The general question, crucial to an understanding of the internal structure of the nucleon, of how to split the total angular momentum of a photon or gluon into spin and orbital contributions is one of the most important and interesting challenges faced by gauge theories like Quantum Electrodynamics and Quantum Chromodynamics. This is particularly challenging since all QED textbooks state that such an splitting cannot be done for a photon (and a fortiori for a gluon) in a gauge-invariant way, yet experimentalists around the world are engaged in measuring what they believe is the gluon spin! This question has been a subject of intense debate and controversy, ever since, in 2008, it was claimed that such a gauge-invariant split was, in fact, possible. We explain in what sense this claim is true and how it turns out that one of the main problems is that such a decomposition is not unique and therefore raises the question of what is the most natural or physical choice. The essential requirement of measurability does not solve the ambiguities and leads us to the conclusion that the choice of a particular decomposition is essentially a matter of taste and convenience. In this review, we provide a pedagogical introduction to the question of angular momentum decomposition in a gauge theory, present the main relevant decompositions and discuss in detail several aspects of the controversies regarding the question of gauge invariance, frame dependence, uniqueness and measurability. We stress the physical implications of the recent developments and collect into a separate section all the sum rules and relations which we think experimentally relevant . We hope that such a review will make the matter amenable to a broader community and will help to clarify the present situation.C.Lorce@ulg.ac.be 30 1. The Stueckelberg symmetry 30 2. Towards a more refined classification 31 3. Origin and geometrical interpretation of the Stueckelberg symmetry 33 4. Measurability and the controversy about Stueckelberg symmetry 35 D. The Lorentz transformation properties 38 1. The standard approach 38 2. Critique of the standard approach 39 3. Lorentz transformation law of the pure-gauge and physical fields 40 V. The proton spin decomposition 41 A. The QCD energy-momentum and covariant angular momentum tensors 42 B. Decompositions of the proton momentum and the proton spin 44 1. The canonical decompositions 44 2. The kinetic decompositions 45 3. The master decomposition 46 C. Non-abelian Stueckelberg and Lorentz transformations 48 Bel,z 74 2. Lattice calculation of J q Bel,T 76 3. Evaluation of L q Ji,z in a longitudinally polarized nucleon, from GPDs 77 4. Evaluation of L q Ji,z in a longitudinally polarized nucleon, from GTMDs 78 B. Expressions for the canonical version of L 79 C. The orbital angular momentum in quark models 79 D. The phase-space distribution of angular momentum 82 VIII. Qualitative summary and experimental implications 84 A. Gauge invariance and measurability 84 B. Two kinds of decompositions 85 C. Sum rules vs. relations 86 1...

Comprehensive review paper on the theory and phenomenology of polarized deep inelastic scattering, to appear in Physics ReportsComment: 113 pages, latex, 40 figures not included (hard copies available via mail upon request to anselmino@to.infn.it

We present a new NLO QCD analysis of the world data on inclusive polarized deep inelastic scattering. Comparing to our previous analysis: i) the values of g A and a 8 = 3F −D are updated ii)the MRST'99 instead of the MRST'98 parametrization for the input unpolarized parton densities is used and iii) the recent SLAC E155 proton data on the spin asymmetry A1 are included in the analysis. A new set of polarized parton densities is extracted from the data and the sensitivity of the results to different positivity constraints is discussed.

Motivated by recent dramatic developments in the field, this book provides a thorough introduction to spin and its role in elementary particle physics. Starting with a simple pedagogical introduction to spin and its relativistic generalisation, the author successfully avoids the obscurity and impenetrability of traditional treatments of the subject. The book surveys the main theoretical and experimental developments, as well as discussing exciting plans for the future. Emphasis is placed on the importance of spin-dependent measurements in testing QCD and the Standard Model. This book will be of value to graduate students and researchers working in all areas of quantum physics and particularly in elementary particle and high energy physics. It is suitable as a supplementary text for graduate courses in theoretical and experimental particle physics.

The high energy and large p(T) inclusive polarized process, (A,SA) + (B,SB) -> C + X, is considered under the assumption of a generalized QCD factorization scheme. For the first time all transverse motions, of partons in hadrons and of hadrons in fragmenting partons, are explicitly taken into account; the elementary interactions are computed at leading order with noncollinear exact kinematics, which introduces many phases in the expressions of their helicity amplitudes. Several new spin and k(perp)-dependent soft functions appear and contribute to the cross sections and to spin asymmetries; we put emphasis on their partonic interpretation, in terms of quark and gluon polarizations inside polarized hadrons. Connections with other notations and further information are given in some Appendixes. The formal expressions for single and double spin asymmetries are derived. The transverse single spin asymmetry A(N), for p(uparrow) p -> pi X processes is considered in more detail, and all contributions are evaluated numerically by saturating unknown functions with their upper positivity bounds. It is shown that the integration of the phases arising from the noncollinear kinematics strongly suppresses most contributions to the single spin asymmetry, leaving at work predominantly the Sivers effect and, to a lesser extent, the Collins mechanism