Matching between Collinear Twist-3 and TMD Fragmentation Function Contributions to Polarized Hyperon Production in SIDIS

TL;DR

This paper demonstrates the consistency and matching between collinear twist-3 and TMD factorization approaches for polarized hyperon production in SIDIS, confirming they describe the same physics in overlapping kinematic regions.

Contribution

It establishes the equivalence of twist-3 and TMD frameworks for hyperon polarization in SIDIS at intermediate transverse momentum, clarifying their relationship.

Findings

TMD and twist-3 formalisms agree in the intermediate P_T region.

The polarizing fragmentation function can be expressed via twist-3 FFs.

Matching confirms both frameworks describe the same QCD effects.

Abstract

We investigate the consistency between the collinear twist-3 factorization and the transverse-momentum-dependent (TMD) factorization for the transversely polarized hyperon production in semi-inclusive deep inelastic scattering, $ep\to e\Lambda^\uparrow X$. In particular, we focus on the contributions from the twist-3 fragmentation functions (FFs) and the TMD polarizing FF in the region of the hyperon's intermediate transverse momentum $P_T$, $\Lambda_{\rm QCD}\ll P_T\ll Q$, where both frameworks are valid. In this region the polarizing FF can be expressed in terms of the twist-3 FFs including the purely gluonic ones, and the resulting TMD factorization formula for $ep\to e\Lambda^\uparrow X$ agrees with the small-$P_T$ limit of the corresponding twist-3 cross section. This matching of the two calculations indicates that the two frameworks describe the same effect in QCD and provide complementary frameworks for the process in different kinematic regions.