Baryon Antibaryon Nonets

The baryon-antibaryon SU(3) nonets are proposed as a scheme to classify the increased number of experimentally observed enhancements near the baryon antibaryon mass threshold. The scheme is similar to the Fermi-Yang-Sakata model, which was put forth about fifty years ago in explaining the mesons observed at that time. According to the present scheme, many new baryon-antibaryon bound states are predicted, and their possible productions in quarkonium decays and B decays are suggested for experimental search.


I. INTRODUCTION
Low mass baryon-antibayron enhancements have recently been observed in charmonium and B decays.In charmonium decays, pp and pΛ enhancements are observed in J/ψ → γpp [1], ψ ′ → π 0 pp, ηpp [2], and J/ψ → pΛK − + c.c. [3], as well as in ψ ′ → pΛK − + c.c. decays [3] by BES collaboration.In B decays, many baryon-antibayron-pair-contained final states have been measured by CLEO, Belle and BABAR collaborations, such as B 0 → D * − pn [4], B ± → ppK ± [5], B 0 → D * 0 pp, D 0 pp [6], B 0 → pΛπ − [7], B + → ppπ + , ppK * + , B 0 → ppK 0 [8], B + → ΛΛK + [9], B 0 → D * 0 pp, D 0 pp [10], and so on, with observed enhancements in pp, pΛ and ΛΛ mass spectra.Except for the enhancement in J/ψ → γpp, which is claimed to be very narrow and below the pp mass threshold, all other states are slightly above the baryon antibaryon mass threshold and the widths are a few ten to less than 200 MeV/c 2 .Stimulated by recent experimental results, a number of theoretical speculations and investigations are put forth [11,12], some focus on the interpretation of a particular final state [11], for instance J/ψ → γpp, while others discuss the final states containing baryon and antibaryon pair [12].Most of these works devote to the improvement of previous models or exploration of the production and decay dynamics, but it is still far from understanding the problem.
The discovery of increased number of baryonantibaryon enhancements near thresholds can not help reminding us of the era prior to the development of SU (3) quark model, when the so-called elementary particles emerged one by one.In this Letter, instead of studying the dynamics of the production or decay of these states, we try to find a way to classify them.We suggest a nonet scheme to accommodate the baryon-antibaryon enhancements observed in charmonium and B decays.We surmise, with certain kind of interaction, for example, the residual strong force between the quarks inside the * Electronic address: yuancz@mail.ihep.ac.cn baryons, some multiplets can be formed as the baryonantibaryon bound states.Our idea is enlightened by the Fermi-Yang-Sakata (FYS) model, in which the mesons were interpreted as baryon-antibaryon bound states.In the following parts of the Letter, we first review the FYS model briefly, then put forward a baryon-antibaryon nonet scheme, by virtue of which, many new baryonantibaryon bound states are expected.Finally, the search for these states are discussed.

