The exotic baryon mass spectrum and \\ the {10}--{8} and $\overline{10}$--{8} mass difference in the Skyrme model
G. Duplan\v{c}i\'{c}
The {8}, {10}, and $\overline{10}$ baryon mass spectrum as a function of the Skyrme charge $e$ and the SU(3)$_f$ symmetry breaking parameters is given in tabular form. We also estimate the decuplet--octet and the antidecuplet--octet mass difference. Comparison with existing literature is given.
hep-ph0402027.tex
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\title{The exotic baryon mass spectrum and \\
the {\bf 10}--{\bf 8} and $\overline{\bf 10}$--{\bf 8} mass difference in the Skyrme model}


%\title{The {\bf 10}--{\bf 8} and $\overline{\bf 10}$--{\bf 8} baryon mass difference 
%and the {\bf 8}, {\bf 10}, and $\overline{\bf 10}$ spectrum in the Skyrme model}

\author{G. Duplan\v{c}i\'{c}}
\affiliation{Theoretical Physics Division, Rudjer Bo\v skovi\' c Institute, 
Zagreb, Croatia}
%\author{H. Pa\v{s}agi\'{c}}
%affiliation{Faculty of Transport and Traffic Engineering, University of Zagreb, \\
%P.O. Box 195, 10000 Zagreb, Croatia} 
%\author{M. Prasza{\l}owicz}
%\affiliation{M. Smoluchowski Institute of Physics Jagellonian University,\\
% Reymonta 4, 30-059 Krak\' ow, Poland}
\author{J.Trampeti\'{c}}
\affiliation{Theoretical Physics Division, Rudjer Bo\v skovi\' c Institute, 
Zagreb, Croatia}
\affiliation{Theory Division, CERN, CH-1211 Geneva 23, Switzerland}
\affiliation{Theoretische Physik, Universit\"{a}t M\"{u}nchen, Theresienstr. 37, 80333 M\"{u}nchen, Germany}


\date{\today}

\begin{abstract}
The {\bf 8}, {\bf 10}, and $\overline{\bf 10}$ baryon mass spectrum
as a function of the Skyrme charge $e$ and the SU(3)$_f$ symmetry breaking parameters is given in tabular form. 
We also estimate the decuplet--octet and the antidecuplet--octet mass difference.
Comparison with existing literature is given. 
\end{abstract}

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\pacs{12.38.-t, 12.39.Dc, 12.39.-x, 14.20.-c}
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%\large
Recently we applied the concept of minimal SU(3) extended Skyrme model
to nonleptonic hyperon and $\Omega^-$decays \cite{dppt}
producing reasonable agreement with experiment.
This concept uses only one free parameter, the Skyrme charge $e$,
and flavor symmetry breaking (SB) term, proportional to $\lambda_8$ in the kinetic 
and the mass term.
The main aim of this brief report is the application of the same concept 
in an attempt to predict the baryonic decuplet--octet ($\Delta$) and antidecuplet--octet ($\overline{\Delta}$)
mass difference as well as to evaluate the mass spectrum for octet, decuplet, and 
the recently discovered antidecuplet baryons. 

The experimental discovery \cite{penta1} and the later confirmation \cite{penta2} 
of the exotic, presumably spin 1/2, baryon 
of positive strangeness, $\Theta^+$,
was recently supported by the NA49 Collaboration \cite{penta3} discovery of the exotic isospin 3/2 baryon 
with strangeness -2, $ \Xi^{--}_{3/2}$. In this way, the antidecuplet, and possibly the other states 
of the higher SU(3)$_f$ representation,
moved from pure theory into the real world of particle physics.

The first successful prediction of mass of one member of the $\overline{\bf 10}$ baryons, 
known as penta-quark or $\Theta^+$-baryon, in the framework of the 
Skyrme model was presented in Ref. \cite{MP}.
Later, many authors used different types of quark, chiral soliton, diquark, etc. 
models \cite{dia1,wei1,WK,K,pra3,Glo,Itz,Kar,Bor,Zhu,Ger,Hua,Bij,JW,DP,Ell}, to estimate 
the higher SU(3) representation (${\overline{\bf 10}},\;{\bf 27}, \; {\rm etc.} $) mass spectrum, 
relevant mass differences and other baryon properties. 

In this brief report, like in Ref. \cite{dppt}, we use the minimal SU(3) extension of 
the Skyrme Lagrangian introduced in \cite{wei}:
\begin{eqnarray}
{\cal L} = {\cal L}_{\sigma} + {\cal L}_{Sk} + {\cal L}_{WZ} + {\cal L}_{SB} ,
\label{2a} 
\end{eqnarray}
where  ${\cal L}_{\sigma}$, ${\cal L}_{\rm Sk}$, ${\cal L}_{\rm WZ}$, and ${\cal L}_{\rm SB}$ denote 
the $\sigma$-model, Skyrme, Wess--Zumino and symmetry breaking Lagrangians 
\cite{sky,tho,wess,witt,adk,adk1,gua,yab,desw}, respectively.

For profile function $F(r)$ we use the arctan ansatz \cite{dia,prat2}:
\begin{eqnarray}
F(r) = 2{\rm arctan} \left[ \left({\frac{r_0}{r}}\right)^2 \right].
\label{11}
\end{eqnarray}
Here $r_0$ - the soliton size - is the variational parameter and the second power of $r_0/r$ is determined 
by the long-distance behavior of the equations of motion. After rescaling $x=ref_{\pi}$, we obtain the ratio
$r/r_0=x/x_0$. The quantity $x_0$ has the meaning of a dimensionless size of a soliton 
(or rather in units of $(ef_{\pi})^{-1}$). 
The advantage of using (\ref{11}) is that all integrals involving
the profile function $F(x/x_0)$ can be evaluated analytically. 

