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The next-to-next-to-leading order (NNLO) pQCD prediction for the$\gamma\gamma^* \to \eta_c$ form factor was evaluated in 2015 usingnonrelativistic QCD (NRQCD). A strong discrepancy between the NRQCD predictionand the BaBar measurements was observed. Until now there has been no solutionfor this puzzle. In this paper, we present a NNLO analysis by applying thePrinciple of Maximum Conformality (PMC) to set the renormalization scale. Bycarefully dealing with the light-by-light diagrams at the NNLO level, theresulting high precision PMC prediction agrees with the BaBar measurementswithin errors, and the conventional renormalization scale uncertainty iseliminated. The PMC is consistent with all of the requirements of therenormalization group, including scheme-independence. The application of thePMC thus provides a rigorous solution for the $\gamma\gamma^* \to \eta_c$ formfactor puzzle, emphasizing the importance of correct renormalizationscale-setting. The results also support the applicability of NRQCD to hardexclusive processes involving charmonium.

A solution to the $\gamma\gamma^*\rightarrow\eta_c$ puzzle using the Principle of Maximum Conformality