II. FERMI-YANG-SAKATA MODEL
In 1950s, as the number of the so-called elementary particles increased, it became less likely that all of them were truly elementary.Under such circumstance, as a tentative scheme, Fermi and Yang proposed [13] that the π-meson may be a composite particle formed by the association of a nucleon and an anti-nucleon, with strong attractive force in between which binds them together.Since the mass of the π-meson is substantially smaller than twice the mass of a nucleon, it is necessary to assume that the binding energy is extremely large which is unappealing theoretically.
In 1955 after the discovery of the strangeness, Sakata extended Fermi-Yang's idea by including a strange baryon Λ and its anti-particle [14], and intended providing a physical meaning for the Nishijima-Gell-Mann's rule [15].Four years later, the most modern-like version of the FYS model was developed by Ikeda, Ogawa and Ohnuki [16].They assumed that proton p, neutron n and Λ are basic particles which compose other baryons and mesons as suggested by the FYS model.They proposed a framework which explicitly assures the equivalence of the three basic particles, p, n and Λ, in the limit of an mass.This leads to the introduction of a new invariance under the exchange of Λ and p or Λ and n in addition to the usual charge independence and the conservation of electrical and hyperonic charge.They utilized U (3) group to analyze the symmetry of the FYS model and obtained exactly the same classification of the pseudoscalar mesons as the quark model as long as the basic elements p, n and Λ are replaced by u, d and s quarks.The symmetry analysis of Ikeda, Ogawa and Ohnuki was so successful that all the pseudoscalar mesons known by 1961 could be accounted for, and moreover, a new particle η was predicted which was shortly discovered [17].
However, after the theory of unitary symmetry of strong interactions was put forward [18], especially when hyperon Ω − was predicted definitely by Gell-Mann [19] and its existence was confirmed experimentally [20], the FYS model became a history for the quark model.In fact, even when the FYS model was proposed, it encountered a profound difficulty which was the enormous binding energy for sticking the nucleons together to form a meson.On the contrary, for the newly observed baryon antibaryon enhancements near thresholds, the binding energy is small compared with the mass of a nucleon.So we turn to the FYS model to classify these bound states.
We come back to the FYS model, but from a different point of view.In our scheme, the baryon-antibaryon bound states do not refer to ordinary mesons, such as π, K, η, but to the bound states formed by baryon and antibaryon.The interaction between the baryon and antibaryon is probably the residual force between the strong interaction of the quarks and gluons inside the baryon or antibaryon.On one hand, the masses of the three-quark systems (the baryon and the antibaryon) increase by a small amount due to the residual forces required to form the bound state; on the other hand, the binding energy between the two three-quark systems decreases the mass of the baryon-antibaryon system to lower than the sum of the masses of the three-quark systems, but very close to the baryon-antibaryon mass threshold.This supplies as a phenomenological surmise, the real physics awaits for the validity of the quantum chromodynamics.
Similar to the SU (3) quark-antiquark nonets, we postulate the existence of special octets and singlets (nonets) whose elements are baryon-antibaryon bound states, as shown in Fig. 1.Hereafter, we limit our study to the low-mass baryons: p, n and Λ.For a baryon-antibaryon bound state, its quantum numbers are obtained in the following way: • Its spin (S) is 0 or 1, from the addition of the component baryons.
• The parity is (−1) L+1 , where L is the orbital angular momentum between the baryon and the antibaryon.In case of S-wave (L = 0), the parity is odd (−), while for P -wave, the parity is even (+).
• For pure neutral system, such as nn, pp, or ΛΛ, the C-parity is (−1) L+S .For charged members, we define the generalized C-parity [21] by the neutral member of the nonet, but under C-parity transformation, the particle changes into its anti-particle.
The property of the S-wave spin-singlet states (J P = 0 − ) or the S-wave spin-triplet states (J P = 1 − ) nonet FIG.
is summarized in Table I, which leads to the relation of their production rates in experiments.For simplicity, we assign the particles in the nonets the same names as the meson nonets formed by quark-antiquark, but with a subscript B for distinction.For example, the 0 − isospin vector states are denoted as π + B , π 0 B , and π − B , while the 1 − strange particles are referred to as K * 0 B , K * + B , and their anti-particles.In general, there is mixing between the 8th component of the SU (3) octet and the SU (3) singlet.Since the masses of proton and neutron differ by only 1.3 MeV/c 2 , but the mass of Λ is 177 MeV/c 2 greater, one is invited to assume ideal mixing between them, thus one is pure (pp + nn) and the other is pure ΛΛ.This is to be verified by experiments.
If the electromagnetic interaction is neglected, the production rates of these baryon-antibaryon bound states in J/ψ and ψ ′ decays can be simply related by SU (3) symmetry except for a phase space factor.For example, the production rates of baryon-antibaryon bound states with J P = 1 − accompanying by a pseudoscalar meson are re-lated by: π 0 ρ 0 Here X η , X η ′ , Y η , and Y η ′ are the mixing coefficients of η and η ′ [22]: Assuming aforementioned states predominantly decay to baryonantibaryon pair, and considering the fact that ρ 0 B → nn and ω B → nn are hard to be detected experimentally, above relation can be reformulated in terms of the experimentally detected final states: π 0 (pp) : π + (np) : π − (np) : 2 : 1 : 1 : 1 : 1 : 1 : 1 : The production rates of baryon-antibaryon bound states with other quantum numbers are expressed similarly.The phase space is proportional to p 3 for the production of the J P = 1 − (0 − ) baryon-antibaryon bound state with an accompanying pseudoscalar (vector) meson, where p is the momentum of the baryon-antibaryon bound state.
The pp state observed in J/ψ radiative decays is η B or π 0 B if it is a S-wave state due to spin-parity conservation, and the pΛ states in J/ψ decays is K * + B or K + B .In B decays, since parity is not conserved, the spin-parity of the state is to be determined by the angular distributions of the final state particles.