The SU(3) extension of the Skyrme Lagrangian ${\cal L}$ uses set of parameters ${\hat x}, 
{\beta}', {\delta}'$ introduced in \cite{wei}:
\begin{eqnarray}
 {\hat x}&=&\frac{2m^2_K f^2_K}{m^2_{\pi}f^2_{\pi}} -1, \;\;\beta' =\frac{f^2_K - f^2_{\pi}}{4(1-{\hat x})}, 
\nonumber\\
\delta' &=& \frac{m^2_{\pi}f^2_{\pi}}{4} =\frac{m^2_K f^2_K}{2(1+{\hat x})}.
\label{34a}
\end{eqnarray}
The $\delta'$ term is required to split pseudoscalar meson masses, while the $\beta'$ term is required
to split pseudoscalar decay constants.

Including the previously introduced arctan ansatz for the profile function $F(r)$, 
we calculate the SU(3) extended classical soliton mass ${\cal E}_{\rm csol}$, 
the decuplet--octet mass splitting $\Delta$,
the antidecuplet--octet mass splitting $\overline\Delta$, i.e., 
the moment of inertia $\lambda_c$ for rotation in coordinate space, 
and the moment of inertia $\lambda_s$ for flavor rotations in the direction of the strange degrees of freedom,
except for the eighth direction \cite{wei,prat2}, 
and the symmetry breaking quantity $\gamma$. The quantity $\gamma$ is  
the coefficient in the SB 
piece ${\cal L}_{\rm SB} = -\frac{1}{2} \gamma (1-D_{88})$ of a total collective Lagrangian ${\cal L}$ 
and is linear in the SB parameter $(1-{\hat x})$. The above--mentioned quantities are given by
the following equations:
\begin{eqnarray}
{\cal E}_{\rm csol} 
&=& \hspace{-1mm}3{\sqrt 2}{\pi}^2\frac{f_{\pi}}{e} 
\label{27} \\
&\times& \left[x_0 + \frac{15}{16x_0} + \frac{2}{f^2_{\pi}}\left(3{\beta}'x_0 +
\frac{4}{3} \frac{\delta'}{e^2 f^2_{\pi}} x^3_0 \right)\right], \nonumber  \\
%\end{eqnarray}
%\begin{eqnarray}
{\Delta} &=& \frac{3}{2\lambda_c (x_0)},\;\;
%\end{eqnarray}
%\begin{eqnarray}
{\overline\Delta} =\frac{3}{2\lambda_s (x_0)} ,\label{28} \\
%\end{eqnarray}
%\begin{eqnarray}
\lambda_c 
&=&\frac{\sqrt 2 \pi^2}{3e^3 f_{\pi}} \left[6\left( 1 + 
2\frac{\beta'}{f^2_{\pi}} \right)x^3_0 + \frac{25}{4} x_0\right],\label{29} \\
%\end{eqnarray}
%\begin{eqnarray}
\lambda_s 
&=&\frac{\sqrt 2 \pi^2}{4e^3 f_{\pi}} \left[4\left( 1 - 
2(1+2{\hat x})\frac{\beta'}{f^2_{\pi}} \right)x^3_0 + \frac{9}{4} x_0\right],\label{30} \\
%\end{eqnarray}
%\begin{eqnarray}
\gamma  
&=& 4 \sqrt 2 {\pi}^2 \frac{1-{\hat x}}{ef_{\pi}} \left({\beta}'x_0 -
\frac{4}{3} \frac{\delta'}{e^2 f^2_{\pi}} x^3_0 \right) .
\label{33} 
\end{eqnarray}
It is important to note that nowadays everybody agrees that the SU(3) extended Skyrme model 
classical soliton mass ${\cal E}_{\rm csol}$ receives to large value.
The consequence of this is unrealistic baryonic mass spectrum.
The ${\cal E}_{\rm csol}$ is connected with octet 
mass mean ${\cal M}_{\bf 8}$. From experiment we know 
${\cal M}_{\bf 8}=\frac{1}{8}\sum^8_{B=1}M^{\bf 8}_B =1151$ MeV.
Taking all that into account it is more appropriate to express mass formulas by 
${\cal M}_{\bf 8}$ instead by ${\cal E}_{\rm csol}$.
However, we are using the result for the classical soliton mass (\ref{27})
to obtain $x_0$, by minimalizing ${\cal E}_{\rm csol}$:
\begin{eqnarray}
x^2_0 = \frac{15}{8} \left[ 1 + \frac{6\beta'}{f^2_{\pi}} + 
\sqrt {\left(1+ \frac{6\beta'}{f^2_{\pi}}\right)^2 + 
\frac{30\delta'}{e^2 f^4_{\pi}}} \; \right]^{-1}.
\label{34} 
\end{eqnarray}
The dimensionless size of the skyrmion $x_0$  
includes dynamics of SB effects which takes place within skyrmion. It is clear from 
the above equation that a
skyrmion effectively shrinks when one ``switches on'' the SB effects and it shrinks more when the 
Skyrme charge $e$ receives smaller values.

