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

Optimal Power Allocation for A Massive MIMO Relay Aided Secure Communication

In this paper, we address the problem of optimal power allocation at the relay in two-hop secure communications under practical conditions. To guarantee secure communication during the long-distance transmission, the massive MIMO (M-MIMO) relaying techniques are explored to significantly enhance wireless security. The focus of this paper is on the analysis and design of optimal power assignment for a decode-and-forward (DF) M-MIMO relay, so as to maximize the secrecy outage capacity and minimize the interception probability, respectively. Our study reveals the condition for a nonnegative the secrecy outage capacity, obtains closed-form expressions for optimal power, and presents the asymptotic characteristics of secrecy performance. Finally, simulation results validate the effectiveness of the proposed schemes