Probe $CP$ property in $H\gamma\gamma$ coupling through interference

The diphoton invariant mass distribution of interference between $gg\to H \to \gamma\gamma$ and $gg\to \gamma\gamma$ is almost antisymmetric around the Higgs mass $M_H$. We propose a new observable $A_{int}$ to quantify this effect, which is a ratio of a sign-reversed integral around $M_H$ ( e.g. $\int^{M_H}_{M_H-5~\mbox{GeV}} -\int_{M_H}^{M_H+5~\mbox{GeV}}$) and the cross section of the Higgs signal. We study $A_{int}$ in Standard Model (SM) and various $CP$-violating $H\gamma\gamma$ couplings. The $A_{int}$ in SM ($A_{int}^{SM}$) has a significance of $3\sigma$ for 30~fb$^{-1}$ integrated luminosity, and is possible to be detected in current experiment. Meanwhile, for $CP$-violating $H\gamma\gamma$ couplings, $A_{int}$ could range from $A_{int}^{SM}$ to minus $A_{int}^{SM}$, which makes it a good observable to study new physics. The $A_{int}$ with both $CP$-violating $H\gamma\gamma$ and $Hgg$ couplings are also studied and its value range is further extended.