Q2 evolution of the neutron spin structure moments using a 3He target

The spin structure of the nucleon

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, have 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 Dirac's front form and light-front quantization which provide a frame-independent, relativistic 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, their predictions for the spin content of nucleons, the computation of PDFs and of hadron masses.

Measurement of the Q^{2} Dependence of the Deuteron Spin Structure Function g_{1} and its Moments at Low Q^{2} with CLAS

We measured the g_{1} spin structure function of the deuteron at low Q^{2}, where QCD can be approximated with chiral perturbation theory (χPT). The data cover the resonance region, up to an invariant mass of W≈1.9  GeV. The generalized Gerasimov-Drell-Hearn sum, the moment Γ_{1}^{d} and the spin polarizability γ_{0}^{d} are precisely determined down to a minimum Q^{2} of 0.02  GeV^{2} for the first time, about 2.5 times lower than that of previous data. We compare them to several χPT calculations and models. These results are the first in a program of benchmark measurements of polarization observables in the χPT domain.

Optically polarized 3He

This article reviews the physics and technology of producing large quantities of highly spin-polarized 3He nuclei using spin-exchange (SEOP) and metastability-exchange (MEOP) optical pumping. Both technical developments and deeper understanding of the physical processes involved have led to substantial improvements in the capabilities of both methods. For SEOP, the use of spectrally narrowed lasers and K-Rb mixtures has substantially increased the achievable polarization and polarizing rate. For MEOP nearly lossless compression allows for rapid production of polarized 3He and operation in high magnetic fields has likewise significantly increased the pressure at which this method can be performed, and revealed new phenomena. Both methods have benefitted from development of storage methods that allow for spin-relaxation times of hundreds of hours, and specialized precision methods for polarimetry. SEOP and MEOP are now widely applied for spin-polarized targets, neutron spin filters, magnetic resonance imaging, and precision measurements.

Probing quark-gluon interactions with transverse polarized scattering

We have extracted QCD matrix elements from our data on doubly polarized inelastic scattering of electrons on nuclei. We find the higher twist matrix element d˜2, which arises strictly from quark-gluon interactions, to be unambiguously nonzero. The data also reveal an isospin dependence of higher twist effects if we assume that the Burkhardt-Cottingham sum rule is valid. The fundamental Bjorken sum rule obtained from the a0 matrix element is satisfied at our low momentum transfer.

Quark-hadron duality in neutron (3He) spin structure

We present experimental results of the first high-precision test of quark-hadron duality in the spin-structure function g_{1} of the neutron and 3He using a polarized 3He target in the four-momentum-transfer-squared range from 0.7 to 4.0 (GeV/c);{2}. Global duality is observed for the spin-structure function g_{1} down to at least Q;{2}=1.8 (GeV/c);{2} in both targets. We have also formed the photon-nucleon asymmetry A1 in the resonance region for 3He and found no strong Q2 dependence above 2.2 (GeV/c);{2}.

Low-energy theorem for virtual compton scattering and generalized sum rules of the nucleon

We formulate the low-energy theorem for virtual Compton scattering off a nucleon and examine its consequences for generalized nucleon polarizabilites. As a result of a new, model-independent definition of the low-energy limit for doubly virtual Compton scattering, all generalized sum rules of the nucleon have a continuous limit for real photons and obtain contributions from the t channel that were not included previously.

3He spin-dependent cross sections and sum rules

We present a measurement of the spin-dependent cross sections for the 3He over -->(e over -->,e')X reaction in the quasielastic and resonance regions at a four-momentum transfer 0.1< or =Q2< or =0.9 GeV2. The spin-structure functions have been extracted and used to evaluate the nuclear Burkhardt-Cottingham and extended Gerasimov-Drell-Hearn sum rules for the first time. The data are also compared to an impulse approximation calculation and an exact three-body Faddeev calculation in the quasielastic region.

Q2 dependence of the neutron spin structure function g2(n) at low Q2

We present the first measurement of the Q2 dependence of the neutron spin structure function g2(n) at five kinematic points covering 0.57 (GeV/c)2 < or = Q2 < or = 1.34 (GeV/c)2 at x approximately = 0.2. Though the naive quark-parton model predicts g2 = 0, nonzero values occur in more realistic models of the nucleon which include quark-gluon correlations, finite quark masses, or orbital angular momentum. When scattering from a noninteracting quark, g2(n) can be predicted using next-to-leading order fits to world data for g1(n). Deviations from this prediction provide an opportunity to examine QCD dynamics in nucleon structure. Our results show a positive deviation from this prediction at lower Q2, indicating that contributions such as quark-gluon interactions may be important. Precision data obtained for g1(n) are consistent with next-to-leading order fits to world data.

Experimental determination of the evolution of the Bjorken integral at low Q2

We extract the Bjorken integral Gamma1(p-n) in the range 0.17 < Q2 < 1.10 GeV2 from inclusive scattering of polarized electrons by polarized protons, deuterons, and 3He, for the region in which the integral is dominated by nucleon resonances. These data bridge the domains of the hadronic and partonic descriptions of the nucleon. In combination with earlier measurements at higher Q2, we extract the nonsinglet twist-4 matrix element f2.

Measurement of the generalized forward spin polarizabilities of the neutron

The generalized forward spin polarizabilities gamma(0) and delta(LT) of the neutron have been extracted for the first time in a Q2 range from 0.1 to 0.9 GeV2. Since gamma(0) is sensitive to nucleon resonances and delta(LT) is insensitive to the Delta resonance, it is expected that the pair of forward spin polarizabilities should provide benchmark tests of the current understanding of the chiral dynamics of QCD. The new results on delta(LT) show significant disagreement with chiral perturbation theory calculations, while the data for gamma(0) at low Q2 are in good agreement with a next-to-leading-order relativistic baryon chiral perturbation theory calculation. The data show good agreement with the phenomenological MAID model.