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In this work, we study the isospin-violating decay of $\phi\to \omega\pi^0$and quantify the electromagnetic (EM) transitions and intermediate mesonexchanges as two major sources of the decay mechanisms. In the EM decays, thepresent datum status allows a good constraint on the EM decay form factor inthe vector meson dominance (VMD) model, and it turns out that the EM transitioncan only account for about $1/4\sim 1/3$ of the branching ratio for $\phi\to\omega\pi^0$. The intermediate meson exchanges, $K\bar{K}(K^*)$ (intermediate$K\bar{K}$ interaction via $K^*$ exchanges), $K\bar{K^*}(K)$ (intermediate$K\bar{K^*}$ rescattering via kaon exchanges), and $K\bar{K^*}(K^*)$(intermediate $K\bar{K^*}$ rescattering via $K^*$ exchanges), which evade thenaive Okubo-Zweig-Iizuka (OZI) rule, serve as another important contribution tothe isospin violations. They are evaluated with effective Lagrangians whereexplicit constraints from experiment can be applied. Combining these threecontributions, we obtain results in good agreement with the experimental data.This approach is also extended to $J/\psi(\psi^\prime)\to \omega\pi^0$, wherewe find contributions from the $K\bar{K}(K^*)$, $K\bar{K^*}(K)$ and$K\bar{K^*}(K^*)$ loops are negligibly small, and the isospin violation islikely to be dominated by the EM transition.

Isospin violation in $\phi, J/\psi, \psi^\prime \to \omega \pi^0$ via hadronic loops