JLAB-PHY-18-2760 SLAC{PUB{17279 The Spin Structure of the Nucleon Alexandre Deur Thomas Jefferson National Accelerator Facility, Newport News, VA 23606, USA Stanley J. Brodsky SLAC National Accelerator Laboratory, Stanford University, Stanford, CA 94309, USA Guy F. de T´eramond Universidad de Costa Rica, San Jos´e,Costa Rica July 17, 2018 [email protected], arXiv:1807.05250v1 [hep-ph] 13 Jul 2018 [email protected], [email protected], This material is based upon work supported by the U.S. Department of Energy, Office of Science, Office of High Energy Physics, under Contract DE-AC02-76SF00515. 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 nu- cleon 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, and it 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 unpo- larized 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 experi- ments provide various ways to investigate non-perturbative QCD. Fundamental sum rules { such as the Bjorken sum rule for polarized photoabsorption on polarized nucle- ons { 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 the development of holographic QCD ideas based on the AdS/CFT or gauge/gravity cor- respondence, 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 Dirac's front form and light-front quantization which provide a frame-independent, rel- ativistic description of hadron structure and dynamics, the derivation of spin-sum rules, and a direct connection to the QCD Lagrangian. We then discuss experimental and theoretical advances in the nonperturbative domain { in particular the development of light-front holographic QCD and superconformal quantum mechanics, its predictions for the spin content of nucleons, the computation of PDFs and of hadron masses. Contents 1 Preamble5 2 Overview of QCD and the nucleon structure8 2.1 Charged lepton-nucleon scattering . 10 2.1.1 The first Born approximation . 10 2.1.2 Kinematics . 11 2.1.3 General expression of the reaction cross-section . 12 2.1.4 Leptonic and hadronic tensors, and cross-section parameterization 13 2.1.5 Asymmetries . 14 2.2 Nucleon-Nucleon scattering . 15 2.3 e+ e− annihilation . 17 3 Constraints on spin dynamics from scattering processes 17 3.1 Deep inelastic scattering (DIS) . 17 3.1.1 Mechanism . 17 3.1.2 Bjorken scaling . 18 3.1.3 DIS: QCD on the Light-front . 18 3.1.4 Formalism and structure functions . 25 3.1.5 Single-spin asymmetries (SSA) . 27 3.1.6 Photo-absorption asymmetries . 27 3.1.7 Structure function extraction . 29 3.1.8 The Parton Model . 30 3.1.9 The nucleon spin sum rule and the \spin crisis" . 35 3.1.10 Definitions of the spin sum rule components . 37 3.2 The resonance region . 40 3.2.1 Constituent Quark Models . 41 3.2.2 The Resonance Spectrum of Nucleons . 43 3 3.2.3 A link between DIS and resonances: hadron-parton duality . 44 3.3 Elastic and quasi-elastic scatterings . 44 3.3.1 Elastic cross-section . 45 3.3.2 Quasi-elastic scattering . 48 3.4 Summary . 49 4 Computation methods 49 4.1 The Operator Product Expansion (OPE) . 51 4.2 Lattice gauge theory . 53 4.2.1 Calculations of structure functions . 55 4.2.2 Direct calculation of hadronic PDFs: Matching LFQCD to LGT 56 4.3 Chiral perturbation theory . 57 4.3.1 Chiral symmetry in QCD . 57 4.3.2 Connection to conformal symmetry . 58 4.4 The light-front holographic QCD approximation . 58 4.5 Summary . 60 5 Sum rules 60 5.1 General formalism . 61 5.2 GDH and forward spin polarizability sum rules . 61 5.3 δLT sum rule . 63 5.4 The Burkhardt-Cottingham sum rule . 63 5.5 Sum rules for deep inelastic scattering (DIS) . 64 5.6 Color polarizabilities . 69 6 World data and global analyses 69 6.1 Experiments and World data . 69 6.2 Global analyses . 72 6.3 PQCD in the high-xBj domain . 74 6.3.1 A1 in the DIS at high-xBj ...................... 75 6.3.2 Quark models and other predictions of A1 for high-xBj DIS . 75 6.3.3 A1 results . 