QCD calculations: a community white paper

https://par.nsf.gov/servlets/purl/10058007

The field of fragmentation functions of light quarks and gluons is reviewed. In addition to integrated fragmentation functions, attention is paid to the dependence of fragmentation functions on transverse momenta and on polarization degrees of freedom. Higher-twist and di-hadron fragmentation functions are considered as well. Moreover, the review covers both theoretical and experimental developments in single-inclusive hadron production in electron-positron annihilation, deep-inelastic lepton-nucleon scattering, and proton-proton collisions.

/pdf/parton-fragmentation-functions-33z4y02wdl.pdf

Parton Fragmentation Functions

There are two established approaches to look at the composition of the proton spin: the frame-independent spin structure (or the Ji sum rule) and the infinite-momentum-frame or parton spin structure (or the Jaffe–Manohar sum rule).In the frame-independent approach, the quark orbital and gluon angular momentum contributions can be extracted from the moments of the generalized parton distributions. Results from the Jefferson Lab 6 GeV and HERMES experiments suggest that there is a substantial quark orbital contribution.In terms of partons, the quark and gluon helicity contributions have a simple physical interpretation, and the result from Relativistic Heavy Ion Collider spin experiments has provided a first important constraint on the total gluon helicity.The development of a large-momentum effective theory along with lattice quantum chromodynamics simulations provide first-principles calculations of the spin structure. The results on the quark and gluon helicity contributions, and the quark orbital and gluon angular momentum contributions have provided the first complete theoretical picture.The Jefferson Lab 12 GeV programme will provide better information on the quark orbital angular momentum and gluon angular momentum. The future Electron-Ion Collider will provide high-precision measurements on the gluon helicity and gluon angular momentum.There are two established approaches to look at the composition of the proton spin: the frame-independent spin structure (or the Ji sum rule) and the infinite-momentum-frame or parton spin structure (or the Jaffe–Manohar sum rule).In the frame-independent approach, the quark orbital and gluon angular momentum contributions can be extracted from the moments of the generalized parton distributions. Results from the Jefferson Lab 6 GeV and HERMES experiments suggest that there is a substantial quark orbital contribution.In terms of partons, the quark and gluon helicity contributions have a simple physical interpretation, and the result from Relativistic Heavy Ion Collider spin experiments has provided a first important constraint on the total gluon helicity.The development of a large-momentum effective theory along with lattice quantum chromodynamics simulations provide first-principles calculations of the spin structure. The results on the quark and gluon helicity contributions, and the quark orbital and gluon angular momentum contributions have provided the first complete theoretical picture.The Jefferson Lab 12 GeV programme will provide better information on the quark orbital angular momentum and gluon angular momentum. The future Electron-Ion Collider will provide high-precision measurements on the gluon helicity and gluon angular momentum.

/pdf/what-we-know-and-what-we-don-t-know-about-the-proton-spin-9f9c49p7vp.pdf

What we know and what we don't know about the proton spin after 30 years

Author(s): Aschenauer, Elke-Caroline; Bazilevsky, Alexander; Diehl, Markus; Drachenberg, James; Eyser, Kjeld Oleg; Fatemi, Renee; Gagliardi, Carl; Kang, Zhongbo; Kovchegov, Yuri V; Lajoie, John; Lee, Jeong-Hun; Nocera, Emanuele-R; Pitonyak, Daniel; Prokudin, Alexei; Sassot, Rodolfo; Seidl, Ralf; Sichtermann, Ernst; Sievert, Matt; Surrow, Bernd; Stratmann, Marco; Vogelsang, Werner; Vossen, Anselm; Wissink, Scott W; Yuan, Feng | Abstract: Time and again, spin has been a key element in the exploration of fundamental physics. Spin-dependent observables have often revealed deficits in the assumed theoretical framework and have led to novel developments and concepts. Spin is exploited in many parity-violating experiments searching for physics beyond the Standard Model or studying the nature of nucleon-nucleon forces. The RHIC spin program plays a special role in this grand scheme: it uses spin to study how a complex many-body system such as the proton arises from the dynamics of QCD. Many exciting results from RHIC spin have emerged to date, most of them from RHIC running after the 2007 Long Range Plan. In this document we present highlights from the RHIC program to date and lay out the roadmap for the significant advances that are possible with future RHIC running.

/pdf/the-rhic-spin-program-achievements-and-future-opportunities-1ij3ide7lk.pdf

The RHIC SPIN Program: Achievements and Future Opportunities

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The RHIC SPIN Program: Achievements and Future Opportunities