Spin observables and spin structure functions: inequalities and dynamics

TL;DR

This paper reviews model-independent inequalities and identities relating spin observables in reactions, exploring their implications for physical models, quantum entanglement, and constraints on spin-dependent functions, with detailed examples and applications.

Contribution

It introduces a unified formalism for deriving inequalities among spin observables and applies it to specific reactions and structure functions, highlighting new constraints and their quantum and dynamical implications.

Findings

Derived new positivity constraints for reaction observables.

Established inequalities for spin-dependent structure functions.

Applied constraints to specific reactions like proton-antiproton scattering.

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.