Model-independent identities and inequalities which relate the various spin observables of collisions in nuclear and particle physics are reviewed in a unified formalism. Their physical interpretation and their implications for dynamical models are also discussed. These constraints between observables can be obtained in several ways: from the explicit expression of the observables in terms of a set of helicity or transversity 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 spins in the initial or final state of the reaction or its crossed channels. The inequalities resulting from positivity need to be projected to single out correlations between two or three observables. The quantum aspects of the information carried by spins, in particular entanglement, are considered when deriving and discussing the constraints Several examples are given, with a comparison with experimental data in some cases. 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 for the simplest observables of single-particle inclusive reactions are reviewed. They also apply to spin-dependent structure functions and parton distributions, both integrated or transverse-momentum dependent. The corresponding inequalities are shown to be preserved by the evolution equations of quantum chromodynamics.Inequalities on spin observables 3

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The flavor changing rare decay B → K * (→ Kπ) + − is one of the most studied modes due to its sensitivity to physics beyond the standard model and several discrepancies have come to light among the plethora of observables that are measured. In this paper we revisit the analogous baryonic decay mode Λ b → Λ(→ pπ) + − and we present a complete set of ten angular observables that can be measured using this decay mode. Our calculations are done retaining the finite lepton mass so that the signal of lepton non-universality observed in B → K * + − can be corroborated by the corresponding baryonic decay mode. We show that due to the parity violating nature of the subsequent Λ → pπ decay there exist at least one angular asymmetry that is non-vanishing in the large recoil limit unlike the case in B → K * + − decay mode, making it particularly sensitive to new physics that violates lepton flavor universality.

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