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Carbon-carbon burning plays an important role in many stellar environments.Recently, using the indirect Trojan horse method A. Tumino {\em et al.}reported [Nature {\bf 557} 687 (2018)] a strong rise of the astrophysicalfactor for the carbon-carbon fusion at low resonance energies. In this paper,we demonstrate that this rise is the artifact of using an invalid plane-waveapproximation. It is shown that the calculated renormalization factor decreasesthe astrophysical factor from [A. Tumino {\em et al.}, Nature {\bf 557} 687(2018)] at the resonance energies of $E=0.8-0.9$ MeV by as much as $\approx10^{3}$ times.

Astrophysical factors of ${}^{12}{\rm C}+{}^{12}{\rm C}$ fusion from Trojan horse method