Indications of the existence of quasi-bound states in the N-Nbar system are
presented. Measurements by BES discovered a broad enhancement close to the
p-pbar threshold in the S wave, isospin 0 state formed in radiative decays of
J/psi. Another enhancement located about 50 MeV below the threshold was found
in mesonic decays of J/psi. In terms of the Paris potential model it was shown
that these are likely to represent the same state. Antiprotonic atomic data
provide some support for this interpretation and indicate the existence of
another fairly narrow quasi-bound state in a P wave.Comment: 6 pages, 6 figures - Contribution to EXA2014 Vienna to appear in a
  special edition of Hyperfine Interaction

Dedonder, J. P.

Loiseau, B.

Wycech, S.

English

arXiv

S. Wycech

J.-P. Dedonder

B. Loiseau

Springer - Publisher Connector

Hyperfine Interact (2015) 234:141–148
DOI 10.1007/s10751-015-1150-z
Baryonium, a common ground for atomic and high
energy physics
S. Wycech · J.-P. Dedonder ·B. Loiseau
Published online: 3 April 2015
© The Author(s) 2015. This article is published with open access at Springerlink.com
Abstract Indications of the existence of quasi-bound states in the NN system are pre-
sented. In their measurements, the BES collaboration has discoverd a broad enhancement
close to the pp threshold in the S wave, isospin 0 state formed in radiative decays of J/ψ .
Another enhancement located about 50 MeV below the threshold was found in mesonic
decays of J/ψ . In terms of the Paris potential model it was shown that these are likely to rep-
resent the same state. Antiprotonic atomic data provide some support for this interpretation
and indicate the existence of another fairly narrow quasi-bound state in a P wave.
Keywords Baryonium · J/psi decays · antiprotonic atoms J/ψ
1 Introduction
Nucleon-antinucleon quasi-bound states, or states coupled to these, were searched for in
the days of LEAR at CERN. Nothing has been found, but broad states or states close to
the threshold were not excluded. References [1], [2] indicate conclusions of a long series
of measurements. In reference [1] a search for narrow signals in the γ spectrum from pp
Proceedings of the International Conference on Exotic Atoms and Related Topics (EXA 2014), Vienna,
Austria, 15-19 September
S. Wycech ()
Andrzej Soltan Institute for Nuclear Studies, Hoza 69, 00-681 Warsaw, Poland
e-mail: wycech@fuw.edu.pl
J.-P. Dedonder · B. Loiseau
Laboratoire de Physique Nucle´aire et de Hautes E´nergies, Sorbonne Universite´s, Universite´ Pierre et
Marie Curie, Sorbonne Paris Cite´, Universite´ Paris Diderot and IN2P3-CNRS UMR 7585,
4 place Jussieu, 75252 Paris, France
J.-P. Dedonder
e-mail: dedonder@univ-paris-diderot.fr
B. Loiseau
e-mail: loiseau@lpnhep.in2p3.fr
142 S. Wycech et al.
Table 1 Low energy pp states allowed in the J/ψ → γpp decays. The first column gives decay modes
and specifies the internal states of pp pair. For both photon and J/ψ the JPC = 1(−−). The second column
gives JPC for the pp system
Decay mode JPC(pp)
γpp(1S0) 0−+
γpp(3P0) 0++
γpp(3P1) 1++
Table 2 Decay modes and the pp states allowed in the J/ψ → boson pp decays
Decay mode Branching pp states allowed
γpp 3.8(±1.0) · 10−4 [8] 1S0,3 P1,3 P0
ωpp 1.1(±0.15) · 10−3[9] 11S0,13 P1,13 P0
π0pp 1.19(±.08) · 10−3[8] 33S1,31 P1
pp 2.12(±0.1) · 10−3 [8] 13S1
annihilation at rest was performed and no discoveries were found in the region below 1770
MeV and  < 25 MeV. Another experiment looking for missing mass in the reactions
pp → π−X and pd → pX brought similar conclusions. On the experimental side, one
possible reason for the failure is the large background due to annihilation processes. Another
is the large number of allowed partial waves. On the theory side, it was assumed that the
annihilation reaction involve ∼ 2Mp mass transfer and by the uncertainty principle it has
to be very short ranged. It was thus expected that widths of quasi-bound states might be
narrow. The first part of the argument is still true but it is also known from scattering data
that the annihilation potential is strong already at p − p separation of 1fm.
A convincing detection requires selective experiments, and the first such measurement is
that of the decay
J/ψ → γpp, (1)
studied by the BES Collaboration [3]. A strong threshold enhancement appears in the invari-
