What do we learn from the ρ-π puzzle

The experimental observation indicates that the branching ratio of psi' --> 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, this decay mode should be suppressed. Numerical calculations are needed to determine how it is suppressed. We calculate the branching ratios of J/psi --> rho pi and pi pi in the framework of QCD. The results show that the branching ratios are proportional to (m(u) + m(d)/M-J/psi)(2) for the rho pi mode (m(u) - m(d)/M-J/psi)(2) and for the pi pi mode which is isospin violated. The theoretical prediction of the ratio of J/psi --> rho pi is smaller than data, but not too small to invoke a completely new mechanism. Thus the puzzle is still standing even though we learn much knowledge towards the puzzle and this will help to finally interpret the puzzle and then gain a deeper insight to the heavy quarkonia.