Exploring the Υ(6S) → χ_bJφ and Υ(6S) → χ_bJω hidden-bottom hadronic transitions

In this work, we investigate the hadronic loop contributions to the Υ(6S) → χ_bJφ (J = 0, 1, 2) along with Υ(6S) → χ_bJω (J=0, 1, 2) transitions. We predict that the branching ratios of Υ(6S) → χ_b0φ, Υ(6S) → χ_b1φ and Υ(6S) → χ_b2φ are (0.68-4.62) x 10^-6, (0.50-3.43) x 10^-6 and (2.22-15.18) x 10^-6, respectively, and those of Υ(6S) → χ_b0ω, Υ(6S) → χ_b1ω and Υ(6S) → χ_b2ω are (0.15-2.81) x 10^-3, (0.63-11.68) x 10^-3, and (1.08-20.02) x 10^-3, respectively. Especially, some typical ratios, which reflect the relative magnitudes of the predicted branching ratios, are given, i.e., for Υ(6S) → χ_bJφ transitions, R^φ₁₀ = B[Υ(6S) → χ_b1φ]/B[Υ(6S) → χ_b0φ] ∼ 0.74, R^φ₂₀ = B[Υ(6S) → χ_b2φ]/B[Υ(6S) → χ_b0φ] ∼ 3.28, and R^φ₂₁ = B[Υ(6S) → χ_b2φ]/B[Υ(6S) → χ_b1φ] ∼ 4.43, and for Υ(6S) → χ_bJω transitions, R^ω₁₀ = B[Υ(6S) → χ_b1ω]/B[Υ(6S) → χ_b0ω] ∼ 4.11, R^ω₂₀ = B[Υ(6S) → χ_b2ω]/B[Υ(6S) → χ_b0ω] ∼ 7.06, and R^ω₂₁ = B[Υ(6S) → χ_b2ω]/B[Υ(6S) → χ_b1ω] ∼ 1.72. With the running of BelleII in the near future, experimental measurement of these two kinds of transitions will be a potential research issue. (orig.)