Study on contributions of hadronic loops to decays of $J/\psi\to$ vector $+$ pseudoscalar mesons

Abstract

In this work, we evaluate the contributions of the hadronic loops to the amplitudes of $J/\psi\to PV$ where $P$ and $V$ denote light pseudoscalar and vector mesons respectively. By fitting data of two well measured channels of $J/\psi\to PV$, we obtain the contribution from the pure OZI process to the amplitude which is expressed by a phenomenological quantity $|\mathcal{G}^{PV}_{S}|$, and a parameter $\alpha$ existing in the calculations of the contribution of hadronic loops. In terms of $\alpha$ and $|\mathcal{G}^{PV}_{S}|$, we calculate the branching ratios of other channels and get results which are reasonably consistent with data. Our results show that the contributions from the hadronic loops are of the same order of magnitude as that from the OZI processes and the interference between the two contributions are destructive. The picture can be applied to study other channels such as PP or VV of decays of $J/\psi$.