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We discuss the single transverse-spin asymmetry (SSA) to be observed in the$D$-meson production with large transverse-momentum in semi-inclusive deepinelastic scattering, $e p^\uparrow \rightarrow e D X$. This contribution isembodied as a twist-3 mechanism in the collinear factorization, which isinduced by purely gluonic correlation inside the transversely-polarizednucleon, in particular, by the three-gluon correlation effects. The completeformula for the corresponding SSA in the leading-order QCD is expressed interms of the four independent gluonic correlation functions and reveals thefive independent structures with respect to the dependence on the azimuthalangle for the produced $D$-meson. We present the numerical calculations of theSSA formula at the kinematics relevant to a future Electron Ion Collider.

Single Transverse-Spin Asymmetry in Large $P_T$ Open Charm Production at an Electron-Ion Collider