Self-consistent analysis for the ${\eta }_c\to \gamma \gamma$ process

Abstract

The next-to-next-to-leading-order (NNLO) pQCD predictions for both the decay width and the transition form factor in the ${\eta }_c\to \gamma \gamma$ process, based on nonrelativistic QCD (NRQCD), deviate from precise experimental measurements. These significant discrepancies have cast doubt on the applicability of NRQCD to charmonium processes. In this paper, we analyze the ${\eta }_c\to \gamma \gamma$ process by applying the Principle of Maximum Conformality (PMC), a systematic method for eliminating renormalization scheme and scale ambiguities. The PMC renormalization scales are determined by absorbing the non-conformal $\beta$ terms which govern the behavior of the QCD running coupling via the Renormalization Group Equation. We obtain the PMC scale $Q_{\star }=4.49m_c$ for the ${\eta }_c\to \gamma \gamma$ decay width. Even after using the PMC method, the convergence of the pQCD series is still poor, which indicates the importance of uncalculated NNNLO and higher-order terms. The resulting value for ${\Gamma }_{{\eta }_c\to \gamma \gamma }$ is in agreement with the Particle Data Group's reported value of ${\Gamma }_{{\eta }_c\to \gamma \gamma }=5.1\pm 0.4$ keV within the bounds of uncertainties. Moreover, the transition form factor obtained using the PMC is also in good agreement with precise experimental measurements. The application of the PMC suggests a potential resolution to ${\eta }_c\to \gamma \gamma$ puzzle and supports the applicability of NRQCD to charmonium processes.

arXiv comment7 pages, 5 figures

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Cited by in corpus (2)

• Renormalisation
• Transition Form-Factor for ${\eta }_Q$ at NNLO in the strong coupling ${\alpha }_s$ and with all-order $v^2$ resummation