  We study the $\eta_c$ photoproduction in $ep$ collisions in this paper. The
short-distance coefficients for $c\bar{c}(^1S_0^{[1]})$,
$c\bar{c}(^1S_0^{[8]})$, $c\bar{c}(^3S_1^{[8]})$, and $c\bar{c}(^1P_1^{[8]})$
photoproductions are evaluated at leading order in $\alpha_s$ expansion, where
the color-singlet contribution is achieved for the first time. We have
carefully analyzed different kinematic distributions of the cross sections and
found that the color-singlet contribution is considerably suppressed comparing
with the color-octet parts. This feature renders the $\eta_c$ photoproduction
process an ideal laboratory to test the color-octet mechanism in
nonrelativistic QCD. By taking different sets of long-distance matrix elements,
we have observed some apparently distinguishable predictions, which can be
utilized to scrutinize the validity of these matrix elements.

High Energy Physics - Phenomenology