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Probing the twist-3 multi-gluon correlation functions by pp \to DX

We study the single spin asymmetry (SSA) for the D-meson production $A_N^D$ in the $pp$ collision, $p^\uparrow p\to DX$, in the framework of the collinear factorization. Since the charm quark is mainly produced through the $c\bar{c}$-pair creation from the gluon-fusion process, this is an ideal process to probe the twist-3 triple-gluon correlation functions in the polarized nucleon. We derive the corresponding cross section formula for the contribution of the triple-gluon correlation function to $A_N^D$ in $p^\uparrow p\to DX$, applying the method developed for $ep^\uparrow\to eDX$ in our previous study. As in the case of $ep^\uparrow\to eDX$, our result differs from a previous study in the literature. We will also present a simple estimate of the triple-gluon correlation functions based on the preliminary data on $A_N^D$ by RHIC.