Role of transverse gluon in SSA

It is known the single transverse spin asymmetry in semi-inclusive deep inelastic scattering can be factorized by a twist-3 distribution function $T_F$, which contains a gluon field strength tensor. With transverse gluon included in the power expansion, we find the gluon field strength tensor can be recovered definitely in soft-gluon-pole contribution at leading order of ${\alpha }_s$ expansion. This conclusion holds in Feynman and light-cone gauges.