ant pp mass distribution (see Fig. 3). There are three final pp states allowed by P and C
conservation in the γpp channel. These are listed in Tables 1 and 2 and denoted by 2S+1LJ
or 2I+1,2S+1LJ , S,L, J being the spin, angular momentum, total momentum of the pair
and I denotes the isospin. Radiative decay does not conserve isospin but already in ref. [3]
and ref. [4] it was realized that I = 0 is the state which leads to the enhancement. From
potential descriptions of NN interactions based on the G-parity rule it is known that the
pion exchange potential is very strong in this state, being capable to form bound states.
On the other hand the annihilation and short range interactions act repulsively, thus quasi-
bound states are not guaranteed. In particular the Paris potential generates a 52 MeV broad
quasi-bound state at 4.8 MeV below threshold [5] but the the Bonn-Ju¨lich potential does not
generate bound state in this wave [6]. Both can describe the threshold enhancement [6],[7].
The radiative process itself is puzzling as the decay rate is comparable to the mesonic
decay rates although the conventional coupling constants α/g2NN,meson are ∼ 10−3. Thus, a
strong enhancement mechanism has to exist. In Section 2, this question is discussed jointly
with the origin of the threshold enhancement.
Baryonium, a common ground for atomic and high energy physics 143
Fig. 1 The photon is emitted
either from J/ψ or during the
hadronisation stage of the
process and the final baryons are
formed in the S wave
Fig. 2 Final state interactions
described by half-off shell T
matrix generated by the Paris
potential
There are other indications of Np structures existing below threshold coming from
antiprotonic atoms. These are discussed in Section 3. In Section 4 we list possible
experimental researches of the baryonia which could be performed in a near future.
2 Final state interactions in J/ψ decays
We have attempted calculations of the radiative and mesonic decay rates presented in
Table 2, assuming that mesons are emitted in the final states of the decay when the baryons
have been formed. With conventional meson-nucleon coupling constants this model repro-
duces the branching ratios of pp −meson channels relative to the basic pp channel [10]. It
offers also a consistent description of the spectra in cases of π0 and ω meson production at
the expense of one free parameter, the NN formation radius R = 0.28 fm. However, this
model fails in the description of radiative decays in two ways: first, the branching ratio is
only about 1/3 of the experimental one, and second, the threshold enhancement is not repro-
duced. The transition to 1S0 state is a magnetic one and it turns out that in the intermediate
stage of such decay one has both pp and nn as intermediate states. Since magnetic moments
of p and n have opposite sign the effect of final state enhancement cancels strongly. At the
same time such a model indicates that final state interactions increase the overall decay rate
by an order of magnitude in the I = 1 states.
In this note we report an extension of the final state interactions (FSI) calculations of
ref. [7] which is now used to cover the whole photon spectrum. The basic assumption
of this approach (also that in ref. [6]) is that the photon is emitted before the baryons
are formed. The two related processes are plotted in diagrams Figs. 1, 2 and the FSI is
calculated in terms of half-off shell T matrix generated by the Paris potential [5] plot-
ted in Fig. 4. This approach allows to calculate the spectrum but not the absolute decay
rate. One free parameter, the radius R (=0.28 fm) of a Gaussian source function is used
to describe the creation of a γpp state (see Fig. 1). However, in order to reproduce
in a better way both maxima in Fig. 3 (the X(1859) and X(2170) in BES terminol-
ogy), it turns out profitable to assume the radius to be weakly dependent on the photon
144 S. Wycech et al.
Fig. 3 The pp invariant mass obtained under the assumption that photon is emitted before the baryons are
formed. The missing strength at large pp invariant mass, Mpp , comes from the photon radiated by final
hadrons [10]. The experimental points from ref. [3]
Fig. 4 The Paris NN real potential in the 11S0 wave. It generates a 50 MeV broad quasi-bound state at ∼
