Moments of Spin Structure Functions: Sum Rules and Polarizabilities

Nucleon structure study is one of the most important research areas in modern physics and has challenged us for decades. Spin has played an essential role and often brought surprises and puzzles to the investigation of the nucleon structure and the strong interaction. New experimental data on nucleon spin structure at low to intermediate momentum transfers combined with existing high momentum transfer data offer a comprehensive picture in the strong region of the interaction and of the transition region from the strong to the asymptotic-free region. Insight for some aspects of the theory for the strong interaction, Quantum Chromodynamics (QCD), is gained by exploring lower moments of spin structure functions and their corresponding sum rules. These moments are expressed in terms of an operator-product expansion using quark and gluon degrees of freedom at moderately large momentum transfers. The higher-twist contributions have been examined through the evolution of these moments as the momentum transfer varies from higher to lower values. Furthermore, QCD-inspired low-energy effective theories, which explicitly include chiral symmetry breaking, are tested at low momentum transfers. The validity of these theories is further examined as the momentum transfer increases to moderate values. It is found that chiral perturbation theory calculations agree reasonably well with the first moment of the spin structure function g_1 at low momentum transfer of 0.05 - 0.1 GeV^2 but fail to reproduce some of the higher moments, noticeably, the neutron data in the case of the generalized polarizability Delta_LT. The Burkhardt-Cottingham sum rule has been verified with good accuracy in a wide range of Q^2 assuming that no singular behavior of the structure functions is present at very high excitation energies.Comment: 10 pages, 8 figures, review article based on a talk at 2008 fall DNP meeting, to appear in International Journal of Modern Physics

Latest Results on g1g_1 and g2g_2 at high xx

Recent progress from Jefferson Lab has significantly improved our understanding of the nucleon spin structure in the high-$x$ region. Results of a precision measurement of the neutron spin asymmetry, $A_1^n$, in the high-$x$ (valence quark) region are discussed. The up and down quark spin distributions in the nucleon were extracted. $A_2^n$ was also measured. The results were used, in combination with existing data, to extract the second moment, $d_2^n$. Preliminary results on $A_1^p$ and $A_1^d$ in the high-$x$ region have also become available. Finally, the results of a precision measurement of the $g_2$ structure function to study higher twist effects will be presented.Comment: 4 pages, 2 figures, to appear in the DIS2005 Proceedings (AIP

Spin Sum Rules at Low Q2Q^2

Recent precision spin-structure data from Jefferson Lab have significantly advanced our knowledge of nucleon structure at low $Q^2$. Results on the neutron spin sum rules and polarizabilities in the low to intermediate $Q^2$ region are presented. The Burkhardt-Cuttingham Sum Rule was verified within experimental uncertainties. When comparing with theoretical calculations, results on spin polarizability show surprising disagreements with Chiral Perturbation Theory predictions. Preliminary results on first moments at very low $Q^2$ are also presented.Comment: 4 pages, to be published in the Proceedings of the 10th Conference on Intersections of Nuclear and Particle Physics (CIPANP

The consistency of estimator under fixed design regression model with NQD errors

In this article, basing on NQD samples, we investigate the fixed design nonparametric regression model, where the errors are pairwise NQD random errors, with fixed design points, and an unknown function. Nonparametric weighted estimator will be introduced and its consistency is studied. As special case, the consistency result for weighted kernel estimators of the model is obtained. This extends the earlier work on independent random and dependent random errors to NQD case

Flux-lattice melting in LaO1−x_{1-x}Fx_{x}FeAs: first-principles prediction

We report the theoretical study of the flux-lattice melting in the novel iron-based superconductor $LaO_{0.9}F_{0.1}FeAs$ and $LaO_{0.925}F_{0.075}FeAs$. Using the Hypernetted-Chain closure and an efficient algorithm, we calculate the two-dimensional one-component plasma pair distribution functions, static structure factors and direct correlation functions at various temperatures. The Hansen-Verlet freezing criterion is shown to be valid for vortex-liquid freezing in type-II superconductors. Flux-lattice meting lines for $LaO_{0.9}F_{0.1}FeAs$ and $LaO_{0.925}F_{0.075}FeAs$ are predicted through the combination of the density functional theory and the mean-field substrate approach.Comment: 5 pages, 4 figures, to appear in Phys. Rev.

Spin Sum Rules and Polarizabilities

The Gerasimov-Drell-Hearn sum rule and related dispersive integrals connect real and virtual Compton scattering to inclusive photo- and electroproduction. Being based on universal principles as causality, unitarity, and gauge invariance, these relations provide a unique testing ground to study the internal degrees of freedom that hold a system together. The present contribution reviews the spin-dependent sum rules and cross sections of the nucleon. At small momentum transfer, the data sample information on the long range phenomena (Goldstone bosons and collective resonances), whereas the primary degrees of freedom (quarks and gluons) become visible at large momentum transfer (short distance). The rich body of new data covers a wide range of phenomena from coherent to incoherent processes, and from the generalized spin polarizabilities on the low-energy side to higher twist effects in deep inelastic scattering.Comment: 15 pages, 7 figures, Proc. of Spin structure at long distance, Newport News, Virginia, 200