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\title{$J/\Psi$ Decays, chiral Dynamics and OZI Violation}


\author{J.A. Oller, U.-G. Mei{\ss}ner }

\address{Forschungszentrum J\"ulich, Institut f\"ur Kernphysik (Theorie), D-52425 
J\"ulich, Germany \\E-mail: j.a.oller@fz-juelich.de,  Ulf-G.Meissner@fz-juelich.de}



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\maketitle

\abstracts{The $J/\Psi \rightarrow \phi (\omega) \pi^+\pi^-,\,K^+K^-$ up to energies 
$\sqrt{s}\lesssim 1.2$ GeV are well reproduced. These decays turn out to be very 
sensitive to OZI violating physics lending further credit to the statement that the OZI 
rule is subjected to large corrections in the $0^{++}$ sector.}

%\section{Introduction}

The $0^{++}$ meson sector is a unique one mainly because in it really strong 
interactions between hadrons take place. This is contrary to what can be 
expected from large $N_c$ QCD (the only known general explanation of the OZI rule) 
which predicts that QCD in this limit is a weak coupling theory when formulated in 
terms of hadronic degree of 
freedoms. These large corrections to large $N_c$ (OZI rule) give rise to very large 
rescattering effects between hadrons that dynamically generate meson-meson 
resonances.\cite{osaka} 
%Nevertheless, during the last years a new approach which stresses the role of unitarity 
%but also allows one to include explicit resonance fields and to match with 
%next--to--leading Chiral Perturbation Theory (CHPT), has been developed. This scheme has 
%prooved 
%to be very fruitful and sounded when dealing with the scalar sector, having clarified 
%its dynamics and associated spectrum. 
%See ref.\cite{osaka} 
%for a recent summary of its implications and references therein. 



%\section{Modelling the $J/\Psi \rightarrow$Vector Meson--Meson Decays}

Experimentally, the strong scattering data in the $0^{++}$ is not precise enough to 
disentangle the underlying dynamics and has to be supplied with data from 
meson--meson production mechanisms. In the latter case the strong interactions manifest 
themselves through Final 
State Interactions (FSI). This is why we discuss here, following ref.\cite{ome}, the 
S-wave contribution to the $J/\Psi$ decays to a vector and two pseudoscalars. By 
taking into account the experimental fact that the $\phi$ is a spectator which does not 
interact appreciably with the pions, one derives\cite{ome} the following Lagrangian 
for the considered $J/\Psi$ decays: ${\mathcal{L}}=g \Psi_\mu \phi^\mu S$ with 
$S=\bar{s}s+
\bar{n}n$ and $\bar{n}n=(\bar{u}u+\bar{d}d)/\sqrt{2}$.\footnote{In ref.\cite{ome} is 
also shown that in the energy interval considered here and because of the large 
$J/\Psi$ mass, more complicated derivative structures can be reduced to the present one.
 } This can be easily generalized to SU(3) without including any new free 
parameter.\cite{ome} 



\begin{figure}[t]
%\figurebox{20pc}{15pc}{} % to have a box alone
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\epsfbox{oller.jfig00.eps} % postscript image file name
\caption{a) and b): $\pi^+\pi^-$ event distributions for the $J/\Psi \rightarrow \phi 
(\omega)\pi^+ \pi^-$, respectively.
\label{fig:event}}
\end{figure}



Thus, the problem is reduced\cite{ome} to calculate the strange 
$\langle 0|\bar{s}s|MM'\rangle$ and non--strange  $\langle 0|\bar{n}n|MM'\rangle $ 
scalar form factors. Notice that 
$\lambda_\phi$ is a OZI suppressed constant since in 
this limit case the $\phi=\bar{s}s$ requiring that $\lambda_\phi=0$. The calculation of 
the scalar form factors is 
done in ref.\cite{ome} using a non--perturbative chiral approach 
to derive the strong scattering amplitudes.\cite{npa} In this way 
unitarity is fulfilled and furthermore the $\sigma$ and $f_0(980)$ mesons are 
generated dynamically and appear as meson--meson resonances. A general expression 
giving the scalar form factors in terms of the 
next--to--leading CHPT ones and the previous T-matrix is also derived in ref.
\cite{ome} Incidentally the 
${\mathcal{O}}(p^4)$ $K\bar{K}$ CHPT scalar form factors are for the first time 
calculated there. Because of the matching to CHPT  our expressions 
for the decay amplitudes depend on the low energy counterterms $L_5$, $L_8$, $L_4$ 
and $L_6$. The values of $L_5$ and $L_8$ are taken from their recent determination 
in ref.\cite{talavera}. However, $L_4$ and $L_6$ are not well known and we 
fit them, together with $\lambda_\phi$, to several event 
distributions of $J/\Psi \rightarrow \phi \pi \pi$. The $J/\Psi \rightarrow \omega 
\pi \pi$ decay can be considered as a prediction of the model, see fig.1.

The value of $\lambda_\phi$ results definitively different from zero as well as the one 
of $L_4$, being the latter rather large. These facts clearly indicate large OZI 
violations. However, $L_6$ is in agreement with OZI 
suppression. Let us remark\cite{ome} that the value of $L_4$ and $L_6$ is in agreement 
with ${\mathcal{O}}(p^6)$ $SU(2)$ CHPT determinations.\cite{talavera} 






%\section*{Acknowledgments}
% This work has been 
%supported in part by funds from DGICYT under contract PB96-0753 and from the EU TMR 
%network Eurodaphne, contract no. ERBFMRX-CT98-0169.  


\vspace{-0.45cm}

\begin{thebibliography}{99}
\bibitem{osaka}J.A.Oller, hep-ph/0007349.

\bibitem{ome}U.-G.Mei{\ss}ner and J.A.Oller, hep-ph/0005253. To appear in Nucl.Phys.A.

\bibitem{npa}J.A.Oller and E.Oset, Nucl. Phys. A620 (1997) 438, (E)-ibid.A652 (1999) 
407.

\bibitem{talavera}G.Amoros, J.Bijnens and P.Talavera, Phys. Lett. B480 (2000) 71; 
G.Amoros, J.Bijnens and P.Talavera, JHEP 9805 (1998) 014.  


\end{thebibliography}

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