5 MeV binding. The well and barrier structure generate the shape resonance visible in the spectrum in Fig. 3
at 2170 MeV
energy. It was found to change from 0.28 fm at maximal k ∼ 1.2 GeV to 0.39 fm at
k = 0 (Fig. 4).
Inspection of Fig. 3 shows that both states may be reproduced by the potential NN
interactions related at large distances via G-parity transformation to the NN interactions.
However, the proper description of both peaks involves a distant extrapolation of the TNN
matrices off energy shell, which corresponds to very short ranged interactions. This figure
shows also that a sizable portion of the spectrum is missing and this part comes from the
photon emission by the NN pair and exchange currents [10].
As already discussed, the threshold enhancement indicates a ”nearby singularity” that
might describe an analogue of the bound state or the virtual state known from the physics
Baryonium, a common ground for atomic and high energy physics 145
Fig. 5 The spectral function XS representing the X(1835) shape. The parameter of the annihilation range is
rf = 0.45 fm. This S-wave contribution has been normalized to reproduce the data close to the X(1835)
peak. The experimental points are from ref. [11], calculation from ref. [12]
Table 3 Ratios of N(np) and N(pp) capture rates from atomic states
Atom Lower Upper Radiochemistry
96Zr 0.95(9) 1.53(29) 2.6(3)
124Sn 1.79(10) 2.44(39) 5.0(6)
106Cd 1.64(80) 2.10(80) 0.5(1)
112Sn 1.90(13) 2.43(49) 0.79(14)
The last column shows experimental numbers from radiochemical experiments. Other columns (see text)
give ratios calculated with optical potential and plausible nuclear densities based on experimental results
from Ref. [13].
of two nucleons. To discern these possibilities one has to test directly the sub-threshold
region.
3 Studies of the NN sub-threshold region
One way to look below the threshold is the detection of NN decay products. The specific
decay mode
J/ψ → γπ+π−η′ (2)
has been studied by the BES collaboration [11]. This reaction is attributed by BES to an
intermediate pp configuration in the JPC(pp) = 0−+ state, that is in the 1S0 wave. A peak
in the invariant mass of the mesons has been observed and interpreted as a new baryon state
and named X(1835).
Under the assumption that all mesons are produced in relative S waves, the reaction (2),
if attributed to an intermediate pp, is even more restrictive than the reaction (1). It allows
only one intermediate state, the pp 1S0, which coincides with the previous findings. The
intermediate state of pp in reaction (2) is possible but not warranted. In ref. [12] a more
consistent interpretation is obtained with the dominance of the 11S0 state which is a mixture
146 S. Wycech et al.
Table 4 Binding energies in
MeV of the close to threshold
quasi-bound states in the Paris
potential [5]
2T +1 2S+1LJ E − iΓ /2
11S0 −4.8 − i26
33P1 −4.5 − i9.0
of pp and nn pairs. It has been argued that the peak is due to an interference of a quasi-
bound, isospin 0, NN state with a background amplitude. A typical interference pattern
obtained in this way is plotted in Fig. 5. It is fairly close to the data. The same quasi-bound
state was found in ref. [7] to be responsible for the threshold enhancement in reaction (1).
In this sense the Paris potential unifies the two effects and attributes it to single quasi-bound
state with an energy dependent width.
Testing the subthreshold amplitudes may be also realized in few body systems, in par-
ticular in light antiprotonic atoms or at extreme nuclear peripheries. In these conditions
nucleons are bound and the effective subthreshold energies are composed of binding ener-
gies and recoil of theNp pair with respect to the rest of the system. For valence nucleons the
Ebinding + Erecoil may reach down to - 40 MeV below threshold. Let us indicate an atomic
experiment that discovered an interesting anomaly. Table 3 shows the ratios of antiproton
capture rates on neutrons and protons C(np)/C(pp) bound to nuclear peripheries. These
reflect the ratios of neutron and proton densities. The second and third columns indicate
such ratios extracted from the widths of two antiprotonic atomic levels the ”lower” and the
”upper” one. These widths are determined at nuclear densities ∼ 10 % and ∼ 5 % of the
central density ρ0. The last column is obtained with radiochemical studies of final nuclei
