# Supernarrow Dibaryons

L.V<EMAIL_ADDRESS>P.N. Lebedev Physical Institute RAS,
Leninskiy Prospect 53, Moscow, 119991, Russia

###### Abstract

An analysis of the experimental search for supernarrow dibaryons (SNDs) have
been performed. The sum rules for SND masses have been constructed. The
calculated values of the SND masses are in good agreement with the existing
experimental values. It has been shown that the SND decay leads to the
formation of $N^{*}$ with small masses. Experimental observations of $N^{*}$
is an additional confirmation of the possibility of the SND existence.

###### pacs:

13.75.Cs, 14.20.Pt, 12.39.Mk

##  I Introduction

Supernarrow dibaryons (SNDs) are 6-quark states, a decay of which into two
nucleons is forbidden by the Pauli exclusion principle fil1 ; fil2 ; alek1 .
Such states satisfy the following condition:

$(-1)^{T+S}P=+1$ (1)

where $T$ is the isospin, $S$ is the internal spin, and $P$ is the dibaryon
parity. In the $NN$ channel, these six-quark states would correspond to the
following forbidden states: even singlets and odd triplets with the isotopic
spin $T=0$ as well as odd singlets and even triplets with $T=1$. These six-
quark states with the masses $M<2m_{N}+m_{\pi}$ ($m_{N}(m_{\pi})$ is the
nucleon (pion) mass) can mainly decay by emitting a photon. This is a new
class of metastable six-quark states with the decay widths $<1$keV.

The experimental discovery of the SNDs would have important consequences for
particle and nuclear physics and astrophysics. This would lead to a deeper
understanding of the evolution of compact stars and the new possibility of
quark-gluon plasma observation. In nuclear physics there would be a new
concept: SND-nuclei.

In the framework of the MIT bag model, Mulders et al. muld  calculated masses
of different dibaryons, in particular, masses of $NN$-decoupled dibaryons.
They predicted dibaryons $D(T=0;J^{P}=0^{-},1^{-},2^{-};M=2.11$ GeV) and
$D(1;1^{-};2.2$ GeV) corresponding to the forbidden states ${}^{13}P_{J}$ and
${}^{31}P_{1}$ in the $NN$ channel. However, the dibaryon masses obtained
exceed the pion production threshold. Therefore, these dibaryons
preferentially decay into the $\pi NN$ channel and their decay widths are
larger than 1 MeV.

Using the chiral soliton model, Kopeliovich kop  predicted that the masses of
$D(1,1^{+})$ and $D(0,2^{+})$ SNDs could exceeded the two nucleon mass by 60
and 90 MeV, respectively. These values are lower than the pion production
threshold.

In the framework of the canonically quantized biskyrmion model, Krupnovnickas
et al. riska  obtained an indication on possibility of the existence of one
dibaryon with $J=T=0$ and two dibaryons with $J=T=1$ with masses smaller than
$2m_{N}+m_{\pi}$.

In the present paper we analyze the experimental search for SNDs, construct
and analyze the mass formula for SNDs, and suggest a possible interpretation
of exotic narrow baryons with low masses.

##  II Supernarrow dibaryons

We will consider the following SNDs: $D(T=1,J^{P}=1^{+},S=1)$ and
$D(1,1^{-},0)$.

It is worth noting, that the state $(T=1,J^{P}=1^{-})$ corresponds to the
states ${}^{31}P_{1}$ and ${}^{33}P_{1}$ in the NN channel. The former is
forbidden and the latter is allowed for a two-nucleon state. In our work we
will study the dibaryon $D(1,1^{-},0)$, a decay of which into two nucleons is
forbidden by the Pauli principle (i.e. ${}^{31}P_{1}$ state).

SNDs can be formed in processes of interaction with the deuteron only if the
nucleons in the deuteron overlap sufficiently, such that a 6-quark state with
deuteron quantum numbers can be formed. In this case, an interaction of a
photon or a meson with this state can change its quantum numbers so that a
metastable state can form. Therefore, the probability of the production of
such dibaryons is proportional to the probability $\eta$ of the 6-quark state
existing in the deuteron.