To obtain the {\bf 8}, {\bf 10} and $\overline{\bf 10}$ absolute mass spectrum, we use the following 
definition of the mass formulas:
\begin{eqnarray}
M^{\bf 8}_B &=& {\cal M}_{\bf 8} - \frac{1}{2} \;\delta^{\bf 8}_B \;\gamma(x_0) , \nonumber \\
M^{\bf 10}_B &=& {\cal M}_{\bf 8} +\frac{3}{2\lambda_c (x_0)}- \frac{1}{2} \;\delta^{\bf 10}_B \;\gamma(x_0) , \nonumber \\
M^{\overline{\bf 10}}_B &=& {\cal M}_{\bf 8} +\frac{3}{2\lambda_s (x_0)}- \frac{1}{2} \;
\delta^{\overline{\bf 10}}_B \;\gamma(x_0) ,
\label{34b}
\end{eqnarray}
where ${\cal M}_{\bf 8}$ is defined earlier and the splitting constants $\delta^{\bf R}_B$ are given in 
Eqs. (17) to (19) of Ref. \cite{pra3}. Also, from 
experiment we know ${\cal M}_{\bf 10}=\frac{1}{10}\sum^{10}_{B=1}M^{\bf 10}_B 
=1382$ MeV.

Formulas (\ref{34b}) imply equal spacing for antidecuplets. From the existing experiments
($\Theta^+=1540$ MeV and $ \Xi^{--}_{3/2}=1861$ MeV) we estimate that spacing to be 
$\overline{\delta}=(1861-1540)/3=107$ MeV.
Next we estimate masses of antidecuplets N*=1647 MeV, $\Sigma^*_{\overline{10}} =1754$ MeV and the  
${\overline{\bf 10}}$ mean mass 
${\cal M}_{\overline{\bf 10}}=\frac{1}{10}\sum^{10}_{B=1}M^{\overline{\bf 10}}_B =1754$ MeV.
Finally we obtain the antidecuplet--octet mass splittings
${\overline\Delta}_{\rm exp} ={\cal M}_{\overline{\bf 10}}-{\cal M}_{\bf 8}=603$ MeV.
However, the decuplet--octet mass splittings ${\Delta}_{\rm exp} =231$ MeV represent the true experimental value.


Now we calculate the mass splittings $\Delta$ and $\overline\Delta$ for\\
(i) the SB with the approximation 
$f_{\pi} = f_K= 93$ MeV, ($\beta^{\prime} = 0, \;\;\delta^{\prime}=4.12 \times 10^7 \;{\rm MeV}^4$); and for\\ 
(ii) the SB with $f_{\pi} = 93$ MeV, $f_K = 113$ MeV,  
($\beta^{\prime}= -28.6 \;{\rm MeV}^2$ and $\delta^{\prime}=4.12 \times 10^7 \;{\rm MeV}^4$). \\
The results are presented in Table I.
\renewcommand{\arraystretch}{1.4}
\begin{table}[hbt]
\caption{The mass splittings $\Delta$ and $\overline\Delta$ for cases (i) and (ii) as a functions of $e$.}
\begin{center}
\begin{tabular}{|c|ccc|ccc|c|}
\hline
$ $ & $ $ & $ (\rm i) $ & $ $ & $ $ & $ (\rm{ii}) $ & $  $ & $ $\\
\hline
${\rm Mass \;Spl.}\backslash e$ & $3.4$ & $4.2$ & $4.6$ & $3.4$ & $4.2$ & $4.6$ & ${\rm Exp.}$  \\
\hline \hline
$ \Delta \; (\rm MeV)$ & $ 129 $ & $ 229$ & $ 294$ & $ 128$ & $ 227 $ & $ 291$ & $ 231 $  \\
\hline
$ \overline\Delta  \; (\rm MeV)$ & $ 354 $ & $ 621$ & $ 795$ & $ 273$ & $ 474 $ & $ 604$ & $ 603 $ \\
\hline \hline
\end{tabular}
\label{t:tab1.4}
\end{center}
\end{table}

We have chosen the three values of Skyrme charge $e=3.4;\;4.2;\;4.6$. The reason for this lies in the fact that 
in our minimal approach, case (ii), $e=3.4$ gives the best fit for 
the nucleon axial coupling constant $g_A = 1.25$ \cite{dppt}, 
$e=4.2$ fits nicely $\Delta_{\rm exp}$, and $e=4.6$ gives the best fit for $\overline\Delta_{\rm exp}$. 
However, from Table I, we see that a
certain middle value of $e(=4.2)$ supports also the case (i), i.e. in good agreement with experiment. 
%Case (ii), however, shows a stronger 
%$e$ dependence for both $\Delta$ and $\overline\Delta$ differences.

The {\bf 8}, {\bf 10}, and $\overline{\bf 10}$ baryon mass spectrum (\ref{34b})
as a function of the SB effects and the Skyrme charge $e$ is given in Table II.
\renewcommand{\arraystretch}{1.2}
\begin{table}[hbt]
\caption{The {\bf 8}, {\bf 10}, and $\overline{\bf 10}$ baryon mass spectrum (MeV) 
for cases (i) and (ii) as a functions of $e$.}
\begin{center}
\begin{tabular}{|c|ccc|ccc|c|}
\hline
$ $ & $ $ & $ (\rm i) $ & $ $ & $ $ & $ (\rm{ii}) $ & $  $ & $ $\\
\hline
${\rm Mass}\backslash e$ & $3.4$ & $4.2$ & $4.6$ & $3.4$ & $4.2$ & $4.6$ & $
{\rm Exp}^{[34]}$  \\
\hline \hline
$ \rm N$ & $ 934 $ & $ 1024$ & $ 1051$ & $ 793$ & $ 934 $ & $ 977$ & $ 939 $  \\

