An anlaysis on $J/ψ\toπ^0γ^*$ within resonance chiral theory

TL;DR

This work uses resonance chiral theory to analyze the first BESIII measurement of the $e^+e^-$ invariant-mass spectrum in $J/\psi\to\pi^0 e^+ e^-$. It shows that a coherent combination of strong-interaction amplitudes, electromagnetic transitions, and charmonium effects is required to describe the data, and it extracts the time-like doubly-virtual pion transition form factor $\mathcal{F}_{\pi^0 \gamma^* \gamma^*}(q_1^2,q^2)$ as well as branching ratios for $J/\psi\to\pi^0 l^+l^-$. The analysis provides a unified description of $J/\psi\to \pi^0 V$ decays ($V=\rho,\omega,\phi$) and shows that $J/\psi\to \pi^0\rho^0$ is mainly driven by the LO strong interaction, while $J/\psi\to \pi^0\omega$ and $\pi^0\phi$ are dominated by EM transitions, with interference shaping the observed spectrum. The results validate the use of RChT in the charmonium region and offer predictions for future experimental tests of time-like TFFs and lepton-pair spectra.

Abstract

In this study, we analyze the first measurement of the electron-positron invariant mass spectrum in $J/ψ\to π^0 e^+e^-$ by BESIII, using the framework of resonance chiral theory. Our results indicate that both strong interaction and electromagnetic transition are essential to accurately describe the data. We obtain the $π^0$ transition form factor for $J/ψ\to π^0γ^*$ and the corresponding decay branching ratios for $J/ψ\to π^0 l^+l^-$. The decay process $J/ψ\to π^0 V$ is also examined. It is found that $J/ψ\to π^0 ρ^0$ is dominated by the strong interaction, while the other two channels, $J/ψ\to π^0 ω$ and $π^0 φ$, arise primarily from electromagnetic transitions.

Figures (5)

• Figure 1: Feynman diagrams of $J/\psi\to \pi^0\gamma^*$. The LO results are shown in the first row, and the electromagnetic correction and charmonium contribution are listed in the other rows. The double line represents vector resonance.
• Figure 2: Feynman diagrams of $J/\psi\to \pi^0V$. The LO result is from (a), and the electromagnetic transition are from (b-e).
• Figure 3: Normalized TFF and $e^+e^-$ invariant mass spectrum for $J/\psi\to\pi^0 e^+e^-$. The data is taken from Ref. BESIII:2025xjh.
• Figure 4: The ' LO', ' EM', and ' $c\bar{c}$' contributions to the TFF of $\psi\pi^0\gamma^*$.
• Figure 5: Predictions of $\frac{\mathrm{dBr}[{J/\psi\to\pi^0\mu^+\mu^-}] }{\mathrm{d}\sqrt{q^2} }$.