The magnitude of $\eta$ can be estimated from the deuteron form factor at
large $Q^{2}$ (see for example bur ; grach ). However, the values obtained
depend strongly on the model of the form factor of the 6-quark state over a
broad region of $Q^{2}$. Another way to estimate this parameter is to use the
discrepancy between the theoretical and experimental values of the deuteron
magnetic moment kim ; bhad ; kon2 . This method is free from the restrictions
quoted above and gives $\eta\leq 0.03$ kon2 .

Figure 1: The diagram of the SND decay into $\gamma NN$

Since the energy of nucleons, produced in the decay of the SNDs under study
with $M<2m_{N}+m_{\pi}$, is small, it is expected that the main contribution
to a two nucleon system should come from the ${}^{31}S_{0}$ (virtual singlet)
state (Fig. 1).

Table 1:  Decay widths of the dibaryons $D(1,1^{+},1)$ and $D(1,1^{-},0)$ at various dibaryon masses $M$. $M$(GeV) | 1.904 | 1.926 | 1.942 | 1.965 | 1.985 | 2.006
---|---|---|---|---|---|---
$\Gamma_{t}(1,1^{-})$ | 0.0514 | 0.327 | 0.771 | 1.909 | 3.495 | 5.073
(eV) |  |  |  |  |  |
$\Gamma_{t}(1,1^{+})$ | 0.206 | 1.307 | 3.083 | 7.635 | 13.98 | 23.49
(eV) |  |  |  |  |  |

The results of calculations of the decay widths of the dibaryons into $\gamma
NN$ on the basis of such assumptions at $\eta=0.01$ are listed in Table I.

As a result of the SND decay through ${}^{31}S_{0}$ in the intermediate state,
the probability distribution of such a decay over the emitted photon energy
$\omega$ should be characterized by a narrow peak at the photon energy close
to the maximum value $\omega_{m}=(M^{2}-4m^{2}_{N})/2M$ (Fig. 2). Note that
the interval of the photon energy from $\omega_{m}$ to $\omega_{m}-1$ MeV
contains about 75% of the contribution to the width of the decay
$D(1,1^{\pm})\to\gamma NN$. This leads to a very small relative energy of the
nucleons from the SND decay and these nucleons are emitted into a narrow angle
cone with respect to the direction of the SND motion.

Figure 2: The distribution of the decay probability of the isovector SND over
$\omega_{m}-\omega$ at $M=1904$ MeV. Figure 3: The distribution of the decay
probability of SNDs over $\theta_{1,2}$

Moreover, the distribution of the SND decay probability over the angle between
the final nucleons should be characterized by a narrow angular cone.

The dependence of SND decay probability on the angle between the final
nucleons $\theta_{12}$ is shown in Fig. 3. This figure demonstrates that the
nucleons from the decay of SNDs should be mainly emitted in a very narrow
angular cone. These dependencies should be taken into account when looking for
SNDs.

##  III Previous works

For the first time, SNDs have been searched for in the reactions $pd\to
p+pX_{1}$ and $pd\to p+dX_{2}$ konob ; izv ; yad ; prc ; conf1 ; conf2 ; epj ;
hadr . The experiment was carried out at the Proton Linear Accelerator of INR
with 305 MeV proton beam using the two-arm mass spectrometer TAMS.

Several software cuts have been applied to the mass spectra in these works. In
particular, the authors limited themselves by the consideration of intervals
of the proton energy and angles from the decay of the $pX_{1}$ states, and
very narrow angular cone between final nucleons, which were determined by the
kinematics of the SND decay into $\gamma NN$ channel. Such cuts are very
important as it provides a possibility to suppress the contribution from the
background reactions and random coincidences essentially.

