Twist-3 gluon fragmentation contribution to polarized hyperon production in unpolarized proton-proton collision

Understanding the origin and mechanism of the transverse polarization of hyperons produced in unpolarized proton-proton collision, $pp\ensuremath{\rightarrow}{\mathrm{\ensuremath{\Lambda}}}^{\ensuremath{\uparrow}}X$, has been one of the longstanding issues in high-energy spin physics. In the framework of the collinear factorization applicable to large-${p}_{T}$ hadron productions, this phenomenon is a twist-3 observable which is caused by multiparton correlations either in the initial protons or in the process of fragmentation into the hyperon. We derive the twist-3 gluon fragmentation function (FF) contribution to this process in the leading order (LO) with respect to the QCD coupling constant. Combined with the known results for the contribution from the twist-3 distribution function and the twist-3 quark FF, this completes the LO twist-3 cross section. We also found that the model-independent relations among the twist-3 gluon FFs based on the QCD equation of motion and the Lorentz invariance property of the correlation functions guarantee the color gauge invariance and the frame independence of the cross section.