− ( u + v + ( u − v ) $^{2}$) 8 uv r 2 − ( 3 2 + ( u + v ) 4 uv ) R 2 + 1 8 r 4 + ( 2( u 2 + v 2 − uv ) + ( u + v ) 2 + ( u 2 + v 2 + 4 uv ) 16 uv ) · r $^{2}$R2 + 1 4 R 4 + 1 8 ( u + v + 2( u 2 + v 2 + 6 uv ) r $^{4}$R2 − 1 2 ( u 2 + v 2 − uv ) r $^{2}$R4 − 1 8 uv r $^{6}$R2 − 1 16 ( u 2 + v 2 + 4 uv ) r $^{4}$R4 ] } . (17) The symmetry of these event densities under ( x, y ) and hence ( u, v ) interchange is a consequence of C -parity in- variance. There are singularities in these events densities along the lines x = 0 ( u = ∞ ) and y = 0 ( v = ∞ ), corre- sponding to M 2 pm = m 2 p and M 2 ¯ pm = m 2 $_{p}$. These are due to the poles of the p and ¯ p propagators in the Feynman diagrams for the decay process Ψ → p ¯ p → p ¯ pm (Fig.1) and lie outside the physical regions of the Dalitz plots. As a first application we will evaluate the partial width for J/ψ → p ¯ pπ 0 assuming this meson emission decay mechanism. The PDG [26] quotes a branching fraction of which is the average of early measurements by Mark-I [27], DASP [28] and Mark-II [29]. There are also more recent experimental results on this decay from BES-II [1]. Using the current PDG value for the J/ψ total width of 93 . 2 ± 2 . 1 keV, this branching fraction corresponds to a partial width of To evaluate this partial width in the meson emission model we simply integrate the theoretical event density (7) over the Dalitz plot. This event density is given by where the dimensionless density function ρ is This is consistent with the experimental value of 102 ± 9 eV quoted in Eq.(19). This excellent agreement is somewhat fortuitous, since this version of the model gives a value of g$_{J/ψp}$$_{¯}$ p = 1 . 62 · 10 − $^{3}$, as was quoted previ- ously in Ref.[24]. Using these couplings in Eq.(24) gives our meson emission model prediction To complete this estimate we require numerical values for the NNπ and J/ψN ¯ N coupling constants. For NNπ there is general agreement from meson exchange mod- els of NN scattering that g$_{NNπ}$ ≈ 13 (see for example [14–21]); we accordingly set g$_{NNπ}$ = 13 . 0. The value of the J/ψN ¯ N coupling constant (here g$_{J/ψp}$$_{¯}$ $_{p}$) can be es- timated from the measured partial width to p ¯ p , which is (again using PDG numbers) Γ( J/ψ → p ¯ p ) = 202 ± 8 eV. Equating this to the theoretical decay rate We evaluate 〈 ρ 〉 and A$_{D}$ numerically, assuming phys- ical hadron masses; we use PDG masses rounded to 0.1 MeV; m$_{π}$ 0 = 0 . 1350 GeV, m$_{p}$ = 0 . 9383 GeV and m$_{J/ψ}$ = 3 . 0969 GeV, which leads to 〈 ρ 〉 = 3 . 070 · 10 − 3 and A$_{D}$ = 9 . 265 GeV $^{4}$, and a partial width of where 〈 ρ 〉 is the mean value of ρ ( x, y ) in the Dalitz plot, which has (physical) area A$_{D}$ ; 4 1 2 3 4 5 M 2 p  [GeV$^{2}$] 1 2 3 4 5 M 2 $_{p}$π   [GeV 2 ] 0.6 0.4 0.2 0.7 1.0 0.8 0.9 0.9 0.8 FIG. 2: The J/ψ → p ¯ pπ 0 DP event density predicted by the meson emission decay mechanism J/ψ → p ¯ p → p ¯ pπ $^{0}$, Eq.(7). Contours of equal density are shown. Γ( J/ψ → p ¯ pπ $^{0}$) = α$_{J/ψ}$ α$_{π}$ m$_{p}$ · 〈 ρ 〉 · A$_{D}$/m 4 $_{p}$. (22) ∫∫ DP ρ dx dy = 〈 ρ 〉 · A$_{D}$/m 4 $_{p}$. (23) Γ( J/ψ → p ¯ pπ $^{0}$) = 34 . 44 · α$_{J/ψ}$ α$_{π}$ MeV . (24) Γ( J/ψ → p ¯ p ) = α$_{J/ψ}$ β$_{p}$ (1 + 2 /R $^{2}$) M/ 3 (25) Γ( J/ψ → p ¯ pπ $^{0}$) = 97 eV . (26) ρ ( x, y ) = 1 12 πR 3 { ( u + v ) 2 uv − 2( u + v )( u + v + 1) r 2 + 2 uv r 4 − ( u 2 + v $^{2}$) r $^{2}$R2 } . (21) d $^{2}$Γ( J/ψ → p ¯ pπ $^{0}$) dxdy = α$_{J/ψ}$ α$_{π}$ m$_{p}$ ρ ( x, y ) (20) Γ( J/ψ → p ¯ pπ $^{0}$) = 102 ± 9 eV . (19) B ( J/ψ → p ¯ pπ $^{0}$) = 1 . 09 ± 0 . 09 · 10 − 3 (18) This (parameter-free) relative event density, scaled to the maximum value in the physical region, is shown in Fig.2. Integrating (20) over the Dalitz plot gives III. APPLICATIONS A. The J/ψ → p ¯ pπ 0 partial width