Higher twist fragmentation functions related to the spin asymetries*

The large single-transverse spin asymmetries(SSAs) were first observed in pion production and polarized lambda production in '70s. Because the conventional perturbative QCD calculation failed to predict such large asymmetries in high energy hadron scatterings, the development of the perturbative QCD framework was needed to describe the large SSAs. The higher twist approach in the collinear factorization framework have been well developed in the past decades as a successful framework to reproduce the large SSAs observed in the hadronic scattering processes like proton-proton collision in RHIC. The origin of the SSA has been a controversial issue. Much theoretical effort has been devoted in order to answer the question "Which is dominant, the distribution contribution or the fragmentation contribution ?". Recent numerical simulations suggested that the fragmentation contribution can be a dominant source of the large SSAs. This result motivated a lot of theoretical work to calculate an accurate magnitude of the fragmentation contribution in order to clarify the origin of the SSAs observed in both the pion production and the polarized lambda production. In this talk, I will present recent significant theoretical developments in the perturbative QCD calculation for the higher twist fragmentation contributions, leading-order result for the spin-dependent cross section, scale evolution equations of the twist-3 fragmentation functions and the first calculation of the next-leading order contribution to the cross section.