$ \Lambda$ & $ 1079 $ & $ 1109$ & $ 1118$ & $ 1032$ & $ 1079 $ & $ 1093$ & $ 1116 $ \\

$ \Sigma$ & $ 1223 $ & $ 1193$ & $ 1184$ & $ 1270$ & $ 1223 $ & $ 1209$ & $ 1193 $  \\
 
$ \Xi$ & $ 1295 $ & $ 1236$ & $ 1218$ & $ 1390$ & $ 1295 $ & $ 1267$ & $ 1318 $  \\
 
$ \Delta$ & $ 1190 $ & $ 1327$ & $ 1403$ & $ 1130$ & $ 1287 $ & $ 1370$ & $ 1232 $  \\

$ \Sigma^*$ & $ 1280 $ & $ 1380$ & $ 1445$ & $ 1279$ & $ 1378 $ & $ 1442$ & $ 1385 $ \\

$ \Xi^*$ & $ 1371 $ & $ 1433$ & $ 1487$ & $ 1428$ & $ 1468 $ & $ 1514$ & $ 1530 $  \\

$ \Omega$ & $ 1461 $ & $ 1486$ & $ 1529$ & $ 1578$ & $ 1558 $ & $ 1587$ & $ 1672 $  \\

$ \Theta^+$ & $ 1325 $ & $ 1666$ & $ 1862$ & $ 1125$ & $ 1444 $ & $ 1611$ &
$1540^{[2, 3]} $  \\

$ \rm N^*$ & $ 1415 $ & $ 1719$ & $ 1904$ & $ 1274$ & $ 1535 $ & $ 1683$ & $ - $  \\
 
$ \Sigma^*_{\overline{10}}$ & $ 1505 $ & $ 1772$ & $ 1946$ & $ 1424$ & $ 1625 $ & $ 1755$ & $ - $ \\

$ \Xi^{--}_{3/2}$ & $ 1595 $ & $ 1825$ & $ 1988$ & $ 1573$ & $ 1715 $ & $ 1828$
& $ 1861^{[4]} $  \\
\hline \hline 
\end{tabular}
\label{t:tab1.4}
\end{center}
\end{table}
Since we are using the most simple version of the total Lagrangian (\ref{2a}),
i.e., we omit vector meson effects, the so-called static kaon fluctuations \cite{wei} and other fine--tuning effects 
in the expressions (\ref{27})--(\ref{34b}), our results given in Tables I and II,
do agree roughly with the other Skyrme model based estimates \cite{MP,pra3,dia1,wei1,WK,K}. 
In particular, our approach is similar to the one of Refs. \cite{WK,K}. The main difference is that our
Lagrangian is simpler, i.e. contains only SB proportional to $\lambda_8$, and that we are using the 
arctan ansatz approximation for the profile function $F(r)$. Comparing the pure Skyrme model
prediction of Ref. \cite{K} (fits A and B in Table 2) with our results for $e=4.2$, presented in Table II,
we have found up to the 8 \% differences. 
One of the reasons is due to the fact that the fits A and B in Table 2 of Ref. \cite{K} were obtained for 
different $e$'s, i.e. $e=3.96$ and $e=4.12$. Also, from our Table II one can see that for $e=4.2$, case (ii), 
mass spectrum differs from the experiment $\stackrel{<}{\sim} 8$\% for 
$\Omega^-$, $\Theta^+$ and $\Xi_{3/2}^{--}$. 
All other estimated masses are $\stackrel{<}{\sim}\; 5$\% different from experiment.
From Table II we conclude that in our minimal approach the best fit for 
{\bf 8}, {\bf 10}, and $\overline{\bf 10}$ baryon mass spectrum,
as a function of $e$ and for $f_{\pi}\not= f_K$, would lie between $e\simeq 4.2$ and $e\simeq 4.6$.

Symmetry breaking effects are generally very important and do improve theoretical estimates of the quantities 
like $\Delta$, $\overline\Delta$, the baryon mass spectrum etc. 
%Their internal dynamics is for our minimal approach, with arctan ansatz 
%for the profile function, described by the Eq. (\ref{34}).
Our Tables I and II show implicitely that the inclusion of additional contributions, 
like vector meson contributions, 
the so-called static kaon fluctuations \cite{wei} and other fine--tuning effects into the SB Lagrangian \cite{WK}
does not change the results dramatically. On the contrary, the main effect is coming from the famous
$D_{88}$ term. The difference between $f_{\pi}$ and $f_K$ and the $e$ dependence are important.
All other contributions represent the fine tuning effects of the order of a few percent \cite{foot}. 
This is important for understanding the overall picture of the baryonic mass spectrum as well as for 
further study of other nonperturbative, higher-dimensional operator matrix elements in the Skyrme model \cite{dppt,tra}. 

\vspace{0.3cm}
We would like to thank T. Anti\v ci\' c and K. Kadija for  helpful discussions,
and M. Prasza{\l}owicz for careful reading of the manuscript.
This work was supported by the Ministry of Science and Technology of the Republic of Croatia under Contract 0098002.

