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The hadronization of a high-energy parton is described by fragmentation functions which are introduced through QCD factorizations. While the hadronization mechanism per se remains uknown, fragmentation functions can still be investigated qualitatively and quantitatively. The qualitative study mainly concentrates on extracting genuine features based on the operator definition in quantum field theory. The quantitative research focuses on describing a variety of experimental data employing the fragmentation function given by the parameterizations or model calculations. With the foundation of the transverse-momentum-dependent factorization, the QCD evolution of leading twist transverse-momentum-dependent fragmentation functions has also been established. In addition, the universality of fragmentation functions has been proven, albeit model-dependently, so that it is possible to perform a global analysis of experimental data in different high-energy reactions. The collective efforts may eventually reveal important information hidden in the shadow of nonperturbative physics. This review covers the following topics: transverse-momentum-dependent factorization and the corresponding QCD evolution, spin-dependent fragmentation functions at leading and higher twists, several experimental measurements and corresponding phenomenological studies, and some model calculations.

We investigate the cos2ϕh azimuthal asymmetry contributed by the coupling of the Boer–Mulders function and the Collins function in K±- and Λ-hyperon-produced SIDIS process. The asymmetry is studied under the transverse-momentum-dependent (TMD) factorization framework at the leading order by considering the TMD evolution effects that utilize the parametrization for non-perturbative Sudakov form factors. The DGLAP evolution effects of the collinear counterpart of the Collins function of the final-state hadrons are considered by introducing the approximated evolution kernels. We utilize the available parametrization for the proton Boer–Mulders function and the Collins function of K±. For the Collins function of the Λ hyperon, the result of the diquark spectator model is adopted due to the absence of parametrization. The numerical results of the cos2ϕh azimuthal asymmetry are obtained in the kinematic regions of EIC and EicC. It can be shown that the asymmetry is much smaller than the Sivers asymmetry, which means that the convolution of the Boer–Mulders function and the Collins function may not be the main contributor to the cos2ϕh asymmetry. We emphasize the importance of future measurement of the cos2ϕh asymmetry to unravel different contributors.