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Single Transverse-Spin Asymmetry in Open Charm Production in SIDIS

We discuss the single transverse-spin asymmetry (SSA) to be observed in the $D$-meson production with large transverse-momentum in semi-inclusive DIS (SIDIS), $e p^\uparrow \rightarrow e D X$. This contribution is embodied as a twist-3 mechanism in the collinear factorization, which is induced by purely gluonic correlation inside the transversely-polarized nucleon, in particular, by the three-gluon correlation effects. We derive the first complete formula for the corresponding SSA in the leading-order QCD, revealing the five independent structures with respect to the dependence on the azimuthal angle for the produced $D$-meson. Our result obeys universal structure behind the SSAs in a variety of hard processes. We present the numerical calculations of our SSA formula for the $D$-meson production at the kinematics relevant to a future Electron Ion Collider.