Single/Double-Spin Asymmetry Measurements of Semi-Inclusive Pion Electroproduction on a Transversely Polarized 3He Target through Deep Inelastic Scattering

Parton distribution functions, which represent the flavor and spin structure of the nucleon, provide invaluable information in illuminating quantum chromodynamics in the confinement region. Among various processes that measure such parton distribution functions, semi-inclusive deep inelastic scattering is regarded as one of the golden channels to access transverse momentum dependent parton distribution functions, which provide a 3-D view of the nucleon structure in momentum space. The Jefferson Lab experiment E06-010 focuses on measuring the target single and double spin asymmetries in the 3He(e, e'pi+,-)X reaction with a transversely polarized 3He target in Hall A with a 5.89 GeV electron beam. A leading pion and the scattered electron are detected in coincidence by the left High-Resolution Spectrometer at 16\circ and the BigBite spectrometer at 30\circ beam right, respectively. The kinematic coverage concentrates in the valence quark region, x \sim0.1-0.4, at Q2 \sim 1-3 GeV2. The Collins and Sivers asymmetries of 3He and neutron are extracted. In this review, an overview of the experiment and the final results are presented. Furthermore, an upcoming 12-GeV program with a large acceptance solenoidal device and the future possibilities at an electron-ion collider are discussed.Comment: 14 pages, 6 figures, to be published in Modern Physics Letters

Mode dispersion and delay characteristics of optical waveguides using equivalent TL circuits

A new analysis leading to an exact and efficient algorithm is presented for calculating directly and without numerical differentiation the mode dispersion characteristics of cylindrical dielectric waveguides of arbitrary refractive-index profile. The new algorithm is based on the equivalent transmission-line (T-L) technique. From Maxwell's equations, we derive an equivalent T-L circuit for a cylindrical dielectric waveguide. Based on the TL-circuit model we derive exact analytic formulas for a recursive algorithm which allows direct calculation of mode delay and dispersion. We demonstrate this technique by calculating the fundamental mode dispersion for step, triangular, and linear chirp optical fiber refractive index profiles. The accuracy of the numerical results is also examined. The proposed algorithm computes dispersion directly from the propagation constant without the need for curve fitting and subsequent successive numerical differentiation. It is exact, rapidly convergent, and it results in savings for both storage memory and computing time