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\bibitem{Hua}
%\bibitem{Huang:2003we}
F.~Huang, Z.~Y.~Zhang, Y.~W.~Yu and B.~S.~Zou,
%``A study of pentaquark Theta state in the chiral SU(3) quark model,''
arXiv:hep-ph/0310040.
%%CITATION = HEP-PH 0310040;%%

%%CITATION = HEP-PH 0307370;%%%\cite{Bijker:2003pm}
\bibitem{Bij}
%\bibitem{Bijker:2003pm}
R.~Bijker, M.~M.~Giannini and E.~Santopinto,
%``Spectroscopy of pentaquark states,''
arXiv:hep-ph/0310281.
%%CITATION = HEP-PH 0310281

%\cite{Jaffe:2003sg}
\bibitem{JW}
%\bibitem{Jaffe:2003sg}
R.~L.~Jaffe and F.~Wilczek,
%``Diquarks and exotic spectroscopy,''
Phys.\ Rev.\ Lett.\  {\bf 91}, 232003 (2003)
[arXiv:hep-ph/0307341];
%%CITATION = HEP-PH 0307341;%%
%\cite{Jaffe:2003ci}
%\bibitem{Jaffe:2003ci}
R.~Jaffe and F.~Wilczek,
%``Systematics of exotic cascade decays,''
arXiv:hep-ph/0312369;
%%CITATION = HEP-PH 0312369;%%
%\cite{Jaffe:2004zg}
%\bibitem{Jaffe:2004zg}
R.~Jaffe and F.~Wilczek,
%``A perspective on pentaquarks,''
arXiv:hep-ph/0401034.
%%CITATION = HEP-PH 0401034;%%

%\cite{Diakonov:2003jj}
\bibitem{DP}
%\bibitem{Diakonov:2003jj}
D.~Diakonov and V.~Petrov,
%``Where are the missing members of the baryon antidecuplet?,''
arXiv:hep-ph/0310212.
%%CITATION = HEP-PH 0310212;%%

%\cite{Ellis:2004uz}
\bibitem{Ell}
%\bibitem{Ellis:2004uz}
J.~Ellis, M.~Karliner and M.~Praszalowicz,
%``Chiral-Soliton Predictions for Exotic Baryons,''
arXiv:hep-ph/0401127.
%%CITATION = HEP-PH 0401127;%%


\bibitem{wei}  H. Weigel, Int. J. Mod. Phys. {\bf A11}, 2419 (1996) and references therein;
               J. Schechter and H. Weigel, hep-ph/9907554 (1999). 
            
\bibitem{sky}  T.H.R. Skyrme, Proc. Roy. Soc. {\bf A260}, 127 (1961); Nucl. Phys. {\bf 31}, 556 (1962);
               J. Math. Phys. {\bf 12}, 1735 (1971).
              % For reviews on the Skyrme model, see
               %G. Halzwarth and B. Schwesinger, Rep. Prog. Phys. {\bf 49}, 82 (1986);
               %I. Zahed and G.E. Brown, Phys. Rep. {\bf 142}, 481 (1986).
	       
\bibitem{tho}  G. 't Hooft, Nucl. Phys. {\bf B72}, 461 (1974);
               G. Rossi and G. Veneziano, Nucl. Phys. {\bf B123}, 507 (1977).

%\bibitem{witt}  E. Witten, Nucl. Phys. {\bf B160}, 57 (1979). 
               
%\bibitem{bal}  A.P. Balachandran, V.P. Nair, S.G. Rajeev and A. Stern, Phys. Rev. Lett. {\bf 49}, 1124 (1982);
 %              Phys. Rev. {\bf D27}, 144 (1983);
            
\bibitem{wess}  J. Wess and B. Zumino,  Phys. Lett. {\bf 37B}, 95 (1971).  

\bibitem{witt}  E. Witten, Nucl. Phys. {\bf B160}, 57 (1979); {\bf B223}, 422 (1983) and 433 (1983).

%\bibitem{jac}  A.D. Jackson and M. Rho, Phys. Rev. Lett. {\bf 51}, 751 (1983);
 %              M. Rho, A.S. Goldhaber and G.E. Brown, Phys. Rev. Lett. {\bf 51}, 743 (1983).
	       
\bibitem{adk}  G. Adkins, C.R. Nappi and E. Witten, Nucl. Phys. {\bf B228}, 552 (1983);
               G. Adkins and C.R. Nappi, Nucl. Phys. {\bf B223}, 109 (1984); Phys. Lett. {\bf 137B}, 251 (1984).
               
\bibitem{adk1}  G. Adkins and C.R. Nappi, Nucl. Phys. {\bf B249}, 507 (1985).
            
\bibitem{gua}  E. Guadagnini, Nucl. Phys. {\bf B236}, 35 (1984); 
               P.O. Mazur, M.A. Nowak and M. Prasza{\l}owicz, Phys. Lett. {\bf 147B}, 137 (1984);
               A.V. Manohar, Nucl. Phys. {\bf B248}, 19 (1984);
               M. Sriram, H.S. Mani and R. Ramachandran, Phys. Rev. {\bf D30}, 1141 (1984);
	       M. Chemtob, Nucl. Phys. {\bf B256}, 600 (1985);
               M. Prasza{\l}owicz, Phys. Lett. {\bf 158B}, 264 (1985). 
            
\bibitem{yab}  H. Yabu and K. Ando, Nucl. Phys. {\bf B301}, 601 (1988).  

\bibitem{desw}  J.J. de Swart, Rev. Mod. Phys.  {\bf 35}, 916 (1963);
               P. McNamee, S.J. and F. Chilton, Rev. Mod. Phys.  {\bf 36}, 1005 (1964).                         

