Spin observables and spin structure functions: inequalities and dynamics

Abstract

Model-independent identities and inequalities relating the various spin observables of a reaction are reviewed in a unified formalism, together with their implications for dynamical models, their physical interpretation, and the quantum aspects of the information carried by spins, in particular entanglement. These constraints between observables can be obtained from the explicit expression of the observables in terms of a set of amplitudes, a non-trivial algebraic exercise which can be preceded by numerical simulation with randomly chosen amplitudes, from anticommutation relations, or from the requirement that any polarisation vector is less than unity. The most powerful tool is the positivity of the density matrices describing the reaction or its crossed channels, with a projection to single out correlations between two or three observables. For the exclusive reactions, the cases of the strangeness-exchange proton-antiproton scattering and the photoproduction of pseudoscalar mesons are treated in some detail: all triples of observables are constrained, and new results are presented for the allowed domains. The positivity constraints for total cross-sections and single-particle inclusive reactions are reviewed, with application to spin-dependent structure functions and parton distributions. The corresponding inequalities are shown to be preserved by the evolution equations of QCD.

135 pages, 37 figures, pdflatex, to appear in Physics Reports, new subsections added, typos corrected, references added

Cited by in corpus (35)

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• Determination of the Proton Spin Structure Functions for 0.05 < Q^2 < 5 GeV^2 using CLAS
• Probing the three-gluon correlation functions by the single spin asymmetry in p^\uparrow p\to DX
• Single Spin Asymmetry Scaling in the Forward Rapidity Region at RHIC
• Higher twist parton distributions from light-cone wave functions
• Quasi-parton distribution functions: a study in the diquark spectator model
• Elastic double diffractive production of axial-vector χ_c(1^{++}) mesons and the Landau-Yang theorem
• Nonperturbative and spin effects in the central exclusive production of tensor ${\chi }_c(2^{+})$ meson
• Spin and localization of relativistic fermions and uncertainty relations
• Information Content of Polarization Measurements
• Antiproton physics
• QCD rescattering mechanism for diffractive deep inelastic scattering
• Central exclusive quark-antiquark dijet and Standard Model Higgs boson production in proton-(anti)proton collisions
• Production of vector mesons in the String+${}^3{P}_0$ model of polarized quark fragmentation
• Rotation-invariant observables as Density Matrix invariants
• Polarization observables in the longitudinal basis for pseudo-scalar meson photoproduction using a density matrix approach
• Chiral vortical effect for vector fields
• Spin asymmetries in quasielastic charged current neutrino-nucleon scattering
• A simplified recursive ${}^3{P}_0$ model for the fragmentation of polarized quarks
• Gluonic Transversity from Lattice QCD
• Cut Moments approach in the analysis of DIS data
• Cut moments and a generalization of DGLAP equations
• Analysis of DIS structure functions of the nucleon within truncated Mellin moments approach
• General positivity bounds for spin observables in particle inclusive production
• Positivity bounds on gluon TMDs for hadrons of spin $\le$ 1
• How is transversity related to helicity for quarks and antiquarks inside the proton?
• Positivity bounds for Sivers functions
• SUSY, Casimir scaling and probabilistic properties of gluon and quark jets evolution
• Velocity-like maximum polarization: irreversibility and quantum measurements
• Kinetics of polarization in non-relativistic scattering
• Model-independent constraints on spin observables