In the works conf1 ; conf2 ; epj ; hadr , CD2 and 12C were used as targets.
The scattered proton was detected in the left arm of the spectrometer TAMS at
the angle $\theta_{L}=70^{\circ}$. The second charged particle (either $p$ or
$d$) was detected in the right arm by three telescopes located at
$\theta_{R}=34^{\circ}$, $36^{\circ}$, and $38^{\circ}$.

Figure 4: The missing mass $M_{pX_{1}}$ (a) and $M_{X_{1}}$ (b) spectra of the
reaction $pd\to p+pX_{1}$.

As a result, three narrow peaks in missing mass spectra have been observed
(Fig.4) at $M_{pX_{1}}=1904\pm 2$, $1926\pm 2$, and $1942\pm 2$ MeV with
widths equal to the experimental resolution ($\sim 5$ MeV) and with numbers of
standard deviations (SD) of 6.0, 7.0, and 6.3, respectively. It should be
noted that the dibaryon peaks at $M=1904$ and 1926 MeV had been observed
earlier by same authors in ref. prc ; konob ; izv ; yad  at somewhat different
kinematical conditions.

On the other hand, no noticeable signal of the dibaryons has been observed in
the missing mass $M_{dX_{2}}$ spectra of the reaction $pd\to p+dX_{2}$. The
analysis of the angular distributions of the protons from the decay of
$pX_{1}$ states and the suppression observed of the SND decay into $\gamma d$
showed that the peaks found can be explained as a manifestation of the
isovector SNDs, the decay of which into two nucleons is forbidden by the Pauli
exclusion principle.

An additional information about the nature of the observed states has been
obtained by studying the missing mass $M_{X_{1}}$ spectra of the reaction
$pd\to p+pX_{1}$. If the state found is a dibaryon decaying mainly into two
nucleons then $X_{1}$ is the neutron and the mass $M_{X_{1}}$ is equal to the
neutron mass $m_{n}$. If the value of $M_{X_{1}}$, obtained from the
experiment, differs essentially from $m_{n}$, then $X_{1}=\gamma+n$ and we
have the additional indication that the observed dibaryon is SND.

The simulation of the missing mass $M_{X_{1}}$ spectra of the reaction $pd\to
ppX_{1}$ has been performed conf1 ; conf2 ; epj ; hadr  assuming that the SND
decays as $D\to\gamma+\,^{31}S_{0}\to\gamma pn$ through two nucleon singlet
state ${}^{31}S_{0}$ fil2 ; prc ; epj . As a result, three narrow peaks at
$M_{X_{1}}=965$, 987, and 1003 MeV have been predicted. These peaks correspond
to the decay of the isovector SNDs with masses 1904, 1926, and 1942 MeV,
respectively.

In the experimental missing mass $M_{X_{1}}$ spectrum besides the peak at the
neutron mass due to the process $pd\to p+pn$, a resonance-like behavior of the
spectrum has been observed at $966\pm 2$, $986\pm 2$, and $1003\pm 2$ MeV
conf1 ; conf2 ; epj ; hadr . These values of $M_{X_{1}}$ coincide with the
ones obtained by the simulation and essentially differ from the value of the
neutron mass (939.6 MeV). Hence, for all states under study, we have
$X_{1}=\gamma+n$ in support of the statement that the dibaryons found are
SNDs.

On the other hand, the peak at $M_{X_{1}}=1003\pm 2$ MeV corresponds to the
peak found at SPES3 (Saturne) ref. tat2  and was attributed to an exotic
baryon state $N^{*}$ below the $\pi N$ threshold. In that work the authors
investigated the reaction $pp\to\pi^{+}pX$ and have found altogether three
such states with masses 1004, 1044, and 1094 MeV with SD$\gtrsim 10$. In
additional, states with masses close to 966 and 986 MeV were also extracted at
SPES3, but from a small number of data tat3 .

Therefore, if the exotic baryons with anomalously small masses really exist,
the observed peaks at 966, 986, and 1003 MeV might be a manifestation of such
states. The existence of such exotic states, if proved to be true, will
fundamentally change our understanding of the quark structure of hadrons bald
; walch ; azim .