\bibitem{dia}  D.I. Diakonov, V.Yu. Petrov and M. Prasza{\l}owicz, Nucl. Phys. {\bf B323}, 53 (1989). 

\bibitem{prat2}  M. Prasza{\l}owicz, Act. Phys. Pol. {\bf B22}, 523 (1991).    

\bibitem{rpp} Review of Particle Properties, Eur. Phys.J. {\bf C15}, 1 (2000).  
                             
%\bibitem{toy}  N. Toyota and K. Fujii, Prog. Theor. Phys. {\bf 75}, 340 (1986);
 %           N. Toyota, Prog. Theor. Phys. {\bf 77}, 688 (1987);
  %          Y. Kondo, S. Saito and T. Otofuji, Phys. Lett. {\bf 161B}, 1 (1990).
            
%\bibitem{der}  G.H. Derrick, J. Math. Phys. (NY) {\bf 5}, 1252 (1964).                     

%\bibitem{pati}  J.C. Pati and C.W. Woo, Phys. Rev. {\bf D3}, 2920 (1971). 

\bibitem{foot}  See, for example, footnote [19] in Ref. \cite{dppt}.

\bibitem{tra}   J. Trampetic, Phys. Lett. {\bf 144B}, 250 (1984).
                M. Prasza{\l}owicz and J. Trampetic, Phys. Lett. {\bf 161B}, 169 (1985) 
                and Fizika {\bf 18}, 391 (1986).
		  		           
%\bibitem{kad}  T. Anti\v ci\' c and K. Kadija, private communication. 
           

\end{thebibliography}


\end{document} 

hep-ph0402027.extracted_bib
\begin{thebibliography}{99}

\bibitem{dppt} 
%\cite{Duplancic:2001sm}
%\bibitem{Duplancic:2001sm}
G.~Duplancic, H.~Pasagic, M.~Praszalowicz and J.~Trampetic,
%``Skyrme model and nonleptonic hyperon decays,''
Phys.\ Rev.\ D {\bf 64}, 097502 (2001)
[arXiv:hep-ph/0104281];
%%CITATION = HEP-PH 0104281;%%
%\cite{Duplancic:2001zr}
%\bibitem{Duplancic:2001zr}
G.~Duplancic, H.~Pasagic, M.~Praszalowicz and J.~Trampetic,
%``Nonleptonic Omega- decays and the Skyrme model,''
Phys.\ Rev.\ D {\bf 65}, 054001 (2002)
[arXiv:hep-ph/0109216].
%%CITATION = HEP-PH 0109216;%%

\bibitem{penta1}
%\cite{Nakano:2003qx}
%\bibitem{Nakano:2003qx}
T.~Nakano {\it et al.}  [LEPS Collaboration],
 %``Evidence for a narrow $S=+1$ baryon resonance in photoproduction from the
%neutron,''
Phys.\ Rev.\ Lett.\  {\bf 91}, 012002 (2003)
[arXiv:hep-ex/0301020].
%%CITATION = HEP-EX 0301020;%%
\bibitem{penta2}  
%\cite{Barmin:2003vv}
%\bibitem{Barmin:2003vv}
V.~V.~Barmin {\it et al.}  [DIANA Collaboration],
 %``Observation of a baryon resonance with positive strangeness in K+
%collisions with Xe nuclei,''
Phys.\ Atom.\ Nucl.\  {\bf 66}, 1715 (2003)
[Yad.\ Fiz.\  {\bf 66}, 1763 (2003)]
[arXiv:hep-ex/0304040];
%%CITATION = HEP-EX 0304040;%%%\cite{Stepanyan:2003qr}
%\bibitem{Stepanyan:2003qr}
S.~Stepanyan {\it et al.}  [CLAS Collaboration],
 %``Observation of an exotic S = +1 baryon in exclusive photoproduction from the
%deuteron,''
Phys.\ Rev.\ Lett.\  {\bf 91}, 252001 (2003)
[arXiv:hep-ex/0307018];
%%CITATION = HEP-EX 0307018;%%  
%\cite{Barth:2003es}
%\bibitem{Barth:2003es}
J.~Barth {\it et al.}  [SAPHIR Collaboration],
 %``Observation of the positive-strangeness pentaquark Theta+ in photoproduction
%with the SAPHIR detector at ELSA,''
arXiv:hep-ex/0307083.
%%CITATION = HEP-EX 0307083;%%
\bibitem{penta3} 
	%\cite{Alt:2003vb}
%\bibitem{Alt:2003vb}
C.~Alt {\it et al.}  [NA49 Collaboration],
 %``Observation of an exotic S = -2, Q = -2 baryon resonance in proton proton
%collisions at the CERN SPS,''
arXiv:hep-ex/0310014.
%%CITATION = HEP-EX 0310014;%%

\bibitem{MP}  M. Prasza{\l}owicz, talk at {\it Skyrmions and Anomalies}, 
              M. Je${\dot{\rm z}}$abek and M. Prasza{\l}owicz editors, World Scientific 1987 page 112.

\bibitem{dia1}  D.I. Diakonov, V.Yu. Petrov and M. Polyakov, Z. Phys. {\bf A359}, 305 (1997).

