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# Meson Emission Model of Ψ → $_{N}$¯Nm Charmonium Strong Decays 

$^{a}$Physics Division, Oak Ridge National Laboratory, Oak Ridge, TN 37831-6373, USA 

T.Barnes, a,b ∗ Xiaoguang Li b † and W.Roberts c ‡ 

$^{b}$Department of Physics and Astronomy, University of Tennessee, Knoxville, TN 37996-1200, USA 

$^{c}$Department of Physics and Astronomy, Florida State University, Tallahassee, FL 32306-4350, USA 

(Dated: October 28, 2018) 

In this paper we consider a sequential ”meson emission” mechanism for charmonium decays of the type Ψ → N ¯ Nm , where Ψ is a generic charmonium state, N is a nucleon and m is a light meson. This decay mechanism, which may not be dominant in general, assumes that an N ¯ N pair is created during charmonium annihilation, and the light meson m is emitted from the outgoing nucleon or antinucleon line. A straightforward generalization of this model can incorporate intermediate N ∗ resonances. We derive Dalitz plot event densities for the cases Ψ = η c , J/ψ , χ c $_{0}$, χ c 1 and ψ ′ and m = π $^{0}$, f$_{0}$ and ω (and implicitly, any 0 − $^{+}$, 0++ or 1 −− final light meson). It may be possible to separate the contribution of this decay mechanism to the full decay amplitude through characteristic event densities. For the decay subset Ψ → p ¯ pπ 0 the two model parameters are known, so we are able to predict absolute numerical partial widths for Γ(Ψ → p ¯ pπ $^{0}$). In the specific case J/ψ → p ¯ pπ 0 the predicted partial width and M pπ event distribution are intriguingly close to experiment. We also consider the possibility of scalar meson and glueball searches in Ψ → p ¯ pf$_{0}$ . If the meson emission contributions to Ψ → N ¯ Nm decays can be isolated and quantified, they can be used to estimate meson-nucleon strong couplings { g NNm } , which are typically poorly known, and are a crucial input in meson exchange models of the NN interaction. The determination of g NNπ from J/ψ → p ¯ pπ 0 and the (poorly known) g NNω and the anomalous ”strong magnetic” coupling κ NNω from J/ψ → p ¯ pω are considered as examples. 

Charmonium strong decays of the type Ψ → N ¯ Nm , where Ψ is a generic charmonium state, N is a nucleon and m is a light meson, have recently attracted inter- est both as sources of information regarding the N ∗ spectrum [1–5] and in searches for a low energy N ¯ N enhancement “ X (1835)”, which has been reported in J/ψ → γp ¯ p [6] and J/ψ → γπ $^{+}$π $^{−}$η′ [7, 8], but thus far not in Ψ → p ¯ pm . These decays are also of interest because their partial widths can be used to estimate the p ¯ p → m Ψ associated charmonium production cross sec- tions at PANDA [9, 10]. As we shall show here, they may also provide information on NNm meson-nucleon coupling constants, which could be used to identify un- usual resonances such as molecule or glueball candidates. 

Specific Ψ → N ¯ Nm reactions that have recently been studied experimentally include J/ψ → p ¯ pπ 0 [1], p ¯ pη and p ¯ pη ′ [4], and p ¯ pω [5]; ψ ′ → p ¯ pπ 0 [2], p ¯ pη [2, 11], p ¯ nπ − + h.c. [3], p ¯ pρ [11] and p ¯ pω [11, 12], and (upper limit) p ¯ pφ [11, 12]; and χ$_{cJ}$ → p ¯ pπ 0 and p ¯ pη [13]. 

These decays may prove to be complicated processes in which several decay mechanisms contribute significantly. For this reason it will be useful to have predictions for Ψ → N ¯ Nm Dalitz plot (DP) event densities assuming various decay mechanisms; this paper provides these re- 

PACS numbers: 13.25.Gv, 13.75.Cs, 13.75.Gx, 21.30.-x 

## I. INTRODUCTION 

sults for one such mechanism. In particular we derive the DP event densities that follow from sequential meson emission, in which the charmonium state (generically Ψ) decays to an intermediate N ¯ N state, which radiates the light meson from the N or ¯ N line, Ψ → N ¯ N → N ¯ Nm . The two Feynman diagrams assumed in this model are shown in Fig.1. 

We emphasize that the actual relative importance of this and other Ψ → N ¯ Nm decay mechanisms is unclear at present, and may depend strongly on the charmonium state Ψ and the light meson m ; one purpose of this paper is to determine the rates predicted by this meson emission decay model in isolation for comparison with experiment, so that the importance of this decay mechanism can be estimated. 

The predictions of this Ψ → N ¯ N → N ¯ Nm decay model can be given in some cases with no free parameters, since the strengths of the a priori unknown couplings Ψ N ¯ N and NNm can be estimated from other processes. Here we will give absolute predictions for the set of par- tial widths { Γ(Ψ → p ¯ pπ $^{0}$) } ; we use the known partial widths { Γ(Ψ → p ¯ p ) } to estimate the { Ψ N ¯ N } couplings, 

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