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

In this paper we study the Kotzinian-Mulders effect in 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$\end{document} . As a TMD distribution, the Kotzinian-Mulders function in the coordinate space in the perturbative region can be represented as the convolution of the C-coefficients and the corresponding collinear correlation function. The Wandzura-Wilczek approximation is used to obtain this correlation function. We perform a detailed phenomenological numerical analysis of the Kotzinian-Mulders effect in the SIDIS process within TMD factorization at the kinematics of the HERMES and COMPASS experiments. It is found that the obtained \begin{document}$ x_B$\end{document} -, \begin{document}$ z_h$\end{document} - and \begin{document}$ P_{h\perp}$\end{document} -dependent Kotzinian-Mulders effect are basically consistent with the HERMES and COMPASS measurements. We also make predictions in EIC and EicC kinematics.