Spin Structure Functions

We review the theory and phenomenology of deep inelastic polarized lepton-nucleon scattering in the light of recent data with a deuteron target from the SMC at CERN and a Helium 3 target from the E142 experiment at SLAC. After including higher-order perturbative QCD corrections, mass corrections and updated estimates of higher-twist effects, we find good agreement with the basic Bjorken sum rule, and extract a consistent set of values for the quark contributions to the proton spin: $$\Delta\Sigma \equiv \Delta u + \Delta d + \Delta s = 0.27 \pm 0.11$$ $$\Delta u = 0.82 \pm 0.04, \Delta d = -0.44 \pm 0.04,\Delta s = -0.11 \pm 0.04$$ which are consistent with chiral soliton models and indications from lattice estimates. We also mention the prospects for future experiments on the spin structure of the nucleon.Comment: 18 pages (LateX) + 6 postscript figures encoded through uufiles; CERN-TH-7022/93, TAUP-2094-93; Plenary talk at the PANIC '93 (corrected eq. (3)

Spin structure functions

We review the study of the internal spin structure of the proton and neutron. High-energy scattering of polarized leptons by polarized protons, neutrons, and deuterons provides a measurement of the nucleon spin structure functions. These structure functions give information on the polarized quark contributions to the spin of the proton and the neutron and allow tests of the quark-parton model and quantum chromodynamics. We discuss the formalism of deep inelastic scattering of polarized leptons on polarized nucleons, the past decade of experimental progress, and future programs to measure the polarized gluon contribution to the proton spin

Mathematics for structure functions

We show some of the mathematics that is being developed for the computation of deep inelastic structure functions to three loops. These include harmonic sums, harmonic polylogarithms and a class of difference equations that can be solved with the use of harmonic sums.Comment: 6 pages LaTeX, uses axodraw.sty and npb.sty (included

Virtual Photon Structure Functions

We discuss the perturbatively calculable virtual photon structure functions. First we present the framework for analyzing the structure functions of the virtual photon and derive a first moment of $g_1^\gamma$ of the virtual photon. We then investigate the three positivity constraints satisfied by the eight structure functions of the virtual photon.Comment: 5 pages, LaTeX, 5 eps figures, npb.sty file included Talk given at RADCOR/Loops and Legs 2002, Kloster Banz, Germany, September 8-13, 2002, to appear in the Proceeding