Investigation on the photoproduction of bottom-charmed baryon within NRQCD

TL;DR

This work addresses the photoproduction of bottom-charmed baryons $\Xi_{bc}$ at future $e^+e^-$ colliders using the NRQCD factorization framework. It analyzes both direct $\gamma\gamma$ and resolved $\gamma g$ channels with laser-backscattered photon spectra, modeling $\Xi_{bc}$ formation via intermediate diquark states $\langle bc\rangle[n]$ that transition to the baryon through nonperturbative hadronization. The key finding is that $P$-wave states contribute about $7$–$9\%$ of the $S$-wave production, and with $\mathcal{O}(10^4)\,\mathrm{fb^{-1}}$ luminosity, the expected ground-state $\Xi_{bc}$ yield ranges from roughly $6.9\times10^5$ to $1.1\times10^6$ events over $\sqrt{s}=250$–$1000$ GeV; however, these totals can vary by up to $\sim38$–$44\%$ due to uncertainties in the color-sextet LDME $h_{\mathbf{6}}$. The results underscore the relevance of $P$-wave contributions and provide guidance for experimental searches at future linear colliders. The analysis also highlights the energy-dependent balance between the direct and resolved channels and the role of NRQCD long-distance matrix elements in shaping predictions.

Abstract

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 $γ+γ\rightarrow Ξ_{bc} +\bar{c}+\bar{b}$ and the resolved photoproduction channel $γ+g \rightarrow Ξ_{bc} +\bar{c}+\bar{b}$. 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 $Ξ_{bc}$ 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 $Ξ_{bc}$. 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 $Ξ_{bc}$ baryon have been analyzed. The results show that the contribution of the orbital excited $P$-wave $Ξ_{bc}$ baryon can reach 7%-9% of the $S$-wave, providing a non-negligible contributions.

Figures (2)

• Figure 1: Twelve typical Feynman diagrams for the photoproduction of $\Xi_{bc}$ through the intermediate subprocess $\gamma+g\to \langle bc\rangle[n]+\bar{c}+\bar{b}$, another twelve can be obtained by interchanging the initial photon and gluon lines.
• Figure 2: Kinematic distributions for the photoproduction of $\Xi_{bc}$ at ILC and CLIC with $\sqrt{s}=$$500$$\mathrm{GeV}$.