We present a further theoretical study of the orbital $P$-wave bottom-charmed baryon within the framework of nonrelativistic QCD (NRQCD), considering both the direct photoproduction channel $\gamma+\gamma \rightarrow \Xi_{ bc} +\bar{ c}+\bar{ b}$ and the resolved photoproduction channel $\gamma+g \rightarrow \Xi_{ bc} +\bar{ c}+\bar{ b}$. At future linear colliders, ILC and CLIC, the initial photons can be emitted from the laser back-scattering (LBS) and then the parton gluon can be emitted from the photon. The formation of $\Xi_{ bc}$ can be modeled in two-step: a compact diquark state $\langle bc\rangle[n]$ is formed first and subsequently captures a light quark from the vacuum to hadronize into the baryon $\Xi_{ bc}$. The color and spin quantum number $[n]$ of $\langle bc\rangle$-diquark can be $[{ }^3S_1]_{ \bar{ \textbf{ 3}}/\textbf{ 6}}$, $[{ }^1S_0]_{ \bar{ \textbf{ 3}}/\textbf{ 6}}$, $[{ }^1P_1]_{ \bar{ \textbf{ 3}}/\textbf{ 6}}$ or $[{ }^3P_J]_{ \bar{ \textbf{ 3}}/\textbf{ 6}}$ with $J=0,1,2$. Based on the collision energies and design luminosity of ILC and CLIC, the cross sections, the differential distributions and the estimated produced events of $\Xi_{ bc}$ baryon have been analyzed. The results show that the contribution of the orbital excited $P$-wave $\Xi_{ bc}$ baryon can reach 7%-9% of the $S$-wave, providing a non-negligible contributions.
Categories: hep-ph