Production of doubly heavy baryon at the Muon-Ion Collider
This study forecasts the production of doubly heavy baryons, $Ξ_{cc}$, $Ξ_{bc}$, and $Ξ_{bb}$, within the nonrelativistic QCD framework at the Muon-Ion Collider (MuIC). It examines two production mechanisms: photon-gluon fusion ($γ+ g \to (QQ')[n] +\bar{Q} +\bar{Q'}$) and extrinsic heavy quark channels ($γ+ Q \to (QQ')[n] + \bar{Q'}$), where $Q$ and $Q'$ denote heavy quarks ($c$ or $b$) and $(QQ')[n]$ represents a diquark in specific spin-color configurations. The diquark fragments into $Ξ_{QQ'}$ baryons with high probability. For $Ξ_{cc}$ and $Ξ_{bb}$, the relevant configurations are $[^1S_0]_{\textbf{6}}$ (spin-singlet and color-sextuplet) and $[^3S_1]_{\bar{\textbf{3}}}$ (spin-triplet and color-antitriplet). For $Ξ_{bc}$, the configurations are $[^1S_0]_{\bar{\textbf{3}}}$, $[^1S_0]_{\textbf{6}}$, $[^3S_1]_{\bar{\textbf{3}}}$, and $[^3S_1]_{\textbf{6}}$. The study compares total and differential cross-sections for these channels, highlighting their uncertainties. The results indicate that the extrinsic heavy quark channel, particularly the $[^3S_1]_{\bar{\textbf{3}}}$ configuration, dominates $Ξ_{QQ'}$ production, though other diquark states also contribute significantly. Using quark masses $m_c = 1.80 \pm 0.10$ GeV and $m_b = 5.1 \pm 0.20$ GeV, the study estimates annual event yields at MuIC ($\sqrt{s} = 1$ TeV, luminosity ${\mathcal L}\simeq 40$ ${\rm fb}^{-1}$) of $(3.67^{+1.29}_{-0.91}) \times 10^9$ for $Ξ_{cc}$, $(2.24^{+0.28}_{-0.20}) \times 10^8$ for $Ξ_{bc}$, and $(3.00^{+0.64}_{-0.56}) \times 10^6$ for $Ξ_{bb}$. These findings suggest that MuIC will significantly enhance our understanding of doubly heavy baryons.