  We argue the existence of new $k_\perp$-dependent functions which can be
manifested in the Drell-Yan (SIDIS)-like processes. The presented new functions
resemble the well-known Boer-Mulders function associated with the quark spin
asymmetry, but in contrast they are sensitive to the transverse motion of
partons inside the hadron due to the collective alignment of quark spin
vectors.
