  We discuss the role of gluon poles and the gauge invariance for the hadron
tensors of Drell-Yan and direct photon production processes with the
transversely polarized hadron. These hadron tensors are needed to construct the
corresponding single spin asymmetries. For the Drell-Yan process, we perform
our analysis within both the Feynman and axial-type (contour) gauges for
gluons. In both the Feynman and contour gauges, we demonstrate that the gauge
invariance leads to the need of the new (non-standard) diagrams. Moreover, in
the Feynman gauge, we argue the absence of gluon poles in the correlators
$\langle\bar\psi\gamma_\perp A^+\psi\rangle$ related traditionally to
$dT(x,x)/dx$. As a result, these terms disappear from the final QED gauge
invariant Drell-Yan hadron tensor. For the direct photon production, by using
the contour gauge for gluon fields, we find that there are new twist-$3$ terms
present in the hadron tensor of the considering process in addition to the
standard twist-$3$ terms.

High Energy Physics - Phenomenology