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

There are four new structure functions for the spin-1 deuteron in comparison with 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 by tensor-polarized parton distribution functions in the deuteron. HERMES measurements of $b_1$ are much different from the prediction of the standard deuteron model with D-state admixture. It indicates that the structure functions $b_1$ 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 to start in 2019. On the other hand, the measurement of tensor-polarized distributions is under consideration at Fermilab by the Drell-Yan process with the unpolarized proton beam and tensor-polarized deuteron target. It is expected to provide crucial information on tensor-polarized antiquark distributions. Since the distributions are small quantities, it is important to estimate the tensor-polarized spin asymmetry theoretically to find experimental feasibility for an actual proposal at Fermilab.