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

TL;DR

This paper investigates isospin violation in $ o ext{omega} ext{pi}^0$ decays of $ ext{phi}$, $J/ ext{psi}$, and $ ext{psi}^ extprime$, highlighting the roles of electromagnetic transitions and hadronic loops, with results aligning with experimental data.

Contribution

It provides a detailed analysis of the mechanisms behind isospin violation, especially quantifying the contributions of electromagnetic and hadronic loop processes in these decays.

Findings

Electromagnetic transitions account for about 25-33% of the $ ext{phi} o ext{omega} ext{pi}^0$ decay.

Hadronic loops via meson exchanges significantly contribute to isospin violation in $ ext{phi}$ decay.

In $J/ ext{psi}$ and $ ext{psi}^ extprime$ decays, electromagnetic effects dominate over hadronic loops.

Abstract

In this work, we study the isospin-violating decay of $\phi\to \omega\pi^0$ and quantify the electromagnetic (EM) transitions and intermediate meson exchanges as two major sources of the decay mechanisms. In the EM decays, the present datum status allows a good constraint on the EM decay form factor in the vector meson dominance (VMD) model, and it turns out that the EM transition can 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 the naive Okubo-Zweig-Iizuka (OZI) rule, serve as another important contribution to the isospin violations. They are evaluated with effective Lagrangians where explicit constraints from experiment can be applied. Combining these three contributions, we obtain results in good agreement with the experimental data. This approach is also extended to $J/\psi(\psi^\prime)\to \omega\pi^0$, where we 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 is likely to be dominated by the EM transition.