Photoproduction of $P$-wave doubly charmed baryon at future $e^+e^-$ collider

The photoproduction of $P$-wave doubly charmed baryon ($\Xi_{cc}$) is investigated in the context of future high-energy and high-luminosity $e^+e^-$ colliders. The direct photoproduction via the sub-process $\gamma+\gamma \rightarrow \Xi_{cc} +\bar{c}+\bar{c}$ and the resolved channel $\gamma+g \rightarrow \Xi_{cc} +\bar{c}+\bar{c}$ are considered. Within the framework of non-relativistic QCD, the calculation encompasses four $P$-wave $(cc)$-diquark configurations: $(cc)_{\bar{\textbf{3}}}[{}^1P_1]$, $(cc)_{\textbf{6}}[{}^3P_0]$, $(cc)_{\textbf{6}}[{}^3P_1]$ and $(cc)_{\textbf{6}}[{}^3P_2]$. The two $S$-wave states, $(cc)_{\bar{\textbf{3}}}[{}^3S_1]$ and $(cc)_{\textbf{6}}[{}^1S_0]$, are also included for comparison. The cross sections, as well as the differential distributions involving transverse momentum, rapidity, and angular variables, have been computed. Numerical results reveal that the resolved photoproduction process plays a significant role and can provide dominant contributions. The photoproduction rate of the $P$-wave $\Xi_{cc}$ is approximately one order of magnitude lower than that of the $S$-wave.