A hypothetical spin-1 bottomonium resonance Î¥ with mass 9 GeV/c²is observed in the reaction e⁺e^ˆ’†’ μ⁺μ^ˆ’and in the total electron€“ positron annihilation cross-section. The resonance is too narrow for its width to be resolved directly, but the cross-sections integrated over the vicinity of the resonance are

where E is the total centre-of-mas energy, σ_μ = σ(e⁺e †’ μμ) and σ_t is the total cross-section. Assuming the cross-sections are dominated by a Breit€“Wigner resonance of the form discussed in Section B5.2, evaluate the partial widths Γ(Î¥ †’ e⁺e^ˆ’), Γ(Î¥ †’ μ⁺μ^ˆ’) and the total decay width.

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|o, (E) dE = 10 nb Mev and (E) dE = 300 nb MeV, 10 nb MeV