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The $\eta_c$ meson leptoproduction is calculated within the nonrelativisticQCD framework for the first time. It is found that the colour-singlet channel,although suppressed by a factor of $\alpha_s$ relative to the colour-octetones, provides the most important contribution for almost all the experimentalconditions, which disagrees with some of the expectations before computation.We present the differential cross sections with respect to $p_t^2$,$p_t^{\star2}$, $Q^2$, $W$, and $z$, for both HERA and EIC experimentalconditions as a reference for future studies. The scale dependence andlong-distance-matrix-element dependence are also investigated in this paper.

Kinematic distributions of the $\eta_c$ leptoproduction in association with light hadrons