Probe $CP$-violating $H\gamma \gamma$ coupling through interferometry

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 $A_{\text{int}}$ to quantify this effect, which is a ratio of a sign-reversed integral around $M_H$ ( e.g. ${\int }_{M_H-5GeV}^{M_H}-{\int }_{M_H}^{M_H+5GeV}$) and the cross section of the Higgs signal. We study $A_{\text{int}}$ both in Standard Model (SM) and new physics with various $CP$-violating $H\gamma \gamma$ couplings. The $A_{\text{int}}$ in SM could reach a value of $10\mathrm{\%}$, while for $CP$-violating $H\gamma \gamma$ couplings $A_{\text{int}}$ could range from $10\mathrm{\%}$ to $-10\mathrm{\%}$, which is probable to be detected in HL-LHC experiment. The $A_{\text{int}}$ with both $CP$-violating $H\gamma \gamma$ and $Hgg$ couplings are also studied and its value range is further extended.