Study of isospin violating $\phi$ excitation in $e^+e^- \to \omega\pi^0$

Understand

We study the reaction $e^+ e^-\to \omega\pi^0$ in the vicinity of $\phi$ mass region.

• The isospin-violating $\phi$ excitation is accounted for by two major mechanisms.
• One is electromagnetic (EM) transition and the other is strong isospin violations.
• For the latter, we consider contributions from the intermediate hadronic meson loops and $\phi$-$\rho^0$ mixing as the major mechanisms via the $t$ and s-channel transitions, respectively.