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There are four new structure functions for the spin-1 deuteron in comparisonwith the ones for the spin-1/2 proton, and they are called $b_1$, $b_2$, $b_3$,and $b_4$. The twist-2 structure functions $b_1$ and $b_2$ are expressed bytensor-polarized parton distribution functions in the deuteron. HERMESmeasurements of $b_1$ are much different from the prediction of the standarddeuteron model with D-state admixture. It indicates that the structurefunctions $b_1$ and $b_2$ probe an interesting new aspect in the deuteron.There is an approved experiment at JLab to measure $b_1$ and it is expected tostart in 2019. On the other hand, the measurement of tensor-polarizeddistributions is under consideration at Fermilab by the Drell-Yan process withthe unpolarized proton beam and tensor-polarized deuteron target. It isexpected to provide crucial information on tensor-polarized antiquarkdistributions. Since the distributions are small quantities, it is important toestimate the tensor-polarized spin asymmetry theoretically to find experimentalfeasibility for an actual proposal at Fermilab.

Estimate on Spin Asymmetry for Drell-Yan Process at Fermilab with Tensor-Polarized Deuteron