However, in experiments on a single nucleon, no any significant structure was
observed lvov ; jiang ; kohl . Therefore, the question about a nature of the
peaks observed in epj ; tat2  remains open at present.

In ref. khr  dibaryons with exotic quantum numbers were searched for in the
process $pp\to pp\gamma\gamma$. The experiment was performed with a proton
beam from the JINR Phasotron at an energy of about 216 MeV. The energy
spectrum of the photons emitted at $90^{\circ}$ was measured. As a result, two
peaks have been observed in this spectrum. This behavior of the photon energy
spectrum was interpreted as a signature of the exotic dibaryon resonance
$d_{1}^{*}$. with a mass of about $1956\pm 2stat\pm 6syst$ MeV and possible
isospin $T=2$ or $T=1$.

On the other hand, an analysis cal  of the Uppsala proton-proton
bremsstrahlung data looking for the presence of a dibaryon in the mass range
from 1900 to 1960 MeV gave only the upper limits of 10 and 3 nb for the
dibaryon production cross section at proton beam energies of 200 and 310 MeV,
respectively.

However, it is asserted in ref. khr2  that a more detailed analysis of the
data of ref cal  gives a confirmation of the existence of $d_{1}^{*}(1956)$.

Figure 5: The missing mass $(MM(\gamma,\pi^{0})-m_{d})$ (MeV) spectra of the
reaction $\gamma d\to\pi^{0}\gamma pn$

The reactions $pd\to ppX$ and $pd\to pdX$ have been studied also in the
Research Center for Nuclear Physics at the proton energy 295 MeV over a mass
range of 1898 to 1953 MeV tamii . They did not observe any narrow structure in
the missing mass spectra of $pX$, $dX$, and $X$.

So, these results are at variance both with the SND observation in INR and
with the results of Tatischeff et al. tat2 ; tat3  on the search for exotic
baryons. However, exotic baryons were observed in Ref. tat2  with a
sufficiently high accuracy, which leads to a doubt about correctness of the
result of RCNP tamii .

It is worth noting that the reaction $pd\to NX$ was investigated in other
works, too. However, in contrast to the ref. konob ; izv ; yad ; prc ; conf1 ;
conf2 ; epj ; hadr , the authors of these works did not study either the
correlation between the parameters of the scattered proton and the second
detected particle or the emission of the photon from the dibaryon decay.
Therefore, in these works the relative contributions of the dibaryons under
consideration were small, which hampered their observation.

On the other hand, the preliminary analysis of the missing mass distributions
of the available data on the process $\gamma d\to\pi^{0}\gamma pn$, obtained
at MAMI kash , demonstrates three peaks (Fig. 5), which good enough correspond
to the values of the SND masses found in INR prc ; epj  (red lines).
Unfortunately, the statistic is very poor in this case.

Figure 6: The relatio of $\sigma(\alpha=90^{o})/\sigma(\alpha=0^{o})$ as the
function of $P$.

In order to argue more convincingly that the states found are really SNDs, an
additional experimental investigation of the dibaryon production is needed.

In ref. alek1  a search for SNDs in the processes of pions photoproduction by
the linearly polarized photon was proposed. The cross section of this process
can be written as the following:

$\displaystyle\frac{d\sigma}{d\Omega}=A+\frac{q^{2}}{2}\sin^{2}\theta_{\pi}\,B(1-P\,\cos
2\alpha)$ (2)

where $\alpha$ is the angle of the photon polarization relative to the
reaction plane.

The result of calculations of $\sigma(\alpha=90^{o})/\sigma(\alpha=0^{o})$ for
the process $\overrightarrow{\gamma}d\to\pi^{+}D$ at $M=1904$ MeV is shown on
Fig. 6 as the function of the polarization degree $P$.

