Inequalities for nucleon generalized parton distributions with helicity flip

Kirch, Marc; Pobylitsa, P. V.; Goeke, K.

doi:10.1103/physrevd.72.054019

“…(5.1) of Ref. [10], has been found to be fulfilled by the MIT bag with SU(6) symmetry, in any kinematical region.…”

mentioning

confidence: 86%

“…In that case, at large ÿ 2 , data were underestimated by the cal- Recently, positivity bounds on helicity flip GPDs have been derived in Ref. [10]. The strongest bound on H q T , Eq.…”

mentioning

confidence: 97%

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Model study of generalized parton distributions with helicity flip

Scopetta

¹

2005

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Generalized parton distributions with helicity flip are studied in the quark sector, within a simple version of the MIT bag model, assuming an SU(6) wave function for the proton target. In the framework under scrutiny it turns out that only the generalized transversity distribution, H_T^q, is non vanishing. For this quantity, the forward limit is properly recovered and numerical results are found to underestimate recent lattice data for its first moment. Positivity bounds recently proposed are fulfilled by the obtained distribution. The relevance of the analysis for the planning of measurements of the quark generalized transversity is addressed.Comment: 15 pages, 4 figures; shortened version accepted for publication in Phys. Rev.

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“…where x 1,2 = (x ± ξ)/(1 ± ξ). The positivity constraints should be generalised if one goes beyond the collinear approximation for the initial and final momentum, when the helicity-flip GPD, denoted by E, starts to contribute [221][222][223]. The general analysis of the parton-hadron eight-dimensional helicity matrix, which by use of symmetry properties, may be reduced to dimensions four and two, allows to get [224] the complete set of inequalities involving the full basis of GPD's.…”

Section: Generalised Parton Distributionsmentioning

confidence: 99%

Spin observables and spin structure functions: inequalities and dynamics

Artru,

Elchikh,

Richard

et al. 2008

Preprint

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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.

show abstract

“…The positivity constraints should be generalised if one goes beyond the collinear approximation for the initial and final momentum, when the helicity-flip GPD, denoted by E, starts to contribute [221][222][223]. The general analysis of the parton-hadron eight-dimensional helicity matrix, which by use of symmetry properties, may be reduced to dimensions four and two, allows to get [224] the complete set of inequalities involving the full basis of GPD's.…”

Section: Generalised Parton Distributionsmentioning

confidence: 99%

Spin observables and spin structure functions: Inequalities and dynamics

Artru

¹

,

Elchikh

²

,

Richard

³

et al. 2009

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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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Inequalities for nucleon generalized parton distributions with helicity flip

Abstract: Several positivity bounds are derived for generalized parton distributions (GPDs) with helicity flip.

Cited by 8 publications

References 45 publications

Model study of generalized parton distributions with helicity flip

Model study of generalized parton distributions with helicity flip

Spin observables and spin structure functions: inequalities and dynamics

Spin observables and spin structure functions: Inequalities and dynamics

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