Abstract
The decays of the negative $G$-parity meson $G$-parity 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, $G$-parity decays into positive $G$-parity final states should be dominantly electromagnetic. Nevertheless, the one-photon contribution to $J/\psi \to \pi^+ \pi^-$, that can be estimated by exploiting the cross section $\sigma(e^+e^-\to \pi^+ \pi^-)$, differs from the observed decay probability for {more than} 4.5 standard deviations. We present a computation of the $gg\gamma$ amplitude based on a phenomenological description of the decay mechanism in terms of dominant intermediate states $\eta\gamma$, $\eta'\gamma$ and $f_1(1285)\gamma$. The obtained value is of the order of the electromagnetic contribution.
Highlights
The J /ψ meson, having negative C-parity, CJ/ψ = −1, and isospin IJ/ψ = 0, has negative G-parity GJ/ψ, being GJ/ψ = CJ/ψ (−1)IJ/ψ = −1
In this paper we calculate the imaginary part of the amplitude Aggγ (π +π −) due to the dominant intermediate states by means of a phenomenological procedure based on the Cutkosky rule [11] and experimental rates of the involved J /ψ decays
The G-parity-violating J /ψ decay into π +π − represents a useful testbed for what we called the Bγ -dominance hypothesis, which is summarized by the branching ratio (BR) formula B(π +π −) Bγ (π +π −), with [see Eq (2)]
Summary
In this paper we calculate the imaginary part of the amplitude Aggγ (π +π −) due to the dominant intermediate states by means of a phenomenological procedure based on the Cutkosky rule [11] and experimental rates of the involved J /ψ decays Using such an amplitude we obtain a lower limit for Bggγ (π +π −) and show that, within the errors, it is of the same order of Bγ (π +π −). [12] for a detailed analysis of radiative decays J /ψ → γ + hadrons.) The elements hj of the set P are only light unflavored mesons, which couple strongly (OZI1-allowed process) with the π +π − final state Only in these cases is the underlying mechanism, sketched, the one we want to evaluate. 4π MJ/ψ 4π where pμ is the four-momentum of the photon
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