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Kinematic distributions of the $η_c$ leptoproduction in association with light hadrons

The $η_c$ meson leptoproduction is calculated within the nonrelativistic QCD framework for the first time. It is found that the colour-singlet channel, although suppressed by a factor of $α_s$ relative to the colour-octet ones, provides the most important contribution for almost all the experimental conditions, 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 experimental conditions as a reference for future studies. The scale dependence and long-distance-matrix-element dependence are also investigated in this paper.