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$G$-parity violating amplitudes in the $J/ψ\to π^+ π^-$ decay

Rinaldo Baldini Ferroli, Alessio Mangoni, Simone Pacetti

Abstract

The decays of the negative $G$-parity meson $J/ψ$ into even numbers of pions violate $G$-parity. Such decays, as well as other $G$-parity decays into hadrons, can be parametrized in terms of three main intermediate virtual states: one photon, one photon plus two gluons, and three gluons. Since the electromagnetic interaction does not conserve $G$-parity, $J/ψ$ decays into positive $G$-parity final states should be dominantly electromagnetic. Nevertheless, the one-photon contribution to $J/ψ\to π^+ π^-$, that can be estimated by exploiting the cross section $σ(e^+e^-\to π^+ π^-)$, differs from the observed decay probability for {more than} 4.5 standard deviations. We present a computation of the $ggγ$ amplitude based on a phenomenological description of the decay mechanism in terms of dominant intermediate states $ηγ$, $η'γ$ and $f_1(1285)γ$. The obtained value is of the order of the electromagnetic contribution.

$G$-parity violating amplitudes in the $J/ψ\to π^+ π^-$ decay

Abstract

The decays of the negative -parity meson into even numbers of pions violate -parity. Such decays, as well as other -parity decays into hadrons, can be parametrized in terms of three main intermediate virtual states: one photon, one photon plus two gluons, and three gluons. Since the electromagnetic interaction does not conserve -parity, decays into positive -parity final states should be dominantly electromagnetic. Nevertheless, the one-photon contribution to , that can be estimated by exploiting the cross section , differs from the observed decay probability for {more than} 4.5 standard deviations. We present a computation of the amplitude based on a phenomenological description of the decay mechanism in terms of dominant intermediate states , and . The obtained value is of the order of the electromagnetic contribution.

Paper Structure

This paper contains 12 sections, 74 equations, 12 figures, 2 tables.

Table of Contents

  1. Introduction
  2. The decay channel $J/\psi \to \pi^+ \pi^-$
  3. The contribution ${\rm Im}(\mathcal{A}_{gg\gamma})$
  4. Selection of intermediate mesons
  5. A phenomenological calculation based on the Cutkosky rule
  6. The $g^{J/\psi}_{{\eta\gamma}}$, $g^{J/\psi}_{{\eta'\gamma}}$ and $g^{J/\psi}_{{f_1\gamma}}$ coupling constants
  7. The $g^{\pi\pi}_{{\eta\gamma}}$, $g^{\pi\pi}_{{\eta'\gamma}}$ and $g^{\pi\pi}_{{f_1\gamma}}$ coupling constants
  8. Calculation of $\mathcal{B}_{gg\gamma}^{{\rm Im}}(\pi^+\pi^-)$
  9. The real part
  10. Conclusions
  11. The one-photon decay rate
  12. A possible strategy to calculate $\mathcal{B}_{gg\gamma}^{{\rm Re}}(\pi^+\pi^-)$ in the pseudoscalar case

Figures (12)

  • Figure 1: The three intermediate states: $ggg$, $gg \gamma$ and $\gamma$.
  • Figure 2: BaBar data on the $e^+e^- \to \pi^+\pi^-$ cross section and the fit (red line) from Lees:2012cj. The vertical dashed line shows the ${J/\psi}$ mass.
  • Figure 3: Two-gluon plus one-photon mechanism of the decay ${J/\psi}\to\pi^+\pi^-$ with light unflavored mesons $h_j$ in the intermediate states. The light blue and the yellow areas indicate the domains of the charm and light quarks, respectively.
  • Figure 4: Decay mechanism of the ${J/\psi}$ into $\pi^+\pi^-$ mediated by strongly coupled charmonia $h_c$. The color scheme is the same of Fig. \ref{['fig:ozi2']}.
  • Figure 5: OZI double-suppressed ${J/\psi}$ decay mechanism with charmonia $h_c$ in the intermediate states. The color scheme is the same of Fig. \ref{['fig:ozi2']}.
  • ...and 7 more figures