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. $\int^{M_H}_{M_H-5~\mbox{GeV}} -\int_{M_H}^{M_H+5~\mbox{GeV}}$) 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 $10\%$, while for $CP$-violating $H\gamma\gamma$ couplings $A_{\text{int}}$ could range from $10\%$ to $-10\%$, 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.