Origin of the possible universal strong–electromagnetic phase in charmonium decays

Determine the origin and provide a theoretical explanation for a possibly universal relative phase between the three-gluon–mediated strong amplitude and the virtual-photon–mediated electromagnetic amplitude in decays of J^{PC}=1^{--} charmonium states to hadronic final states (e.g., J/ψ and ψ(2S)).

Background

A striking relative phase of approximately ±90° between the three-gluon strong amplitude and the electromagnetic amplitude has been observed in J/ψ decays, suggesting that the phase might be universal across decay modes and charmonium states. However, SU(3)-based analyses of branching fractions in ψ(2S) and other channels have reported differing values, leading to tensions and motivating further scrutiny.

The paper emphasizes that some theoretical arguments propose that the phase should not vary significantly among charmonium states because the three-gluon amplitude is governed primarily by the charm-quark mass scale. Despite these considerations, the fundamental mechanism producing a universal phase, if it exists, has not been identified, leaving the theoretical origin unresolved.

References

The origin of this possible universal phase and its explanation remain unclear.

— First energy scan measurement of $e^{+}e^{-}\to K^{+}K^{-}$ around the $ψ(2S)$ resonance  (2603.29854 - Collaboration et al., 31 Mar 2026) in Introduction (page 1)

Such an enhancement could in principle reflect additional dynamics, possibly including a hidden vector glueball component, but its microscopic origin cannot be resolved from the present data, see also sec. \ref{sec:glueball}.

— On the failure of the $12\%$ rule in $J/ψ$ and $ψ(2S)$ decays  (2609.24961 - Vereijken et al., 21 Sep 2026) in Section 3, subsection “Decays of the $J/\psi$”