So, we have a large variation between the differential cross sections of pions
propagating parallel to the initial photon polarization and pions propagating
perpendicular to the polarization. It is expected that the cross section for
vector SNDs should be substantially larger for mesons emitted parallel to the
photon polarization than for mesons emitted perpendicularly. Thus, in the
first case, the sensitivity to the contribution of $D(1,1^{-})$ significantly
increased.

Figure 7: The missing mass spectra of the reactions $pd\to p+pX$, and
$\vec{\gamma}d\to\pi^{+}nn\gamma$ when $\pi^{+}//\vec{\gamma}$ and
$\pi^{+}\perp\vec{\gamma}$.

The calculations showed that $D(1,1^{-})$ gives the main contribution to the
amplitude $B$, and its contribution to $A$ is less than 1%. The contributions
of $D(1,1^{+})$ in $A$ and $B$ are almost equal. If we consider the SND masses
up to 1960 MeV, then it is expected that when a pion is emitted parallel to
the photon polarization, 3 peaks should be observed and only 1, when the pion
is emitted perpendiculary.

Such an experiment has been performed at LEGS legs ; norum . They analyzed the
reaction $d(\overrightarrow{\gamma},\pi^{+}n\gamma^{\prime})n$ in the photon
energy range 210 – 340 MeV. The linear polarization of initial photon was
approximately 99%. The results of this experiment and their comparison with
the data obtained at INR prc ; epj  are shown in Fig. 7.

As a result they have observed three peaks in missing mass spectrum when the
$\pi^{+}$ was emitted parallel to the polarization of the incident photon
$\overrightarrow{\gamma}$.

The mass values found are very close to the values obtained in INR prc ; epj

The peak at $M=1926$ MeV in the bottom panel corresponds to the expected
value. However, this peak is too wide, possibly due to insufficient accuracy
in the determination of experimental data in the region of this resonance.

The results obtained in this experiment, support the possibility of the SND
existence. However, these data were limited by the resolution of the pion
detection. So, they did not produce a conclusive proof of the SND existence.

It should be noted that SNDs could be produced in the processes under
consideration, if a pion is only emitted from the 6-quark state of the
deuteron. Therefore the vertexes of $d\to\pi D$ can be written as

$\displaystyle\Gamma_{d\to\pi
D(1,1^{-},0)}=\frac{g_{1}}{M}\sqrt{\eta}\Phi_{\mu\nu}G^{\mu\nu},$ (3)
$\displaystyle\Gamma_{d\to\pi
D(1,1^{+},1)}=\frac{g_{2}}{M}\sqrt{\eta}\varepsilon_{\mu\nu\lambda\sigma}\Phi^{\mu\nu}G^{\lambda\sigma},$
(4)

where $\Phi_{\mu\nu}=r_{\mu}w_{\nu}-w_{\mu}r_{\nu}$,
$G_{\mu\nu}=p_{1\mu}v_{\nu}-v_{\mu}p_{1\nu}$, $w$ and $v$ are 4-vectors of the
dibaryon and deuteron polarizations, respectively; and $r$ and $p_{1}$ are the
dibaryon and deuteron 4-momenta.

The constants $g^{2}_{1}/4\pi$, $g^{2}_{2}/4\pi$, and $\eta$ are unknown.
However, the products of these coupling constants and $\eta$ can be estimated
from the results of work legs  where the SNDs, were searched for in the
process $\overrightarrow{\gamma}d\to\pi^{+}D\to\gamma^{\prime}\pi^{+}nn$.

As a result, we have

$\eta\frac{g_{1}^{2}}{4\pi}=1.4\times
10^{-4},\qquad\eta\frac{g_{2}^{2}}{4\pi}=3\times 10^{-4}.$ (5)

##  IV Mass formula for the SNDs

Using the complete Green function of the dibaryons

$\Delta(p^{2})=\frac{F(p)}{p^{2}-m^{2}-\delta_{D}(p^{2})},$

we determine the SND mass as

$M^{2}=m^{2}+Re\,\delta_{D}(M^{2}),$ (6)

where $\delta_{D}(M^{2})$ is the self energy of the SND under study and $m$ is
the mass of the dibaryon in the intermediate state.

