  There are polarized structure functions $b_{1-4}$ for the spin-1 deuteron. We
calculated the leading-twist tensor structure function $b_1$ by using
convolution description for the deuteron. We found large differences between
our theoretical functions and HERMES experimental data on $b_1$. Although
higher-twist effects should be considered in obtaining experimental $b_1$, it
suggests a possible existence of new hadron physics mechanism for spin-1
hadrons. Furthermore, we found that there are significant distributions at
large Bjorken $x$. In future, an experimental measurement is planned at JLab
for $b_1$ and there is a possibility of a proton-deuteron Drell-Yan experiment
at Fermilab with the tensor-polarized deuteron, so that further theoretical
studies are needed for clarifying the physics origin of tensor structure in
terms of quark and gluon degrees of freedom.
