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 <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:msub><a:mi>f</a:mi><a:mrow><a:mn>1</a:mn><a:mrow><a:mi>L</a:mi><a:mi>L</a:mi></a:mrow></a:mrow></a:msub></a:math>, <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"><c:msub><c:mi>f</c:mi><c:mrow><c:mi>L</c:mi><c:mi>T</c:mi></c:mrow></c:msub></c:math>, and <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"><e:msubsup><e:mi>f</e:mi><e:mrow><e:mn>1</e:mn><e:mi>L</e:mi><e:mi>T</e:mi></e:mrow><e:mrow><e:mrow><e:mo stretchy="false">(</e:mo><e:mn>1</e:mn><e:mo stretchy="false">)</e:mo></e:mrow></e:mrow></e:msubsup></e:math> 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.