Probe $CP$-violating $Hgammagamma$ coupling through interferometry

The diphoton invariant mass distribution of interference between $ggto H to gammagamma$ and $ggto gammagamma$ 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 $Hgammagamma$ couplings. The $A_{text{int}}$ in SM could reach a value of $10%$, while for $CP$-violating $Hgammagamma$ 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 $Hgammagamma$ and $Hgg$ couplings are also studied and its value range is further extended.