Alignment function as a new kind of transverse momentum dependent functions

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.