Twist-3 contribution in the Drell-Yan process with tensor-polarized deuteron

The tensor-polarized structures of the deuteron can be probed through the proton-deuteron Drell-Yan process, where the proton is unpolarized and the deuteron is tensor polarized. This measurement will be conducted at Fermilab in the near future. In this reaction, the twist-3 contribution is not negligible compared to the twist-2 contribution due to the limited invariant mass of the dilepton pair. We calculate the twist-3 contribution for the Drell-Yan cross section with a tensor-polarized deuteron target, preserving the U(1)-gauge invariance of the hadronic tensor. The cross sections and weighted cross sections are expressed in terms of the tensor-polarized parton distribution functions (PDFs), thus one can extract the PDFs $f_{1\scriptscriptstyle{LL}}$, $f_{\scriptscriptstyle{LT}}$, and $f^{(1)}_{\scriptscriptstyle{1LT}}$ from the experimental measurements of Drell-Yan process. Our study should be helpful to solve the puzzle in the tensor-polarized structures of the deuteron.