\bibitem{wei1} 
%\cite{Weigel:1998vt}
%\bibitem{Weigel:1998vt}
H.~Weigel,
%``Radial excitations of low-lying baryons and the Z+ penta-quark,''
Eur.\ Phys.\ J.\ A {\bf 2}, 391 (1998)
[arXiv:hep-ph/9804260].
%%CITATION = HEP-PH 9804260;%%

\bibitem{WK} 
%\cite{Walliser:2003dy}
%\bibitem{Walliser:2003dy}
H.~Walliser and V.~B.~Kopeliovich,
%``Exotic baryon states in topological soliton models,''
J.\ Exp.\ Theor.\ Phys.\  {\bf 97}, 433 (2003)
[Zh.\ Eksp.\ Teor.\ Fiz.\  {\bf 124}, 483 (2003)]
[arXiv:hep-ph/0304058].

\bibitem{K}
%%CITATION = HEP-PH 0304058;%%
%\cite{Kopeliovich:2003he}
%\bibitem{Kopeliovich:2003he}
V.~Kopeliovich,
%``Exotic baryons and multibaryons in chiral soliton models,''
arXiv:hep-ph/0310071.
%%CITATION = HEP-PH 0310071;%%

\bibitem{pra3} %\cite{Praszalowicz:2003ik}
%\bibitem{Praszalowicz:2003ik}
M.~Praszalowicz,
%``Pentaquark in the Skyrme model,''
Phys.\ Lett.\ B {\bf 575}, 234 (2003)
[arXiv:hep-ph/0308114].
%%CITATION = HEP-PH 0308114;%%
%\cite{Jaffe:2003sg}

%\cite{Glozman:2003sy}
\bibitem{Glo}
%\bibitem{Glozman:2003sy}
L.~Y.~Glozman,
%``Theta+ in a chiral constituent quark model and its interpolating fields,''
Phys.\ Lett.\ B {\bf 575}, 18 (2003)
[arXiv:hep-ph/0308232].
%%CITATION = HEP-PH 0308232;%%

%\cite{Itzhaki:2003nr}
\bibitem{Itz}
%\bibitem{Itzhaki:2003nr}
N.~Itzhaki, I.~R.~Klebanov, P.~Ouyang and L.~Rastelli,
%``Is Theta(1540)+ a kaon Skyrmion resonance?,''
arXiv:hep-ph/0309305.
%%CITATION = HEP-PH 0309305;%%

%\cite{Karliner:2003sy}
\bibitem{Kar}
%\bibitem{Karliner:2003sy}
M.~Karliner and H.~J.~Lipkin,
 %``The constituent quark model revisited: Quark masses, new predictions for
%hadron masses and K N pentaquark,''
arXiv:hep-ph/0307243.
%%CITATION = HEP-PH 0307243;%%

%\cite{Borisyuk:2003fk}
\bibitem{Bor}
%\bibitem{Borisyuk:2003fk}
D.~Borisyuk, M.~Faber and A.~Kobushkin,
%``New family of exotic Theta baryons,''
arXiv:hep-ph/0307370.

%\cite{Zhu:2003ba}
\bibitem{Zhu}
%\bibitem{Zhu:2003ba}
S.~L.~Zhu,
%``Understanding pentaquark states in QCD,''
Phys.\ Rev.\ Lett.\  {\bf 91}, 232002 (2003)
[arXiv:hep-ph/0307345].
%%CITATION = HEP-PH 0307345;%%

%\cite{Gerasyuta:2003qg}
\bibitem{Ger}
%\bibitem{Gerasyuta:2003qg}
S.~M.~Gerasyuta and V.~I.~Kochkin,
%``Pentaquarks in a relativistic quark model and nature of Theta-states,''
arXiv:hep-ph/0310227.
%%CITATION = HEP-PH 0310227;%%
%\cite{Huang:2003we}
\bibitem{Hua}
%\bibitem{Huang:2003we}
F.~Huang, Z.~Y.~Zhang, Y.~W.~Yu and B.~S.~Zou,
%``A study of pentaquark Theta state in the chiral SU(3) quark model,''
arXiv:hep-ph/0310040.
%%CITATION = HEP-PH 0310040;%%

%%CITATION = HEP-PH 0307370;%%%\cite{Bijker:2003pm}
\bibitem{Bij}
%\bibitem{Bijker:2003pm}
R.~Bijker, M.~M.~Giannini and E.~Santopinto,
%``Spectroscopy of pentaquark states,''
arXiv:hep-ph/0310281.
%%CITATION = HEP-PH 0310281

%\cite{Jaffe:2003sg}
\bibitem{JW}
%\bibitem{Jaffe:2003sg}
R.~L.~Jaffe and F.~Wilczek,
%``Diquarks and exotic spectroscopy,''
Phys.\ Rev.\ Lett.\  {\bf 91}, 232003 (2003)
[arXiv:hep-ph/0307341];
%%CITATION = HEP-PH 0307341;%%
%\cite{Jaffe:2003ci}
%\bibitem{Jaffe:2003ci}
R.~Jaffe and F.~Wilczek,
%``Systematics of exotic cascade decays,''
arXiv:hep-ph/0312369;
%%CITATION = HEP-PH 0312369;%%
%\cite{Jaffe:2004zg}
%\bibitem{Jaffe:2004zg}
R.~Jaffe and F.~Wilczek,
%``A perspective on pentaquarks,''
arXiv:hep-ph/0401034.
%%CITATION = HEP-PH 0401034;%%

%\cite{Diakonov:2003jj}
\bibitem{DP}
%\bibitem{Diakonov:2003jj}
D.~Diakonov and V.~Petrov,
%``Where are the missing members of the baryon antidecuplet?,''
arXiv:hep-ph/0310212.
%%CITATION = HEP-PH 0310212;%%

%\cite{Ellis:2004uz}
\bibitem{Ell}
%\bibitem{Ellis:2004uz}
J.~Ellis, M.~Karliner and M.~Praszalowicz,
%``Chiral-Soliton Predictions for Exotic Baryons,''
arXiv:hep-ph/0401127.
%%CITATION = HEP-PH 0401127;%%


\bibitem{wei}  H. Weigel, Int. J. Mod. Phys. {\bf A11}, 2419 (1996) and references therein;
               J. Schechter and H. Weigel, hep-ph/9907554 (1999). 
            
