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Inelastic electroproduction of $η_c$ at ep colliders

Using the nonrelativistic QCD factorization formalism, we calculate the electroproduction cross sections of $η_c$ in ep collisions, including the contribution from both the transverse photon and the longitudinal photon. For this process the color-singlet contribution vanishes up to the next to leading order perturbative QCD calculations. The dominant contribution comes from the color-octet ${}^1S_0^{(8)}$ subprocess. The nonperturbative color-octet matrix element of ${}^1S_0^{(8)}$ of $η_c$ is related to that of ${}^3S_1^{(8)}$ of $J/ψ$ by heavy quark spin symmetry, and the latter can be determined from the direct production of $J/ψ$ at large transverse momentum at the Fermilab Tevatron. The measurement of this process at DESY HERA can be viewed as another independent test for the color-octet production mechanism