Photoproduction of doubly heavy baryons at future $e^+e^-$ colliders

The photoprodution of doubly heavy baryon ($\Xi_{cc},\Xi_{bb},\Xi_{bc}$) is investigated in the context of future high-energy and high-luminosity $e^+e^-$ colliders. The study incorporates two sources of initial photons, namely the LBS photon and the WWA photon. Alongside the direct photoproduction via the sub-process $\gamma+\gamma \rightarrow \Xi_{QQ^{'}} +\bar{Q}+\bar{Q^{'}}$ ($Q^{(')}=c,b$), the resolved photoproduction channels are specifically considered, encompassing the sub-processes $\gamma + g \rightarrow \Xi_{QQ^{'}} +\bar{Q}+\bar{Q^{'}}$, $g + g \rightarrow \Xi_{QQ^{'}} +\bar{Q}+\bar{Q^{'}}$, and $q + \bar{q} \rightarrow \Xi_{QQ^{'}} +\bar{Q}+\bar{Q^{'}}$ with $q=u,d,s$. Within the framework of non-relativistic QCD, two $(cc(bb))$-diquark configurations, ${}_{\bar{\textbf{3}}}[{}^3S_1]$ and ${}_{\textbf{6}}[{}^1S_0]$, and four $(bc)$-diquark configurations, $(bc)_{\bar{\textbf{3}}}[{}^3S_1]$, $(bc)_{\textbf{6}}[{}^1S_0]$, $(bc)_{\textbf{6}}[{}^3S_1]$ and $(bc)_{\bar{\textbf{3}}}[{}^1S_0]$, are considered in the calculations. Numerical results show that the single resolved photoproduction processes provide dominant contributions under certain collision configuration. At the future $e^+e^-$ colliders, the doubly heavy baryon generated via the photoproduction mechanism is promisingly observable and can be well studied.