Twist-3 fragmentation functions in a spectator model with gluon rescattering

We study the twist-3 fragmentation functions $H$ and $\tilde{H}$, by applying a spectator model. In the calculation we consider the effect of the gluon rescattering at one loop level. We find that in this case the hard-vertex diagram, which gives zero contribution to the Collins function, does contribute to the fragmentation function $H$. The calculation shows that the twist-3 T-odd fragmentation functions are free of light-cone divergences. The parameters of the model are fitted from the known parametrization of the unpolarized fragmentation $D_1$ and the Collins function $H_1^{\perp }$. We find our result for the favored fragmentation function is consistent with the recent extraction on $H$ and $\tilde{H}$ from pp data. We also check numerically the equation of motion relation for $H$, $\tilde{H}$ and find that relation holds fairly well in the spectator model.