It has been known for a long time that hyperons produced in hadronic collisions are polarized perpendicular to the production plane of the reaction. This effect cannot be described by using twist-2 collinear parton correlators only. Here we compute the contribution of twist-3 fragmentation functions to the production of transversely polarized hyperons in unpolarized proton-proton collisions in the framework of collinear factorization. By taking into account the relations among the relevant twist-3 fragmentation functions which follow from the QCD equation of motion and the Lorentz invariance property of the correlators, we present the leading-order cross section for this term.

We perform a systematic study on the twist-3 gluon distribution and fragmentation functions which appear in the collinear twist-3 factorization for hard inclusive processes. Three types of twist-3 distribution and fragmentation functions, i.e., intrinsic, kinematical and dynamical ones, which are necessary to describe all kinds of twist-3 cross sections, are related to each other by the operator identities based on the QCD equation of motion and the Lorentz invariance properties of the correlation functions. We derive the exact relations for all twist-3 gluonic distribution and fragmentation functions for a spin-1/2 hadron. Those relations allow one to express intrinsic and kinematical twist-3 gluon functions in terms of the twist-2 and dynamical twist-3 functions, which provides a basis for the renormalization of intrinsic and kinematical twist-3 functions. In addition, those model independent relations are crucial to guarantee gauge invariance and frame independence properties of the twist-3 cross sections.

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We investigate the transverse polarization of a hyperon produced in the high-energy unpolarized proton-proton collision, pp → Λ ↑ X, based on the collinear twist-3 factorization formalism. We focus on the contribution from the twist-3 distribution in one of the unpolarized proton and the transversity fragmentation function for the final hyperon. Utilizing the "master formula" for the soft-gluon-pole cross section, we clarify the reason for why it receives only the derivative term of the twist-3 distribution. We also present the first computation of the soft-fermion-pole cross section and found that it vanishes. This means that the derivative of the soft-gluon-pole function is the only source for the twist-3 cross section from the unpolarized twist-3 distribution, which provides a useful basis for a phenomenological analysis.

We study transverse polarization of hyperons produced in unpolarized proton-proton collision, pp → Λ ↑ X, based on the collinear twist-3 factorization. We focus on the twist-3 gluon fragmentation contribution to this process, which is potentially as important as the previously calculated contributions from the twist-3 distribution in the initial proton and the twist-3 quark-fragmentation for Λ ↑ . After summarizing the complete set of the purely gluonic twist-3 fragmentation functions for Λ ↑ , we provide a formalism of calculating its contribution to pp → Λ ↑ X.