with one neutron or one proton removed in the annihilation reaction [13]. The latter pro-
cess is localized at densities ρ ∼ 10−3ρ0. In standard nuclei shown in the upper part of
the table the ratios N(np)/N(pp) ∼ ρn/ρp increase at nuclear peripheries. However, in
some nuclei characterized by small protonbinding, indicated in the lower part of the table,
and typical ( ∼ 8 MeV ) neutron binding the experimental ratio N(np)/N(pp) suddenly
drops at extreme nuclear peripheries. That effect cannot be explained by the nuclear struc-
ture alone and we attribute it to the existence of a narrow bound state in the NN system.
Such a narrow state is in fact predicted by the Paris potential in the 33P1 wave, see Table 4.
A similar effect is indicated by studies of experimental absorption lengths in light
antiprotonic atoms [14], [15]. From the lower and upper atomic level widths one can
extract average S-wave absorption lengths Im a and P -wave absorption volumes Im b. The
results shown in Fig. 6 indicate increase of the absorption in the S wave down below the
threshold. This result is consistent with the presence of the X(1855) state. The absorption
volume extracted from antiprotonic deuterium indicates some enhancement possibly related
to radiochemical anomalies observed in nuclei with loosely bound protons and interpreted
in terms of the Paris potential as the P -wave bound state.
4 New era
Following the indications from antiprotonic atoms and from BES experiments the baryonia
should be searched in the region of 0 − 60 MeV below the NN threshold. With the new
antiprotonic beams expected to operate in J-PARC and FAIR it would be advisable to repeat
two old experiments possibly at different energies, possibly with polarized particles.
Baryonium, a common ground for atomic and high energy physics 147
-40 -30 -20 -10 0 10
1
2
3
ENERGY (MeV)
fm
2L
+1
4
He
3
He
2
H
1
H + np
Im a
p
Im a
n
Im b
p
Im b
n
Fig. 6 The absorptive parts of spin-isospin averaged Np¯ scattering parameters extracted from the atomic
level widths in H, 2H, 3He and 4He p¯. Rectangles: S waves and ellipses : P waves. The bottom scale indicates
the energy below threshold. The curves, calculated with the Paris potential, give the amplitudes separately:
an(p) denote the np¯ or pp¯ S-wave scattering lengths. Similarly bn(p), bp(p) are the corresponding P -wave
volumes. The vertical scale means fm for the lengths and fm3 for the volumes. The strong increase of
absorption in the p¯p S wave is attributed mainly to the 11S0 state
• The search for narrow signals in the γ -spectrum from pp annihilation was performed
at rest [1]. The signals (in the region that we expect them now to exist) were covered by
heavy background due to π0 decays and π−p → γ n. It would be better to perform this
experiment with higher energy antiprotons (a few hundred MeV/c) which could shift
the expected signal away from the heavy background region.
• The pd → pX experiment [2] was performed at 1.3 GeV/c. This gives rather small
chance of pp coupling in the statistically insignificant 11S0 wave. Lower energies and
polarized (one or two particles) would reduce the background.
New instructive experiments that possibly could be performed at FLAIR are:
• Fine structure splitting in light antiprotonic atoms 1H, 2H, 3H, 3He, 4He would allow to
trace energy dependenc of the selected pN amplitudes in the subthreshold region down
to ∼ −40 MeV.
• Studies of mesons emitted from annihilations of p at nuclear peripheries. In particular
nuclei with closed shells with one loosely bound valence nucleon could be profitable. In
the latter case the baryonium signal would be separated from a complicated background
due to other annihilation channels.
Acknowledgments This work has been partially supported by a grant from the French-Polish exchange
program COPIN/CNRS- IN2P3, collaboration 05-115. SW was also supported by Narodowe Centrum Nauki
grant 2011/03/B/ST2/00270
Open Access This article is distributed under the terms of the Creative Commons Attribution License
which permits any use, distribution, and reproduction in any medium, provided the original author(s) and the
source are credited.
Conflict of interests The authors declare that they have no conflict of interest.
148 S. Wycech et al.
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