76 0 6.4 Results on the polarized partial cross-sections σTT and σLT ........ 77 6.5 Results on the generalized GDH integral . 78 6.6 Moments of g1 and g2 ............................ 78 6.6.1 Extractions of the g1 first moments . 79 4 6.6.2 Data and theory comparisons . 79 6.6.3 Results on Γ2 and on the BC and ELT sum rules . 81 6.7 Generalized spin polarizabilities γ0, δLT ................... 82 6.7.1 Results on γ0 ............................. 82 6.7.2 The δLT puzzle . 83 6.8 d2 results . 83 6.8.1 Results on the neutron . 84 6.8.2 Results on the Proton . 84 6.8.3 Discussion . 84 6.9 Higher-twist contributions to Γ1, g1 and g2 ................ 85 6.9.1 Leading and higher-twist analysis of Γ1 .............. 85 6.9.2 Color polarizabilities and confinement force . 87 6.9.3 Higher twist studies for g1, A1, g2 and A2 ............. 87 6.10 Study of the hadron-parton spin duality . 89 6.11 Nucleon spin structure at high energy . 90 6.11.1 General conclusions . 90 6.11.2 Individual contributions to the nucleon spin . 91 6.11.3 High-energy picture of the nucleon spin structure . 95 6.11.4 Pending Questions . 97 6.11.5 Contributions from lower energy data . 97 7 Perspectives: the hadron mass spectrum 99 8 Outlook 101 1 Preamble The study of the individual contributions to the nucleon spin provides a critical window for testing detailed predictions of Quantum Chromodynamics (QCD) for the internal quark and gluon structure of hadrons. Fundamental spin predictions can be tested experimentally to high precision, particularly in measurements of deep inelastic scattering (DIS) of polarized leptons on polarized proton and nuclear targets. The spin of the nucleons was initially thought to originate simply from the spin of the constituent quarks, based on intuition from the parton model. However, experiments have shown that this expectation was incorrect. It is now clear that nucleon spin physics is much more complex, involving quark and gluon orbital angular momenta (OAM) as 5 well as gluon spin and sea-quark contributions. Contributions to the nucleon spin in fact originate from the nonperturbative dynamics associated with color confinement as well as from perturbative (pQCD) evolution. Thus, nucleon spin structure has become an active aspect of QCD research, incorporating important theoretical advances such as the development of generalized parton distributions (GPD) and transverse momentum distributions (TMD). Fundamental sum rules, such as the Bjorken sum rule for polarized DIS or the Drell-Hearn-Gerasimov sum rule for polarized photoabsorption cross sections, constrain critically the spin structure. In addition, elastic lepton-nucleon scattering and other exclusive processes, e.g. Deeply Virtual Compton Scattering (DVCS), also determine important aspects of nucleon spin dynamics. This has led to a vigorous theoretical and experimental program to obtain an effective hadronic description of the strong force in terms of the basic quark and gluon fields of QCD. Furthermore, the theoretical program for determining the spin structure of hadrons has benefited from advances in lattice gauge theory simulations of QCD and the recent development of light-front holographic QCD ideas based on the AdS/CFT correspondence, an approach to hadron structure based on the holographic embedding of light-front dynamics in a higher dimensional gravity theory, together with the constraints imposed by the underlying superconformal alge- braic structure. This novel approach to nonperturbative QCD and color confinement has provided a well-founded semiclassical approximation to QCD. QCD-based models of the nucleon spin and dynamics must also successfully account for the observed spectroscopy of hadrons. Analytic calculations of the hadron spectrum, a long-sought goal, are now being carried out using Lorentz frame-independent light-front holographic methods.