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As a possible source of the single transverse spin asymmetry, we study thecontribution from purely gluonic correlation represented by the twist-3``three-gluon correlation" functions in the transversely polarized nucleon. Wefirst define a complete set of the relevant three-gluon correlation functions,and then derive its contribution to the twist-3 single-spin-dependent crosssection for the $D$-meson production in semi-inclusive deep inelasticscattering, which is relevant to determine the three-gluon correlations. Ourcross-section formula differs from the corresponding result in the literature,and the origin of the discrepancy is clarified.

Contribution of Twist-3 Multi-Gluon Correlation Functions to Single Spin Asymmetry in Semi-Inclusive Deep Inelastic Scattering