2 and the final NNπ coupling is of course well known. Provided that the contribution of the Ψ → N ¯ N → N ¯ Nm decay mechanism can be isolated and quantified experimentally, this information can be used to estimate meson-nucleon strong coupling constants; these are gen- erally poorly known, and play an important role in nu- clear physics as input parameters in meson exchange models of the NN force [14–21]. We will also discuss the determination of the (well known) p ¯ pπ 0 and the (poorly known) p ¯ pω couplings from the decays J/ψ → p ¯ pπ $^{0}$, ψ ′ → p ¯ pπ 0 and J/ψ → p ¯ pω as examples. This provides a third motivation for the study of Ψ → N ¯ Nm decays; they may prove useful for estimat- ing NNm coupling constants, in addition to their rele- vance to N ∗ spectroscopy [1–5] and low-mass p ¯ p dynam- ics [6–8]. Another motivation for studying Ψ → N ¯ Nm is the possibility of observing light scalars, including the “ σ ”, the 980 MeV states and the scalar glueball, in the decays Ψ → p ¯ pf$_{0}$ (and a$_{0}$ ). The areas { A$_{D}$ } of these Dalitz plots are useful for es- timating Γ(Ψ → p ¯ pm ) partial widths [9]. Although A$_{D}$ can be evaluated in closed form for Ψ → p ¯ pm with gen- eral mass ratios r and R , the resulting expression is quite lengthy, so when required we will simply evaluate each A$_{D}$ numerically. In deriving the DP event densities we have usually as- sumed that the Ψ p ¯ p coupling is a constant g$_{Ψ}$$_{p}$$_{¯}$ p times the simplest relevant Dirac matrix for the given Ψ quantum numbers; for example, for the J/ψ we use a pure vector J/ψp ¯ p vertex, − ig$_{J/ψp}$$_{¯}$ $_{p}$γ$_{µ}$ . The order of the hadron la- bels in g$_{abc}$ is meant to reflect the fact that the numerical value of this coupling constant is taken from an a → bc transition, here J/ψ → p ¯ p . This could be a significant concern if form factor effects are large. We proceed similarly for the light mesons π 0 and f$_{0}$ ; for the pion we use a pure pseudoscalar NNπ coupling, with vertex g$_{NNπ}$γ$_{5}$ , and − ig$_{NNf}$$_{0}$I for the NNf$_{0}$ vertex. Since light vector mesons (generically represented by the ω ) have two interesting strong couplings, Dirac (vector) and Pauli (anomalous magnetic), for this special case we assume a vertex with two interactions, Here we will usually specialize to charmonium decays to a p ¯ p pair and a neutral meson, Ψ → p ¯ pm $^{0}$; these decays are reasonably well studied, and enjoy the simpli- fication of equal baryon and antibaryon masses. Our re- sults employ conventions for kinematic variables, meson- baryon couplings and masses that were used in Ref.[24]. In particular, M is the mass of the initial charmonium state, m$_{p}$ is the proton mass, m$_{m}$ is the mass of meson (subscript) m , and dimensionless mass ratios R ≡ M/m$_{p}$ and r ≡ m$_{m}$/m$_{p}$ are defined relative to the proton mass. (Hence the numerical values of R and r depend on the decay process.) We use scaled dimensionless variables x = M 2 $_{pm}$/m 2 p − 1 and y = M 2 ¯ $_{pm}$/m 2 p − 1 and their in- verses u = 1 /x and v = 1 /y to describe Dalitz plots; these greatly simplify our results. The DP event densi- ties we present here are formally partial width densities in x and y , which are related to the more familiar differ- ential partial widths by a trivial overall constant, Ref.[25] assumed a similar J/ψp ¯ p vertex; see Ref.[24] for additional details regarding the couplings assumed here. We generally abbreviate these coupling constants as g$_{Ψ}$ ≡ g$_{Ψ}$$_{N}$ ¯ N and g$_{m}$ ≡ g$_{NNm}$ ; rationalized squared couplings α$_{Ψ}$ ≡ g 2 $_{Ψ}$/ 4 π and α$_{m}$ ≡ g 2 $_{m}$/ 4 π are also used. For the special case of p ¯ pπ 0 final states, these event densities can be obtained by applying crossing relations to our previously published results for the unpolarized differential cross sections for the 2 → 2 processes p ¯ p → π $^{0}$Ψ [24]; the other ( f$_{0}$ and ω ) cases have not been con- sidered previously. The results for all cases considered here are given below. Before we give our results for these event densities, it is useful to recall some general properties of a Ψ → p ¯ pm Dalitz plot. The boundary in the dimensionless variables ( x, y ) is specified by the curves II. FORMULAS Γ ( ω ) µ = − ig$_{NNω}$ ( γ$_{µ}$ + i ( κ$_{NNω}$/ 2 m$_{p}$ ) σ$_{µν}$q$_{ν}$ ) . (5) d $^{2}$Γ( η$_{c}$ → p ¯ pπ $^{0}$) dxdy = α$_{η}$ c α$_{π}$ m$_{p}$ 8 πR 3 { ( u − v ) 2 · ( 1 uv − r $^{2}$R2 ) } (6) d $^{2}$Γ( J/ψ → p ¯ pπ $^{0}$) dxdy = α$_{J/ψ}$ α$_{π}$ m$_{p}$ 12 πR 3 { ( u + v ) 2 uv − 2( u + v )( u + v + 1) r 2 + 2 uv r 4 − ( u 2 + v $^{2}$) · r $^{2}$R2 } (7) d $^{2}$Γ( χ$_{c}$$_{0}$ → p ¯ pπ $^{0}$) dxdy = α$_{χ}$ c 0 α$_{π}$ m$_{p}$ 8 πR 3 { ( u + v ) 2 · ( 1 uv + 4 r 2 − r $^{2}$R2 ) } (8) r ( r + 2) ≤ x ≤ R ( R − 2) . (4) F ( a, x ) ≡ ( a $^{2}$( a 2 − 4) − 2 a $^{2}$x + x $^{2}$)1 / $^{2}$. (3) y$_{±}$ = r $^{2}$R2 + ( r 2 + R 2 − 2) x − x 2 ± F$_{m}$F$_{Ψ}$ 2(1 + x ) (2) d $^{2}$Γ(Ψ → p ¯ pm ) dxdy = m 4 p d $^{2}$Γ(Ψ → p ¯ pm ) dM 2 $_{pm}$dM 2 ¯ pm . (1) where F$_{m}$ = F ( r, x ) and F$_{Ψ}$ = F ( R, x ), with The range of values of x (and y ) in the physical region is