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Fragmentation fraction $f_{Ω_b}$ and the $Ω_b\to ΩJ/ψ$ decay in the light-front formalism

One has measured $f_{Ω_b}{\cal B}(Ω_b^-\to Ω^- J/Ψ)$ at the level of $10^{-6}$, where the fragmentation faction $f_{Ω_b}$ is to evaluate the $b$-quark to $Ω_b^-$ production rate. Using the $Ω_b\to Ω$ transition form factors calculated in the light-front quark model, we predict ${\cal B}(Ω_b^-\to Ω^- J/Ψ) =(5.3^{+3.3+3.8}_{-2.1-2.7})\times 10^{-4}$. In particular, we extract $f_{Ω_b}=(0.54^{+0.34+0.39+0.21}_{-0.22-0.28-0.15})\times 10^{-2}$, demonstrating that the $b$ to $Ω_b$ productions are much more difficult than the $b$ to $Λ_b(Ξ_b)$ ones. Since $f_{Ω_b}$ has not been determined experimentally, $f_{Ω_b}$ added to theoretical branching fractions can be compared to future measurements of the $Ω_b$ decays.