The self energy of the lightest SND will be determined in one loop
approximation through the interaction of the pion with the 6-quark state of
the deuteron. The self energy of the next SND will be obtain through the
interaction of the pion with the lightest SND and so on.

We calculate the SND self energy with the help of the dispersion relations
with two subtractions at $M^{2}=m^{2}$. Then taking into account (6), we
obtain the mass formula for the SNDs mass

$\displaystyle M^{2}$ $\displaystyle=$ $\displaystyle
m^{2}+Re\,\delta_{D}(m^{2})+\left.(M^{2}-m^{2})\frac{d\,Re\,\delta_{D}(M^{2})}{d\,M^{2}}\right|_{M^{2}=m^{2}}+$
(7)
$\displaystyle\frac{(M^{2}-m^{2})^{2}}{\pi}P\\!\\!\\!\int\limits_{(m+\mu)^{2}}^{\infty}\frac{Im\,\delta_{D}(x)\,dx}{(x-M^{2})(x-m^{2})^{2}}.$

Since the subtraction is carried out on the mass shell of the dibaryon in the
intermediate state, the subtraction function $Re\,\delta_{D}(m^{2})$ is equal
to zero. Assuming that this dibaryon is in the ground state, we have
$\left.d\,Re\,\delta_{D}(M^{2})/d\,M^{2}\right|_{M^{2}=m^{2}}=0$.

Finally, the mass formula for SND can be represented as

$\frac{(M^{2}-m^{2})}{\pi}P\int\limits_{(m+\mu)^{2}}^{\infty}\frac{Im\,\delta_{D}(x)\,dx}{(x-M^{2})(x-m^{2})^{2}}=1$

Two subtractions in the dispersion relations provide a very good convergence
of the integrand in (IV). Therefore we restrict ourselves to consideration of
one loop approximation only.

We assume that the SND under study and the dibaryon in the intermediate state
have opposite parities. Then the vertex $D^{\prime}(1^{\mp})\to\pi+D(1^{\pm})$
can be written as

$\Gamma^{(-)}=\frac{\bar{g}_{1}}{M}G_{\mu\nu}\Phi^{\mu\nu}.\qquad$ (8)

As a result of calculations we have got the following expression for the
imaginary part of $\delta_{D}(x)$:

$Im\,\delta_{D}(x)=\left(\frac{\bar{g}^{2}_{1}}{4\pi}\right)\frac{q[(x+m^{2}-\mu^{2})^{2}+2m^{2}x]}{x^{\frac{3}{2}}},$
(9)

where $q$ is the pion momentum equal to
$q=[(x-(m+\mu)^{2})(x-(m-\mu)^{2}]^{1/2}/2x^{1/2}$.

The coupling constant $\bar{g}^{2}_{1}/4\pi$ in the vertex for transition of
the 6-quark state of the deuteron $(D(0,1^{+}))$ plus the pion to the SND
$D(1,1^{-})$ has been fixed by requiring a reproduction of the mass $M=1904$
MeV. It results in

$\frac{\bar{g}^{2}_{1}}{4\pi}=26.5888.$ (10)

Calculations within the framework of the present model yielded very close
values of the SND masses found in channels with $\pi^{0}$ and $\pi^{\pm}$
mesons . Therefore, we take them equal one to another.

In order to calculate the mass of the next SND $D(1,1^{+})$, we take in the
intermediate state the SND $D(1,1^{-})$ with $m=1904$ MeV and the pion. To
calculate the mass of the next $D(1,1^{-})$, we consider SND $D(1,1^{+})$ with
$m=1925$ MeV and pion in the intermediate state and so on.

The coupling constant $\bar{g}_{2}$ in the vertex $D(1,1^{\pm})\to
D(1,1^{\mp})+\pi$ differs from $\bar{g}_{1}$. Due to the isotopic invariance,
we have $\bar{g}^{2}_{2}/4\pi=3/4(\bar{g}^{2}_{1}/4\pi)$.

