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The spin-1 deuteron possesses tensor-polarized structure functions that have no analogue in spin-1/2 hadrons, and an experimental program at JLab is being planned to explore this unique aspect of hadronic structure. In a few GeV$^2$ region of $Q^2$, higher-twist effects may become significant. In this work [1], we showed the first quantitative evaluation of the tensor-polarized twist-3 parton distribution function $f_{LT}(x)$.
Starting from the twist-2 distribution $f_{1LL}(x)$ [2] extracted from the HERMES data on the tensor-polarized structure function $b_1$, we used a Wandzura-Wilczek-like relation [3] to estimate the twist-3 distribution $f_{LT}(x)$. Our analysis demonstrated that the resulting twist-3 distribution $f_{LT}(x)$ is comparable in magnitude to the twist-2 distribution $f_{1LL}(x)$, indicating that twist-3 effects may play a non-negligible role. Furthermore, we found that the twist-3 $f_{LT}(x)$ exhibits an oscillatory behavior in Bjorken-$x$, similar to the twist-2 $f_{1LL}(x)$, and it satisfies a Burkhardt-Cottingham-like sum rule [3], which we verified numerically. These results provide timely input for future experimental studies of spin-1 hadrons.
[1] S. Kumano and K. Kuroki, arXiv:2509.05046.
[2] S. Kumano, Phys. Rev. D 82, 017501 (2010).
[3] S. Kumano and Qin-Tao Song, JHEP 09, 141 (2021).
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