A complete theoretical analysis of the C- conserving semileptonic decays \(\eta ^{(\prime )}\rightarrow \pi ^0l^+l^-\) and \(\eta ^\prime \rightarrow \eta l^+l^-\) (\(l=e\) or \(\mu \)) is carried out within the framework of the Vector Meson Dominance (VMD) model. An existing phenomenological model is used to parametrise the VMD coupling constants and the associated numerical values are obtained from an optimisation fit to \(V\rightarrow P\gamma \) and \(P\rightarrow V\gamma \) radiative decays (\(V=\rho ^0\), \(\omega \), \(\phi \) and \(P=\pi ^0\), \(\eta \), \(\eta ^{\prime }\)). The decay widths and dilepton energy spectra for the two \(\eta \rightarrow \pi ^0l^+l^-\) processes obtained using this approach are compared and found to be in good agreement with other results available in the published literature. Theoretical predictions for the four \(\eta ^{\prime }\rightarrow \pi ^0l^+l^-\) and \(\eta ^\prime \rightarrow \eta l^+l^-\) decay widths and dilepton energy spectra are calculated and presented for the first time in this work.

对C-守恒半轻子衰变\（\ eta ^ {（\ prime）} \ rightarrow \ pi ^ 0l ^ + l ^-\）和\（\ eta ^ \ prime \ rightarrow \ eta l ^ +的完整理论分析l ^-\）（\（l = e \）或\（\ mu \））是在向量介子优势（VMD）模型的框架内进行的。使用现有的现象学模型对VMD耦合常数进行参数化，并通过对\（V \ rightarrow P \ gamma \）和\（P \ rightarrow V \ gamma \）辐射衰减（\（ V = \ rho ^ 0 \），\（\ omega \），\（\ phi \）和\（P = \ pi ^ 0 \），\（\ eta \），\（\ eta ^ {\ prime} \））。衰变宽度和双轻子能谱两个- \（\ \ ETA \ RIGHTARROW \ PI ^0升^ + L ^）使用这种方法进行了比较方法获得的并发现是在与在公开的文献中获得其他的结果吻合良好。四个\（\ eta ^ {\ prime} \ rightarrow \ pi ^ 0l ^ + l ^-\）和\（\ eta ^ \ prime \ rightarrow \ etal ^ + l ^-\）衰减宽度和的理论预测这项工作中首次计算出了双链烯能谱。