我们从$ρ-π$谜题中学到了什么
What do we learn from the $ρ-π$ puzzle
摘要：
实验观察表明，$ψ'\to ρπ$的分支比很小，而$ρ-π$通道是$J/ψ$衰变的主要通道。为了理解这个谜题，人们提出了各种各样的解释。同时，根据强子螺旋度选择定则，衰变模$J/ψ\toρπ$应该被抑制，但具体如何抑制还需要通过数值计算来确定。我们在QCD框架下计算了子过程$J/ψ\to ggg\toρπ$和$\to ggg\toππ$的分支比。结果表明，对于$ρπ$模，分支比与$({m_u+m_d\over M_{J/ψ}})^2$成正比;对于$ππ$模，分支比与$({m_u-m_d\over M_{J/ψ}})^2$成正比，$ππ$模是一个同位旋破坏通道。如果只考虑OZI过程，理论预测的$J/ψ\to ρπ$的比例比数据小，但不会太小。同时，对$ρπ$难题提出了一种可能的解释，即抑制是由于OZI和电磁（EM）贡献之间的干扰。基于这一观察，我们认为，如果通过s通道三胶子中间态的强OZI过程和通过s通道虚光子中间态的电磁OZI过程的振幅具有相同的数量级，并且对$J/ψ\toρπ$产生相长干涉，而对$ψ'\toρπ$产生相消干涉，那么同时$ρπ$之谜就消失了，$J/ψ\to\rhoı$的宽度也是可以理解的.然而，到目前为止，我们还不能从QCD的基本原理推导出相位差。文本中还讨论了其他解释。
英文摘要：
The experimental observation indicates that the branching ratio of $ψ'\to ρπ$ is very small while the $ρ-π$ channel is a main one in $J/ψ$ decays. To understand the puzzle, various interpretations have been proposed. Meanwhile according to the hadronic helicity selection rule the decay mode $J/ψ\toρπ$ should be suppressed, but definitely, numerical computation is needed to determine how it is suppressed. We calculate the branching ratios corresponding to subprocesses $J/ψ\to ggg\toρπ$ and $\to ggg\toππ$ in the framework of QCD. The results show that the branching ratios are proportional to $({m_u+m_d\over M_{J/ψ}})^2$ for $ρπ$ mode and $({m_u-m_d\over M_{J/ψ}})^2$ for $ππ$ mode which is an isospin-violation channel. If only the OZI process is considered, the theoretical prediction on the ratio of $J/ψ\to ρπ$ is smaller than data, but not too drastically small. Meanwhile, a possible interpretation for the $ρπ$ puzzle is proposed that the suppression is due to interference between OZI and electromagnetic (EM) contributions. Thus based on this observation, we suggest that if the amplitudes of the strong OZI process via an s-channel three-gluon intermediate state and electromagnetic one via an s-channel virtual photon intermediate state have the same order of magnitude, and constructively interfere for $J/ψ\toρπ$, but destructively interfere for $ψ'\toρπ$, thus simultaneously the $ρπ$ puzzle disappears and the sizable width of $J/ψ\to\rhoı$ is understandable. However, so far, we cannot derive the phase difference from an underlying principle of QCD yet. Alternative interpretations are also discussed in the text.
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