Near threshold ppbar enhancement in the J/psi ->omega ppbar decay

The near-threshold behavior of the ppbar invariant mass spectrum from the J/psi ->omega ppbar decay reported recently by the BES Collaboration is analyzed. Contrary to the statement made by the BES Collaboration itself our study demonstrates that there is indeed a noticeable enhancement in the ppbar invariant mass spectrum near threshold. Moreover, this enhancement is nicely reproduced by the final state interaction in the relevant 11S0 ppbar partial wave as given by the Julich nucleon--antinucleon model. Therefore, and again contrary to the statement by the BES Collaboration, their new data on J/psi ->omega ppbar decay in fact strongly support the FSI interpretation of the ppbar enhancement, seen also in other decay reactions.

The near-threshold behavior of the pp invariant mass spectrum from the J/ψ→ωpp decay reported recently by the BES Collaboration is analyzed. Contrary to the statement made by the BES Collaboration itself our study demonstrates that there is indeed a noticeable enhancement in the pp invariant mass spectrum near threshold. Moreover, this enhancement is nicely reproduced by the final state interaction in the relevant ( 11 S0) pp partial wave as given by the Jülich nucleonantinucleon model. Therefore, and again contrary to the statement by the BES Collaboration, their new data on J/ψ→ωpp decay in fact strongly support the FSI interpretation of the pp enhancement, seen also in other decay reactions. The study of the decays of mesons like the J/ψ, ψ(2S), B, and Υ as pursued by the BES, Belle, BABAR and CLEO Collaborations is a rather powerful tool for examining systematically the spectrum of light as well as heavier hadrons. Specifically, exclusive measurements of decays into three-meson or meson-baryon-antibaryon channels play a very important role and have already led to the identification of several new structures.
Among the various three-particle channels explored those involving the proton-antiproton (pp) system in the final state have caused considerable attention in the community. The excitement was initiated by the observation of a significant near-threshold enhancement in the pp invariant mass spectrum for the reaction J/ψ→γpp in a high-statistics and high-mass-resolution experiment by the BES Collaboration [1]. Indeed a first indication for a near-threshold enhancement in the pp invariant mass spectrum from the B + →K + pp andB 0 →D 0 pp decays were reported by the Belle Collaboration [2,3] but with much lower statistics and mass resolution. More recently the Belle Collaboration [4,5] found also a near-threshold pp enhancement in the decays B + →π + pp, B 0 →K 0 pp and B + →K * + pp, while the CLEO Collaboration detected such an enhancement in (the unsubtracted) data for Υ(1S) → γpp [6] and the BES Collaboration in ψ(2S) → γpp [7]. Finally, the BABAR Collaboration presented measurements of the B + →K + pp, B 0 →D 0 pp and B 0 →D * 0 pp decays [8,9] confirming the presence of a near-threshold enhancement in the pp invariant mass.
The high-statistics data by the BES Collaboration triggered several theoretical speculations where the observed enhancement in the invariant pp mass spectrum was interpreted as evidence for a pp bound state or baryonium [10,11,12,13], or for exotic glueball states [14,15]. Alternatively, we [16,17] but also others [18,19,20,21,22,23] demonstrated that the near-threshold enhancement in the pp invariant mass spectrum from J/ψ→γpp and other decays leading to a final pp system could be simply due to the final state interaction (FSI) between the outgoing proton and antiproton. Specifically, our calculation based on the realistic Jülich nucleon-antinucleon (NN ) model [24,25], the one by Loiseau and Wycech [21], utilizing the Paris NN model, and those of Entem and Fernández [22], using a NN interaction derived from a constituent quark model, explicitly confirmed the significance of FSI effects estimated in the initial studies [18,19,20] within the effective range approximation. Interestingly, the same FSI mechanism explains the near threshold enhancement of the data on e + e − ↔NN from the PS170 collaboration, from the FENICE collaboration and from BABAR utilizing radiative return, see [26,27].
Very recently the BES Collaboration presented a high-statistics measurement of the J/ψ→ωpp decay [28] where, according to their own words, no obvious nearthreshold pp mass enhancement is observed. This supposed lack of any enhancement is then seen as a hint that the FSI interpretation of the pp enhancement in J/ψ→γpp is disfavoured [28].
In the present paper we want to take a closer look at those J/ψ→ωpp data by the BES Collaboration. As we already argued in our first work on the pp enhancement [16], this specific decay channel is rather interesting for clarifying the role of the pp FSI effects, because here the conservation laws for parity, charge-conjugation and total angular momentum severely restrict the partial waves in the pp system. In particular, near threshold the pp system can only be in the 11 S 0 state. We use here the standard nomenclature (2I+1)(2S+1) L J where I and S are the total isospin and spin, respectively. In contrary, for the extensively discussed J/ψ→γpp decay any combination of the I = 0 and I = 1 amplitudes is allowed because isospin is not conserved in electromagnetic processes.