IV. EXPERIMENTAL SEARCHES
Because of the large phase space, B decays play important roles in the study of the baryon-antibaryon resonances.Many of the baryon-antibaryon-pair-contained final states have been analyzed experimentally as mentioned above, other interesting modes to be searched for are given in Table II.The complexity here is the possible existence of two or more baryon-antibaryon resonances in the same final states and in a very small mass region, since many different J P states can be produced in B decays, depending on the other particles accompanying the baryon-antibaryon resonances.
Charmonium is another domain to study the baryonantibaryon states.Unlike B decays, conservation law holds a rein on a possible decay mode herein.By virtue of the quantum numbers listed in Table I, some decay modes involving the 0 − and 1 − baryon-antibaryon bound states are listed in Table III.
The production of the 0 − baryon-antibaryon bound states in J/ψ (or ψ ′ ) decays can be accompanied by a vector meson.For the iso-vector bound states, one may look for the ρN N (nucleon antinucleon) final states, including ρ + np, ρ 0 pp and ρ − pn; for the iso-scalar bound state, one may look for the ωpp final state; while for the strange states, one may look for the K * + Λp + c.c. and K * 0 Λn + c.c. final states.The neutron or anti-neutron which is not detected may be reconstructed by kinematic fit in the event selection.The SU (3) singlet state can be searched for by measuring φΛΛ final state.The measurement of the 0 − baryon-antibaryon bound states together with an axial-vector meson is less promising since almost all the axial-vector mesons are resonances.The production of the 1 − baryon-antibaryon bound states can be accompanied by a pseudoscalar (π, η, η ′ , K), scalar, tensor or axial-vector meson.The most promising way to look for them is in the decays with a pseudoscalar meson: analyze πN N for the iso-vector bound states; analyze ηpp for iso-scalar bound state; and analyze K + Λp + c.c. and K 0 Λn + c.c. for the strange bound states.The SU (3) singlet bound state can be searched for via η ′ ΛΛ.
It should be noted that the neutral non-strange 0 − baryon-antibaryon bound states can also be produced via radiative decays of J/ψ (or ψ ′ ), while the 1 − baryonantibaryon bound states can not be produced this way due to spin-parity conservation.
Although among charmonium decays J/ψ provides a good source of the baryon-antibaryon bound states because of the large data samples, there are disadvantages: TABLE III: Decay modes containing baryon-antibaryon nonets in charmonium decays.The first J P is for the accompanying particle while the second for the baryon-antibaryon resonance.
the phase space is too small and there are many N * 's near nucleon meson mass threshold, which affect the identification of the states.The ψ ′ decays have larger phase space, however, the data samples are smaller, and there is a large fraction of charmonium transition.CLEOc and BESIII will surely help to improve the statistics, and the partial wave analysis is desirable to take the N * contribution into account correctly.
It is also possible to perform such searches in bottomonium (Υ) decays, with the existing data sample at CLEO-III and possibly more if B-factories take data at Υ(1S).The phase space is much larger than in charmonium, and the N * states are far from the baryon-antibaryon mass threshold.In principle, all modes listed in Table III can be searched for in bottomonium decays.

V. DISCUSSION AND CONCLUSION
Although our discussion is limited to S-wave, SU (3) baryon-antibaryon bound states, it can be easily extended in many aspects.First, the P -wave, D-wave and even higher angular momentum multiplets are also expected to exist.Thus we have J P = 0 + , 1 + , 2 + , • • • , states.Second, the scheme can be extended by including more baryons, for example, the charmed baryon Λ c .As has been reported by the Belle collaboration, an enhancement was observed in Λ c p mass spectrum near the threshold [23].This can be interpreted as a member in the SU (4) multiplets.Last, the extension to the baryonmeson, or the meson-meson bound states is in principle straightforward.Nevertheless, the existence of such kinds of resonances can merely be determined by experiment.
In summary, the observations of the enhancements near the baryon antibaryon mass thresholds in charmonium and B decays bring us fresh ideas in the study of hadron spectroscopy.With the known symmetry properties of strong interaction, we foresee the existence of the nonet baryon-antibaryon bound states and their possible quantum numbers in a revived FYS model, even though we cannot calculate the binding energies from the first principle of QCD at present.In the light of our scheme, we know where to find these bound states in J/ψ, ψ ′ , Υ and B meson decays.The search can be conducted with the existing or soon available CLEOc, BESIII, and B-factory data.

TABLE I :
1: Baryon-antibaryon nonet.The J P of this nonet is either 0 − or 1 − .The three circles in the figure indicate the following three states: (nn − pp)/ Quantum numbers of baryon-antibaryon nonet with J P = 0 − or 1 − .I is isospin, I3 is the third component of I, S is the strangeness and Q is the charge of the state.The column "symbol" gives nomenclature of the 0 − and 1 − states for easy reference in the Letter.

TABLE II :
Possible decay modes containing baryonantibaryon nonets in B decays.