The spin structure of the nucleon

Abstract

We review the present understanding of the spin structure of protons and neutrons, the fundamental building blocks of nuclei collectively known as nucleons. The field of nucleon spin provides a critical window for testing Quantum Chromodynamics (QCD), the gauge theory of the strong interactions, since it involves fundamental aspects of hadron structure which can be probed in detail in experiments, particularly deep inelastic lepton scattering on polarized targets.QCD was initially probed in high energy deep inelastic lepton scattering with unpolarized beams and targets. With time, interest shifted from testing perturbative QCD to illuminating the nucleon structure itself. In fact, the spin degrees of freedom of hadrons provide an essential and detailed verification of both perturbative and nonperturbative QCD dynamics.Nucleon spin was initially thought of coming mostly from the spin of its quark constituents, based on intuition from the parton model. However, the first experiments showed that this expectation was incorrect. It is now clear that nucleon physics is much more complex, involving quark orbital angular momenta as well as gluonic and sea quark contributions. Thus, the nucleon spin structure remains a most active aspect of QCD research, involving important advances such as the developments of generalized parton distributions (GPD) and transverse momentum distributions (TMD).Elastic and inelastic lepton-proton scattering, as well as photoabsorption experiments provide various ways to investigate non-perturbative QCD. Fundamental sum rules -such as the Bjorken sum rule for polarized photoabsorption on polarized nucleons -are also in the non-perturbative domain. This realization triggered a vigorous program to link the low energy effective hadronic description of the strong interactions to fundamental quarks and gluon degrees of freedom of QCD. This has also led to advances in lattice gauge theory simulations of QCD and to the development of holographic QCD ideas based on the AdS/CFT or gauge/gravity correspondence, a novel approach providing a well-founded semiclassical approximation to QCD. Any QCD-based model of the nucleon's spin and dynamics must also successfully account for the observed spectroscopy of hadrons. Analytic calculations of the hadron spectrum, a long sought goal of QCD research, has now being realized using light-front holography and superconformal quantum mechanics, a formalism consistent with the results from nucleon spin studies.We begin this review with a phenomenological description of nucleon structure in general and of its spin structure in particular, aimed to engage non-specialist readers. Next, we discuss the nucleon spin structure at high energy, including topics such as 2

The polarized three-loop anomalous dimensions from on-shell massive operator matrix elements

“…The Feynman integrals were reduced to master integrals using the integration-by-parts (IBP) relations [45] implemented in the package Reduze 2 [46,47]. 5 . There are different techniques available to calculate the master integrals, cf.…”

“…With the availability of the polarized 3-loop anomalous dimensions the present nextto-leading order data analyses of polarized deep-inelastic scattering data [3] can be promoted to the next-to-next-to-leading order level. Precision analyses of this kind are also relevant for the detailed study of the spin-composition of polarized nucleons (for reviews see [4,5]).…”

Unified Description of Polarized and Unpolarized Quark Distributions in the Proton

“…Introduction.-Understanding how the spin of the proton originates from its quark and gluon constituents is one of the most active research frontiers in hadron physics [1,2]. A key challenge is to determine the polarized parton distribution functions (PDFs), Δqðx; QÞ, which describe the difference of the probability density between helicityparallel and helicity-antiparallel quarks in a proton.…”

Orbital angular momentum of the proton and intrinsic five-quark Fock states

“…The latest results from each one of the experimental groups using various facilities: BNL, CERN, DESY, Jlab, and SLAC are given in chronological order in [9]. In spite of a healthy set of experimental data and intensive theoretical investigations, the question is still open; for recent reviews, see, e.g., [10][11][12][13][14][15][16][17].…”

“…The present work is devoted to studying the proton's OAM, which continues to be investigated via various formalisms; see review papers, e.g., [12,[14][15][16][17].…”