Probing CP-violating $h\bar{t}t$ coupling in $e^{+}e^{-}\rightarrow h \gamma$

We investigate the possibility of probing the CP-violating $h\bar{t}t$ coupling in the process $e^{+}e^{-}\rightarrow h \gamma$ at the future high luminosity $e^{+}e^{-}$ colliders. Our numerical results show that the cross section for this process can be significantly increased for the allowed CP phase $\xi$ and center of mass energy. For example the cross section is about 6 times of that in the standard model (SM) for $\sqrt{s}=350~\mathrm{GeV}$ and $\xi =3\pi/5$ (see text for $\xi$ definition). The simulation for the signal process $e^{+}e^{-}\rightarrow h \gamma \rightarrow b \bar{b}\gamma$ and its backgrounds shows that the signal significance can reach more than $4.8\sigma$ and $2.3\sigma$ for $\sqrt{s}=350~\mathrm{GeV},\ 500~\mathrm{GeV}$ respectively, with the integrated luminosity $\mathcal{L}=3~\text{ab}^{-1}$ and $\xi\in[\pi/2,3\pi/5]$. For $\mathcal{L}=10~\text{ab}^{-1}$, the signal significance can be greater than 5 for $\sqrt{s}=350~\mathrm{GeV}$ and 3.9 for $\sqrt{s}=500~\mathrm{GeV}$ with the CP phase $\xi\in[\pi/2,3\pi/5]$. Besides the cross section enhancement, the CP-violating $h\bar{t}t$ coupling will induce the forward-backward asymmetry $A_{FB}$ which is absent in the SM and is a clear signal of new CP violation. Compared with the $A_{FB}$ in the Higgs decay $h\rightarrow l^{+}l^{-}\gamma$, the $A_{FB}$ can be greatly enhanced in the production process. For example $A_{FB}$ can reach 0.5 for $\cos\xi\simeq 0.7$ and $\sqrt{s}=500~\mathrm{GeV}$. Due to the large backgrounds, the significance of the expected $A_{FB}$ can only be observed at $1.7\sigma$ with $\mathcal{L}=10~\text{ab}^{-1}$ and $\sqrt{s}=500~\mathrm{GeV}$. It is essential to trigger the single photon in the final state to separate the bottom jets arising from scalar or vector bosons, in order to isolate the signal from the backgrounds more efficiently.