Probe CP violation in $H\to \gamma Z$ through forward-backward asymmetry

We suggest that the forward-backward asymmetry $(A_{FB})$ of the charged leptons in $gg\to H\to\gamma Z\to\gamma \ell^-\ell^+$ process could be used to probe the CP violating $H\gamma Z$ coupling when the interference from $gg\to\gamma Z\to\gamma \ell^-\ell^+$ process is included. With CP violation in $H\gamma Z$ coupling, the interference effect leads to a non-vanishing $A_{FB}$, which is also sensitive to the strong phase differences. The resonant and non-resonant strong phases together make $A_{FB}(\hat{s})$ change sign around Higgs mass $M_H$. For phenomenology study, we suggest the integral over one-side mass region below $M_H$ to magnify the $A_{FB}$ strength.