Self-consistent analysis for the $η_c\rightarrow γγ$ process
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866909634286059520 |
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| author | Wang, Sheng-Quan Ren, Zhu-Yu Shen, Jian-Ming Wu, Xing-Gang Di Giustino, Leonardo Brodsky, Stanley J. |
| author_facet | Wang, Sheng-Quan Ren, Zhu-Yu Shen, Jian-Ming Wu, Xing-Gang Di Giustino, Leonardo Brodsky, Stanley J. |
| contents | The next-to-next-to-leading-order (NNLO) pQCD predictions for both the decay width and the transition form factor in the $η_c\rightarrow γγ$ 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 $η_c\rightarrow γγ$ 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 $β$ terms which govern the behavior of the QCD running coupling via the Renormalization Group Equation. We obtain the PMC scale $Q_\star=4.49\,m_c$ for the $η_c\rightarrow γγ$ 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 $Γ_{η_c\rightarrow γγ}$ is in agreement with the Particle Data Group's reported value of $Γ_{η_c\rightarrow γγ}=5.1\pm0.4$ 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 $η_c\rightarrow γγ$ puzzle and supports the applicability of NRQCD to charmonium processes. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2501_17681 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Self-consistent analysis for the $η_c\rightarrow γγ$ process Wang, Sheng-Quan Ren, Zhu-Yu Shen, Jian-Ming Wu, Xing-Gang Di Giustino, Leonardo Brodsky, Stanley J. High Energy Physics - Phenomenology High Energy Physics - Experiment The next-to-next-to-leading-order (NNLO) pQCD predictions for both the decay width and the transition form factor in the $η_c\rightarrow γγ$ 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 $η_c\rightarrow γγ$ 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 $β$ terms which govern the behavior of the QCD running coupling via the Renormalization Group Equation. We obtain the PMC scale $Q_\star=4.49\,m_c$ for the $η_c\rightarrow γγ$ 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 $Γ_{η_c\rightarrow γγ}$ is in agreement with the Particle Data Group's reported value of $Γ_{η_c\rightarrow γγ}=5.1\pm0.4$ 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 $η_c\rightarrow γγ$ puzzle and supports the applicability of NRQCD to charmonium processes. |
| title | Self-consistent analysis for the $η_c\rightarrow γγ$ process |
| topic | High Energy Physics - Phenomenology High Energy Physics - Experiment |
| url | https://arxiv.org/abs/2501.17681 |