The results of the calculations of the masses and $J^{P}$ of the SNDs are
listed in table 2.

Table 2: The masses and $J^{P}$ of the SNDs. |  | model | experiment | experimental
---|---|---|---|---
$No$ | $J^{P}$ |  $M$ (MeV) |  $M$ (MeV) | works
1 | $1^{-}$ | 1904 | $1904\pm 2$ | epj
2 | $1^{+}$ | 1925 | $1926\pm 2$ | epj
3 | $1^{-}$ | 1945 | $1942\pm 2$ | epj
4 | $1^{+}$ | 1965 | $1956\pm 6$ | khr
5 | $1^{-}$ | 1985 | $1982$ | predicted epj ; tat2
6 | $1^{+}$ | 2006 |  |

As can be seen from the table, the values of the SND masses obtained are in
good agreement with available experimental data. The existence of the SND with
the mass $M=1982$ MeV was predicted in epj ; tat2  as a consequence of the
observation of the peak in the missing mass spectrum of the reaction
$pp\to\pi^{+}pX$ tat  at $M_{X}=1044$ MeV.

An analysis of the probability of SND decay shows that due to the smallness of
the angle $\theta_{12}$ and difference in the energies of the final nucleons,
resonance-like states with masses
$(p_{1}+k)^{2}\simeq(p_{2}+k)^{2}=M_{N^{*}}^{2}$ appear. The table 3 presents
the values of $M_{N^{*}}$ for various SND masses.

Table 3: The masses of the SNDs and $N^{*}$. $J^{P}$ | $1^{-}$ | $1^{+}$ | $1^{-}$ | $1^{+}$ | $1^{-}$ | $1^{+}$
---|---|---|---|---|---|---
M(D) | $1904\pm 1$ | $1925\pm 1$ | $1945\pm 1$ | $1965\pm 1$ | $1985\pm 1$ | $2006\pm 1$
$M(N^{*}_{SR})$ | $965\pm 2$ | $986\pm 2$ | $1005\pm 2$ | $1025\pm 1$ | $1044\pm 1$ | $1063\pm 1$
$M(N^{*}_{exp})$ | $966\pm 2$ | $986\pm 2$ | $1003\pm 2$ |  | $1044\pm 2$ |
| INRepj  | INRepj  | INRepj  |  | SPES3tat2  |
|  | SPES3tat3  | SPES3tat2  |  |  |

As the SNDs observed in prc ; epj  decay into $NN^{*}$ with the small relative
momentum between $N$ and $N^{*}$, the SND parity has to be determined by the
parity of the $N^{*}$. As seen from tables II and III, the SND parities found
here agree with the results obtained for the $N^{*}$ states.

Thus, the formation of $N^{*}$ is uniquely determined by the existence of
SNDs. $N^{*}$ is not a new particle. This is a kinematic effect associated
with the SND decay form. Consequently, the experimental observation of
$N^{*}$s can be an additional indication of the possibility of the existence
of SNDs.

##  V Summary

The main properties of SNDs have been considered. A number of experiments prc
; epj ; khr ; kash ; legs , where evidence was obtained for the existence of
SNDs, has been analyzed.

Negative results obtained in RCNP tamii  are at variance both with the
observation of SNDs in INR prc ; epj  and with the result of B. Tatischeff et
al. tat2  on search for exotic baryons. On the other hand, the latter was
observed in tat2  with sufficiently high accuracy, which leads to doubt about
correctness of the result of RCNP tamii .

The sum rules for the SND masses have been constructed. The values of the SND
masses obtained by means of the sum rules agree very well with the
experimental data epj ; tat2 .

The decay of SNDs leads to the formation of resonance-like states $N^{*}$. The
predicted values of the masses of $N^{*}$ are in good agreement with available
experimental data.

The experimental observation of $N^{*}$s is an additional conformation of the
possibility of the SND existence.

The author thanks V.L. Kashevarov and B. Norum for helpful discussion.

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