By applying the collinear expansion to the semi-inclusive hadron production process $e^{+}+e^{-}\to h+\overline{q}(\text{jet})+X$ at high energies, we construct a theoretical framework where leading and higher twist contributions at the leading perturbative QCD can be calculated systematically. With this framework, we calculate the contributions up to twist-3 for spin-0, spin-$1/2$, and spin-1 hadrons, respectively. We present the results for the hadronic tensors, the differential cross sections, the azimuthal asymmetries, and the polarizations of the hadrons.

We present for the first time the complete twist-4 result for the semi-inclusive deeply inelastic scattering $e^{-}N\to e^{-}qX$ with polarized electron and proton beams at the tree level of perturbative QCD. The calculations have been carried out using the formalism obtained after collinear expansion where the multiple gluon scatterings are taken into account and gauge links are obtained automatically in a systematical way. The results show in particular that there are twist-4 contributions to all the eight twist-2 structure functions for $e^{-}N\to e^{-}hX$ that correspond to the eight twist-2 transverse-momentum-dependent parton distribution functions. Such higher-twist effects could be very significant and therefore have important impacts on extracting these three-dimensional parton distribution functions from the asymmetry data on $e^{-}N\to e^{-}hX$. We suggest also an approximate way to obtain a rough estimation of such higher-twist contributions.

We calculate the differential cross section for the unpolarized semi-inclusive deeply inelastic scattering process $e^{-}+N\to e^{-}+q+X$ in leading order of perturbative QCD and up to twist-4 in power corrections and study, in particular, the azimuthal asymmetry $⟨\cos 2\varphi ⟩$. The final results are expressed in terms of transverse momentum dependent parton matrix elements of the target nucleon up to twist-4. We also apply it to $e^{-}+A\to e^{-}+q+X$ and illustrate numerically the nuclear dependence of the azimuthal asymmetry $⟨\cos 2\varphi ⟩$ by using a Gaussian ansatz for the transverse momentum dependent parton matrix elements.

We apply collinear expansion to inclusive hadron production in ${e}^{+}{e}^{$-${}}$ annihilation and derive a formalism suitable for systematic study of leading as well as higher-twist contributions to fragmentation functions at the tree level. We make the calculations for hadrons with spin-0, spin-$1/2$ as well as spin-1 and obtain the results in terms of different components of fragmentation functions for the hadronic tensors, the differential cross section as well as hadron polarizations in different cases. The results show a number of interesting features such as the existence of transverse polarization for spin-$1/2$ hadrons at the twist-3 level, the quark polarization independence of the spin alignment of vector mesons.

Using the formalism obtained from collinear expansion, we calculate the differential cross section and azimuthal asymmetries in the semi-inclusive deeply inelastic lepton-nucleon (nucleus) scattering process $e^{-}+N(A)\to e^{-}+q+X$ with both polarized beam and polarized target up to twist-3. We derive the azimuthal asymmetries in terms of twist-3 parton correlation functions. We simplify the results by using the QCD equation of motion that leads to a set of relationships between different twist-3 functions. We further study the nuclear dependence of azimuthal asymmetries and show that they have similar suppression factors as those in the unpolarized reactions.