全国第十八届重味物理和CP破坏研讨会（HFCPV 2021）

Firstly we define a $CP$ violation phase $\xi$ to quantify the mixture of $CP$-even and $CP$-odd states for Higgs boson in new physics beyond Standard Model. Then we show it explicitly in $H\to\gamma\gamma$, $H\to\gamma\ell\ell$ and $H\to 4\ell$ amplitudes. The analytical form gives a good explanation why the $CP$-violation phase could be observed in $H\to 4\ell$ process but not in $H\to\gamma\gamma$ and $H\to\gamma\ell\ell$ processes. Meanwhile, to study the relations of amplitudes, we find a new method of decomposing $H\to\gamma\ell\ell$ and $H\to 4\ell$ amplitudes into $H\to\gamma\gamma$ amplitudes. For a comparison, by using the on-shell approach we study the recursion relations of amplitudes and get a consistent result independently.