On the contribution of twist-3 multi-gluon correlation functions to single transverse-spin asymmetry in SIDIS

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We study the single spin asymmetry (SSA) induced by purely gluonic correlation inside a nucleon, in particular, by the three-gluon correlation functions in the transversely polarized nucleon, p. This contribution is embodied as a twist-3 mechanism in the collinear factorization framework and controls the SSA to be observed in the D-meson production with large transverse-momentum in semi-inclusive DIS (SIDIS), ep → eDX. We define the relevant three-gluon correlation functions in the nucleon, and determine their complete set at the twsit-3 level taking into account symmetry constraints in QCD. We derive the single-spin-dependent cross section for the D-meson production in SIDIS, taking into account all the relevant contributions at the twist-3 level. The result is obtained in a manifestly gauge-invariant form as the factorization formula in terms of the three-gluon correlation functions and reveals the five independent structures with respect to the dependence on the azimuthal angle for the produced D meson. We also demonstrate the remarkable relation between the twist-3 single-spin-dependent cross section and twist-2 cross sections for the D-meson production, as a manifestation of universal structure behind the SSA in a variety of hard processes.