Photon or meson formation in $J/\psi$ decays into $p\overline{p}$

The measurements of the $J/\psi \to \gamma p\overline{p}$ decays by the BES Collaboration indicate an enhancement at the $p\overline{p}$ threshold which, however, is not present in the $J/\psi$ decays into $\omega p\overline{p}$ and into $\pi p\overline{p}$. Here, two processes for describing the decays $J/\psi \to \mathcal{B}p\overline{p}$ where $\mathcal{B}=\gamma ,\omega$ are presented in some detail and the cases $\mathcal{B}=\varphi ,\pi$ are briefly touched on. The first one, applied not only to the radiative decay to reproduce the threshold peak but also to the $\omega p\overline{p}$ decay channel to improve the description of the spectrum, postulates a direct emission of the boson before the baryon pair is formed. The second process assumes that the boson $\mathcal{B}$ is emitted from the baryon pair following the $J/\psi$ decay and includes for the decays into $\gamma p\overline{p}$ a final-state nucleon-antinucleon interaction based on the Paris $N\overline{N}$ potential. The reproduction of the $p\overline{p}$ distribution in the $J/\psi \to \omega p\overline{p}$ decays needs a final-state interaction involving a $N\left(2050\right)3/2^{-}$ resonance. The photon- and meson-emission rates are reproduced in a semiquantitative way.

Figure 1

Photon emission from the $J/\psi$ : the left panel (a) corresponds to the Born term while the right one (b) includes final-state corrections. The nucleon (antinucleon) line is denoted $N$ ($\overline{N}$) with respective momenta ${\mathbf{q}}^{\prime }-\mathbf{k}$ ($-{\mathbf{q}}^{\prime }$) while $p$ ($\overline{p}$) represents a proton (antiptroton) propagating with momentum $\mathbf{q}-\mathbf{k}$ ($-\mathbf{q}$). The wavy line is associated to the photon of momentum $\mathbf{k}$.

Figure 2

The invariant $M_{p\overline{p}}$ mass distribution calculated within the direct emission DE model for different values of the parameter $\beta$. The data (histogram) is extracted from Fig. 1 in Ref. [5].

Figure 3

The left panel (a) displays the real part while the right one (b) displays the absorptive part of the Paris $N\overline{N}$ potential in the isospin 0 isosinglet $S$ wave. The deep well and the barrier are due to the interplay of theoretical one- and two-pion exchange forces supplemented with a short-range phenomenological attraction. The well and barrier structure have the support of 4000 data but the detailed shape of the kink is an artifact of the phenomenological part and it cannot be determined very precisely [8]. The existence of the barrier is nevertheless indicated by the scattering data, in particular those of the $\overline{n}p$ total cross sections.

Figure 4

Photon emission from intermediate baryons: The left graph (a) is associated to the Born term while the right one (b) includes final-state corrections. The various labels have been defined in Fig. 1. Similar diagrams for the emissions from antibaryons are not drawn.

Figure 5

The $M\left(p\overline{p}\right)$ spectra obtained with the DE and baryon emission BC + FSI models. The peak at 3 GeV attributed to the sequential $J/\psi \to {\eta }_c\gamma$ decays is discussed in the text. Histogram as in Fig. 2; data extracted from Ref. [5].

Figure 6

As in Fig. 5 but for the near-threshold region. Note the small $P$-wave renormalized electric contribution.

Figure 7

Left panel (a): the $M_{p\overline{p}}$ spectrum obtained with the BC model. Right panel (b): the $M_{p\overline{p}}$ spectrum obtained with the BC + FSI model. The same arbitrary normalization is used to fit the experimental shape for both graphs. The electric contribution is labeled EE. No FSI contribution in the DE model but the weak energy dependance of the source radius [Eq. (24)] has been kept. Here $R_0=0.28$ fm, $g_{V\omega }^2/\left(4\pi \right)=3.8$, and $g_{T\omega }=0$. Data extracted from Fig. 2 in Ref. [18].

Figure 8

The $M_{p\overline{p}}$ spectrum as in Fig. 7 but for the near-threshold region.

Figure 9

Emission of the $\omega$ meson from intermediate baryons. The left graph (a) corresponds to the Born term while the right one (b) includes final-state corrections involving the $N(3/2^{-})$ nucleon resonance.

Figure 10

The $M_{\omega p}$ spectrum obtained with the BC + FSI + DE model (see Fig. 7 caption). The dash-dotted curve (Basic model) refers to the BC + FSI calculation.