Like in our earlier papers [16,17,26], besides the directly measured pp invariant mass spectrum, we utilize also the total spin-averaged (dimensionless) J/ψ→ωpp reaction amplitude A because that allows us to get rid of trivial kinematical factors. The J/ψ→ωpp decay rate is given in terms of A by [29] dΓ = |A| 2 2 9 π 5 m 2 where the Kallen function λ is defined by λ(x, y, z) = ((x − y − z) 2 − 4yz)/4x , M ≡ M (pp) is the invariant mass of the pp system, Ω p is the proton angle in that system, while Ω ω is the ω angle in the J/ψ rest frame. After averaging over the spin states and integrating over the angles, the differential decay rate is We use Eq. (2) for extracting |A| 2 from the data of the BES Collaboration. The original data [28] are reproduced in Fig. 1 while the extracted values for |A| 2 are shown in Fig. 2. We assume again the validity of the Watson-Migdal approach for the treatment of the FSI effect. It suggests that the reaction amplitude for a production and/or decay reaction that is of short-ranged nature can be factorized in terms of an elementary (basically constant) production amplitude and the pp scattering amplitude T of the particles in the final state so that FIG. 2: Invariant J/ψ→ωpp amplitude |A| 2 as a function of the pp mass. The circles symbolize the experimental values of |A| 2 extracted from the BES data [28] via Eq. (2). The solid curve is the appropriately normalized scattering amplitude squared (|T | 2 ) predicted by the NN model A(OBE) [24] for the 11 S0 partial wave. The dashed curve represents the constant reaction amplitude used for generating the dashed curve in Fig. 1. (cf. Ref. [16] for further details). Thus, we compare the extracted amplitude |A| 2 with the suitably normalized scattering amplitudes |T | 2 that result from the Jülich NN model [24] for the 11 S 0 partial wave. Interestingly, that scattering amplitude reproduces the dependence of the experimental |A| 2 on the invariant mass almost perfectly in the near-threshold region, cf. the solid curve in Fig. 2. Therefore, we feel that we even need to stress that this result is actually a prediction of the model and not a fit. The dashed line represents a constant reaction amplitude and corresponds to the pure phase-space behavior. Obviously the BES data show a clear enhancement as compared to the phase-space behavior in the near-threshold region, contrary to what is concluded by the authors from these data in their own publication [28]. This can be also seen from Fig. 1, where the measured pp mass spectrum is shown directly. The normalization of the phase space is done in the region M (pp)−2m p ≈ 100-140 MeV, where the data indeed follow the phase-space distribution. In principle, one could have also normalized the dashed curve to the lowest data points. Then the first four data points would still be roughly in line with a phase-space behavior, at least within the error bars, but one would end up with a gross overestimation of the data at higher invariant masses and, consequently, be in a situation that one sees and has to explain a suppression in the experimental data in that invariant-mass region.
Note that the disagreement of our model results with the experiment for invariant masses beyond M (pp) − 2m p ≈ 100 MeV is not a reason of concern and, in particular, does not discredit the interpretation of the data in terms of FSI effects. At those energies we expect that contributions from higher partial waves, not considered here, should start to play a more prominent role.
In summary, we have analyzed the near-threshold data on the pp invariant mass spectrum from the J/ψ→ωpp decay reported recently by the BES Collaboration. Contrary to the statement made by the BES Collaboration in [28] our study demonstrates that not only in J/ψ→γpp but also in this reaction there is indeed a noticeable enhancement in the pp invariant mass spectrum near threshold. Moreover, this enhancement is nicely reproduced by the final state interaction in the relevant ( 11 S 0 ) pp partial wave as given by the Jülich NN model [24]. Accordingly, the present result is completely in line with our previous investigations of the pp invariant mass spectrum from the J/ψ→γpp decay [16] measured by the BES Collaboration and the B + →K + pp decay [17] measured by the BABAR Collaboration. In particular, and again contrary to the statement by the BES Collaboration [28], their new data on J/ψ→ωpp decay, in fact, strongly support the FSI interpretation of the pp enhancement seen in other decay reactions. It goes without saying that, the FSI effects for the various decay reactions should not be expected to be quantitatively the same because due to the different quantum numbers and conservation laws as well as different reaction mechanisms, the final pp system can and must be in different partial waves.