A solution to the $\gamma {\gamma }^{\ast }\to {\eta }_c$ puzzle using the Principle of Maximum Conformality

Abstract

The next-to-next-to-leading order (NNLO) pQCD prediction for the $\gamma {\gamma }^{\ast }\to {\eta }_c$ form factor was evaluated in 2015 using nonrelativistic QCD (NRQCD). A strong discrepancy between the NRQCD prediction and the BaBar measurements was observed. Until now there has been no solution for this puzzle. In this paper, we present a NNLO analysis by applying the Principle of Maximum Conformality (PMC) to set the renormalization scale. By carefully dealing with the light-by-light diagrams at the NNLO level, the resulting high precision PMC prediction agrees with the BaBar measurements within errors, and the conventional renormalization scale uncertainty is eliminated. The PMC is consistent with all of the requirements of the renormalization group, including scheme-independence. The application of the PMC thus provides a rigorous solution for the $\gamma {\gamma }^{\ast }\to {\eta }_c$ form factor puzzle, emphasizing the importance of correct renormalization scale-setting. The results also support the applicability of NRQCD to hard exclusive processes involving charmonium.

arXiv comment5 pages, 4 figures. References updated. To be published in Phys.Rev.D

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Cited by in corpus (10)

• ${\gamma }^{\ast }\gamma \to \eta ,{\eta }^{\prime }$ transition form factors
• Extending the Predictive Power of Perturbative QCD
• The ${\gamma }^{\ast }{\gamma }^{\ast }\to {\eta }_c(1S,2S)$ transition form factors for spacelike photons
• Systematic twist expansion of $({\eta }_c,{\eta }_b)\to {\gamma }^{\ast }\gamma$ transition form factors in light-front quark model
• Properties of the decay $H\to \gamma \gamma$ using the approximate ${\alpha }_s^4$-corrections and the principle of maximum conformality
• Next-to-leading-order QCD corrections to a vector bottomonium radiative decay into a charmonium
• Study on ${\eta }_{c2}({\eta }_{b2})$ electromagnetic decay into double photons
• Self-consistent analysis for the ${\eta }_c\to \gamma \gamma$ process
• Elimination of QCD Renormalization Scale and Scheme Ambiguities
• Transition Form-Factor for ${\eta }_Q$ at NNLO in the strong coupling ${\alpha }_s$ and with all-order $v^2$ resummation