\bibitem{sky}  T.H.R. Skyrme, Proc. Roy. Soc. {\bf A260}, 127 (1961); Nucl. Phys. {\bf 31}, 556 (1962);
               J. Math. Phys. {\bf 12}, 1735 (1971).
              % For reviews on the Skyrme model, see
               %G. Halzwarth and B. Schwesinger, Rep. Prog. Phys. {\bf 49}, 82 (1986);
               %I. Zahed and G.E. Brown, Phys. Rep. {\bf 142}, 481 (1986).
	       
\bibitem{tho}  G. 't Hooft, Nucl. Phys. {\bf B72}, 461 (1974);
               G. Rossi and G. Veneziano, Nucl. Phys. {\bf B123}, 507 (1977).

%\bibitem{witt}  E. Witten, Nucl. Phys. {\bf B160}, 57 (1979). 
               
%\bibitem{bal}  A.P. Balachandran, V.P. Nair, S.G. Rajeev and A. Stern, Phys. Rev. Lett. {\bf 49}, 1124 (1982);
 %              Phys. Rev. {\bf D27}, 144 (1983);
            
\bibitem{wess}  J. Wess and B. Zumino,  Phys. Lett. {\bf 37B}, 95 (1971).  

\bibitem{witt}  E. Witten, Nucl. Phys. {\bf B160}, 57 (1979); {\bf B223}, 422 (1983) and 433 (1983).

%\bibitem{jac}  A.D. Jackson and M. Rho, Phys. Rev. Lett. {\bf 51}, 751 (1983);
 %              M. Rho, A.S. Goldhaber and G.E. Brown, Phys. Rev. Lett. {\bf 51}, 743 (1983).
	       
\bibitem{adk}  G. Adkins, C.R. Nappi and E. Witten, Nucl. Phys. {\bf B228}, 552 (1983);
               G. Adkins and C.R. Nappi, Nucl. Phys. {\bf B223}, 109 (1984); Phys. Lett. {\bf 137B}, 251 (1984).
               
\bibitem{adk1}  G. Adkins and C.R. Nappi, Nucl. Phys. {\bf B249}, 507 (1985).
            
\bibitem{gua}  E. Guadagnini, Nucl. Phys. {\bf B236}, 35 (1984); 
               P.O. Mazur, M.A. Nowak and M. Prasza{\l}owicz, Phys. Lett. {\bf 147B}, 137 (1984);
               A.V. Manohar, Nucl. Phys. {\bf B248}, 19 (1984);
               M. Sriram, H.S. Mani and R. Ramachandran, Phys. Rev. {\bf D30}, 1141 (1984);
	       M. Chemtob, Nucl. Phys. {\bf B256}, 600 (1985);
               M. Prasza{\l}owicz, Phys. Lett. {\bf 158B}, 264 (1985). 
            
\bibitem{yab}  H. Yabu and K. Ando, Nucl. Phys. {\bf B301}, 601 (1988).  

\bibitem{desw}  J.J. de Swart, Rev. Mod. Phys.  {\bf 35}, 916 (1963);
               P. McNamee, S.J. and F. Chilton, Rev. Mod. Phys.  {\bf 36}, 1005 (1964).                         

\bibitem{dia}  D.I. Diakonov, V.Yu. Petrov and M. Prasza{\l}owicz, Nucl. Phys. {\bf B323}, 53 (1989). 

\bibitem{prat2}  M. Prasza{\l}owicz, Act. Phys. Pol. {\bf B22}, 523 (1991).    

\bibitem{rpp} Review of Particle Properties, Eur. Phys.J. {\bf C15}, 1 (2000).  
                             
%\bibitem{toy}  N. Toyota and K. Fujii, Prog. Theor. Phys. {\bf 75}, 340 (1986);
 %           N. Toyota, Prog. Theor. Phys. {\bf 77}, 688 (1987);
  %          Y. Kondo, S. Saito and T. Otofuji, Phys. Lett. {\bf 161B}, 1 (1990).
            
%\bibitem{der}  G.H. Derrick, J. Math. Phys. (NY) {\bf 5}, 1252 (1964).                     

%\bibitem{pati}  J.C. Pati and C.W. Woo, Phys. Rev. {\bf D3}, 2920 (1971). 

\bibitem{foot}  See, for example, footnote [19] in Ref. \cite{dppt}.

\bibitem{tra}   J. Trampetic, Phys. Lett. {\bf 144B}, 250 (1984).
                M. Prasza{\l}owicz and J. Trampetic, Phys. Lett. {\bf 161B}, 169 (1985) 
                and Fizika {\bf 18}, 391 (1986).
		  		           
%\bibitem{kad}  T. Anti\v ci\' c and K. Kadija, private communication. 
           

\end{thebibliography}