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

TL;DR

Applying the Principle of Maximum Conformality to NNLO pQCD calculations resolves the long-standing discrepancy between theoretical predictions and BaBar measurements for the $ o ext{eta}_c$ form factor, highlighting the importance of proper scale-setting.

Contribution

This paper introduces the use of PMC for NNLO analysis in $ o ext{eta}_c$ form factor, providing a solution to the previous puzzle and confirming NRQCD's applicability.

Findings

PMC prediction agrees with BaBar data within errors

Eliminates renormalization scale uncertainty

Supports NRQCD for charmonium processes

Abstract

The next-to-next-to-leading order (NNLO) pQCD prediction for the $\gamma\gamma^* \to \eta_c$ 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 $\gamma\gamma^* \to \eta_c$ 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.