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The experimental observation indicates that the branching ratio of $\psi'\to\rho\pi$ is very small while the $\rho-\pi$ channel is a main one in $J/\psi$decays. To understand the puzzle, various interpretations have been proposed.Meanwhile according to the hadronic helicity selection rule the decay mode$J/\psi\to\rho\pi$ should be suppressed, but definitely, numerical computationis needed to determine how it is suppressed. We calculate the branching ratioscorresponding to subprocesses $J/\psi\to ggg\to\rho\pi$ and $\to ggg\to\pi\pi$in the framework of QCD. The results show that the branching ratios areproportional to $({m_u+m_d\over M_{J/\psi}})^2$ for $\rho\pi$ mode and$({m_u-m_d\over M_{J/\psi}})^2$ for $\pi\pi$ mode which is an isospin-violationchannel. If only the OZI process is considered, the theoretical prediction onthe ratio of $J/\psi\to \rho\pi$ is smaller than data, but not too drasticallysmall. Meanwhile, a possible interpretation for the $\rho\pi$ puzzle isproposed that the suppression is due to interference between OZI andelectromagnetic (EM) contributions. Thus based on this observation, we suggestthat if the amplitudes of the strong OZI process via an s-channel three-gluonintermediate state and electromagnetic one via an s-channel virtual photonintermediate state have the same order of magnitude, and constructivelyinterfere for $J/\psi\to\rho\pi$, but destructively interfere for$\psi'\to\rho\pi$, thus simultaneously the $\rho\pi$ puzzle disappears and thesizable width of $J/\psi\to\rho\i$ is understandable. However, so far, wecannot derive the phase difference from an underlying principle of QCD yet.Alternative interpretations are also discussed in the text.

What do we learn from the $\rho-\pi$ puzzle