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Radiative decays of $J / ψ, ψ (2 S) \to γ η^{(')}$ in perturbative QCD with relativistic corrections

Jun-Kang He , Chao-Jie Fan ^*, and Cong Wang ^†

College of Physics and Electronic Science, Hubei Normal University, Huangshi 435002, China

^*Contact author: fancj@hbnu.edu.cn
^†Contact author: wangj@hbnu.edu.cn

Phys. Rev. D 114, 074003 – Published 1 October, 2026

DOI: https://doi.org/10.1103/jsxb-5335

Abstract

We present the first calculation of the radiative decays $J / ψ, ψ (2 S) \to γ η^{(')}$ in perturbative QCD that includes the order- $q^{2}$ relativistic corrections in all three short-distance contributions, namely the quark-antiquark, two-gluon, and QED contributions. The amplitudes are found to be remarkably insensitive to the light-cone distribution amplitude and to the light-quark mass, a robustness that persists through order $q^{2}$ and makes the predictions correspondingly reliable. The relativistic correction enhances the $J / ψ$ branching ratios by roughly a factor of 2, narrowing their shortfall from experiment, whereas for the $ψ (2 S)$ it is about twice as large as for the $J / ψ$ and the low-order expansion converges poorly. In two representative $η - η^{'}$ mixing schemes, the ratio $R_{1 S} = B (γ η^{'}) / B (γ η)$ proves sharply sensitive to the mixing angle and favors the smaller of the two. The predicted $ψ (2 S)$ rates lie well above the data in both channels, already at leading order, and most severely for the anomalously small $γ η$ channel. Such a discrepancy suggests that a mechanism beyond the hard perturbative process is at work. As a physically motivated attempt, we explore the $η_{c}$ -mixing contribution, which adds coherently to the perturbative one and is comparable to it in the $γ η$ channel, and find that the interference can bring the $ψ (2 S)$ rates into agreement with the data, although its extraction is limited by a strong sensitivity to the mixing parameters.

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Phys. Rev. D 114, 074003– Published 1 October, 2026

Vol. 114, Iss. 7 — 1 October 2026

Received 29 July 2026
Accepted 16 September 2026

DOI: https://doi.org/10.1103/jsxb-5335

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Funded by SCOAP³.

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Radiative decays of $J / ψ, ψ (2 S) \to γ η^{(')}$ in perturbative QCD with relativistic corrections

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Radiative decays of J/ψ,ψ(2S)→γη(′) in perturbative QCD with relativistic corrections

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Physics Subject Headings (PhySH)

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References (75)

Radiative decays of $J / ψ, ψ (2 S) \to γ η^{(')}$ in perturbative QCD with relativistic corrections