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Three-gluon decays of radially excited quarkonia ψ(2S) and ϒ(2S) with both relativistic and QCD radiative corrections

Chao-Jie Fan and Jun-Kang He*

  • *Contact author: hejk@hbnu.edu.cn
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Phys. Rev. D 114, 014004 – Published 6 July, 2026

DOI: https://doi.org/10.1103/5hrn-yvk9

Abstract

For the radially excited heavy quarkonia V=ψ(2S) and ϒ(2S), the nodal structure of the wave function renders the three-gluon decay V→ggg acutely sensitive to relativistic corrections, a longstanding challenge for reliable theoretical predictions. Within the Bethe-Salpeter formalism under the covariant instantaneous ansatz, we construct analytic harmonic-oscillator wave functions incorporating the 2S node and derive model-independent relations among the polarized decay widths from helicity-flip and phase-space symmetries. Motivated by the strikingly slow q^2-order convergence driven by destructive interference at the node, we introduce a concise phenomenological treatment of the higher-order contributions that preserves the correct low-momentum limit. Including both relativistic and QCD radiative corrections, our predictions for Γ(V→ggg), Γ(V→e+e−), and RV agree well with experiment, and the extracted βV lies at the lower end of typical phenomenological ranges, reflecting a more localized momentum-space wave function.

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Phys. Rev. D 114, 014004– Published 6 July, 2026
  • Received 6 April 2026
  • Accepted 12 June 2026
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