Kotzinian-Mulders effect in semi-inclusive DIS within TMD factorization

In this study, we investigate the Kotzinian-Mulders effect under semi-inclusive deep inelastic scattering (SIDIS) within the framework of transverse momentum dependent (TMD) factorization. The asymmetry is contributed by the convolution of the Kotzinian-Mulders function begin{document}$ g_{1T}$end{document} and the unpolarized fragmentation function begin{document}$ D_1$end{document}. As a TMD distribution, the Kotzinian-Mulders function in the coordinate space in the perturbative region can be represented as the convolution of the C-coefficients and the corresponding collinear correlation function. The Wandzura-Wilczek approximation is used to obtain this correlation function. We perform a detailed phenomenological numerical analysis of the Kotzinian-Mulders effect in the SIDIS process within TMD factorization at the kinematics of the HERMES and COMPASS experiments. We observe that the obtained begin{document}$ x_B$end{document}-, begin{document}$ z_h$end{document}-, and begin{document}$ P_{hperp}$end{document}-dependent Kotzinian-Mulders effects are basically consistent with the HERMES and COMPASS measurements. We also make predictions at EIC and EicC kinematics.