and perform a global analysis of the experimental data. In conclusion, in this paper, we have studied the twist-three fragmentation function contribution to the inclusive hadron’s SSA in pp scattering p $^{↑}$p → hX . With a simple parametrization for the twist-three fragmentation function, we estimate its contribution to the SSAs of π 0 production at RHIC energy. We find that the contribution of the twist-three fragmentation function is comparable to that of the twist-three distribution function from the polarized nucleon. We comment on the possibility to use our approach to describe the large difference of the SSAs between the η and π 0 meson. We emphasize that one need to include both contributions from twist-three distribution and fragmentation functions into a global analysis, in order to better understand the single spin asymmetry for the inclusive hadron production. We thanks Jianwei Qiu and Yuji Koike for helpful discussions. This work was supported in part by the U.S. Department of Energy under contract DE-AC02-05CH11231. We are grateful to RIKEN, Brookhaven National Laboratory and the U.S. Department of Energy (contract number DE-AC02-98CH10886) for providing the facilities essential for the com- pletion of this work. [1] For a review, see, for example, U. D’Alesio and F. Murgia, Prog. Part. Nucl. Phys. 61 , 394 (2008). [2] S. Heppelmann [STAR Collaboration], arXiv:0905.2840 [nucl-ex]. [3] J. Adams et al. [STAR Collaboration], Phys. Rev. Lett. 92 , 171801 (2004); B.I. Abelev, et al. [STAR Collaboration], Phys. Rev. Lett. 101 , 222001 (2008). [4] D. L. Adams et al. [Fermilab E704 Collaboration], Nucl. Phys. B 510 , 3 (1998). [5] I. Arsene et al. [BRAHMS Collaboration], Phys. Rev. Lett. 101 , 042001 (2008). [6] see, for example, John Lajoie for the PHENIX Collaboration, talk presented at American Physical Society Division of Nuclear Physics Fall Meeting, Hawii, October 13-17, 2009; Mickey Chiu, Private communications. [7] D. W. Sivers, Phys. Rev. D 41 , 83 (1990); Phys. Rev. D 43 , 261 (1991). [8] J. C. Collins, Nucl. Phys. B 396 , 161 (1993). [9] J. C. Collins, S. F. Heppelmann and G. A. Ladinsky, Nucl. Phys. B 420 , 565 (1994). 11