We study the consistency between the transverse momentum dependent (TMD) factorization and the collinear twist-3 factorization for the transversely polarized hyperon production in semi-inclusive deep inelastic scattering (SIDIS).
The TMD approach describes the polarization in the small region of the hyperon's transverse momentum $P_{hT}$, while the twist-3 approach covers that in the large $P_{hT}$ region.
In the intermediate region of $P_{hT}$ where both frameworks are valid, they should match consistently.
This has been confirmed for the contributions from the Boer-Mulders function and the twist-3 distribution function.
Using the recently obtained complete leading-order cross section for the twist-3 fragmentation function contribution to $ep\to e\Lambda^\uparrow X$, we show that it also matches consistently with the polarizing fragmentation function contribution to this process.
This supports the idea that the two frameworks represent a unique QCD effect for the polarization in different kinematic regions.