Spin physics and polarized structure functions

Abstract

A review on the theoretical aspects and the experimental results of polarized deep inelastic scattering and of other hard scattering processes is presented. The longitudinally polarized structure functions are introduced and cross section fromulae are given for the case of photon as well as W ± and Z 0 exchange. Results from the SLAC and CERN polarization experiments are shown and compared with each other as well as their implications for the integrated g 1 (x, Q 2 ) are reviewed. More recent experiments presently underway (like HERMES at DESY) and future projects (like RHIC at BNL, HERA-N and a polarized HERA collider at DESY) are discussed too. The QCD interpretation and the LO and NLO Q 2 -evolution of g 1 , i.e. of the longitudinally polarized parton densities, is discussed in great detail, in particular the role of the polarized gluon density, as well as the expectations for x → 0. Particular emphasis is placed on the first moment of the polarized structure function in various factorization schemes, which is related to the axial anomaly, and on its relevance for understanding the origin of the proton spin. Sum rules (i.e. relations between moments of the structure functions) are derived and compared with recent experimental results. Various other phenomenological applications are discussed as well, in particular the parametrizations of polarized parton densities as obtained from recent data and their evolution in Q 2 . Furthermore, jet, heavy quark and direct photon production are reviewed as a sensitive probe of the polarized gluon density, and the physics prospects of the future polarized experiments at RHIC ( p p) and a polarized HERA collider ( e p) are studied. DIS semi-inclusive asymmetries and elastic neutrino-proton scattering are reviewed, which will help to disentangle the various polarized flavor densities in the nucleon. The status of single and double spin asymmetries, and the observation of handedness in the final state, are discussed as well. Structure 1 functions for higher spin hadrons and nuclei are defined and possible nuclear effects on high energy spin physics are reviewed. The theoretical concept of spin-dependent parton distributions and structure functions of the polarized photon is presented and possibilities for measuring them are briefly discussed. Various nonperturbative approaches to understand the origin of the proton spin are reviewed, such as the isosinglet U A (1) Goldberger-Treiman relation, lattice calculations and the chiral soliton model of the nucleon. The physical interpretation and model calculations of the transverse structure function g 2 are presented, as well as recent twist-3 measurements thereof, and the Burkhardt-Cottingham sum rule is revisited. Finally, the physics of chiral-odd 'transversity' distributions is described and experimental possibilities for delineating them are reviewed, which will be important for a complete understanding of the leading twist-2 sector of the nucleon's parton structure. In the Appendix the full 2-loop anomalous dimension...

Azimuthal and single spin asymmetries in hard scattering processes

“…The rich, low-energy aspects of topics iii) and iv), which may be confronted only with nonperturbative approaches, will also remain uncovered. A comprehensive overview on these subjects and on related topics can be found in several review papers, addressing both their theoretical and experimental aspects [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17]. Here we will focus on the high-energy regime and the treatment in the context of pQCD approaches of transverse SSA's and, marginally, of the transverse polarization of spin 1/2 particles in unpolarized processes.…”

Polarized parton densities and spin dependent structure function of the nucleon

“…In this regard, the polarized nucleon structure function is defined in terms of PPDFs at the NLO as following [17] …”

Sea quark and gluon polarization in the nucleon

“…where the inclusive spin-dependent nucleon structure function g N 1 (x, Q 2 ) can be written at NLO as a convolution between polarized parton densities for quarks and gluons, ∆q i (x, Q 2 ) and ∆g(x, Q 2 ), respectively, and coefficient functions ∆C i (x) [11]; F N 1 (x, Q 2 ) is the unpolarized nucleon structure function that can be written in terms of F N 2 (x, Q 2 ) and R, the ratio of the longitudinal to transverse cross section [12].…”