Improved analysis of double J/ψ production in Z-boson decay

In this paper, we present an improved calculation for the decay rate of the rare Z -boson decay into J/ψ + J/ψ . J / ψ + J / ψ . This decay is dominated by the photon fragmentation mechanism, i.e., the transition Z→ J/ψ + γ * Z → J / ψ + γ ∗ followed by the fragmentation γ *→ J/ψ . γ ∗ → J / ψ . In our calculation, the amplitude of γ *→ J/ψ γ ∗ → J / ψ is extracted from the measured value of Γ (J/ψ → e⁺ e⁻), Γ ( J / ψ → e + e - ) , and the amplitude of Z→ J/ψ + γ * Z → J / ψ + γ ∗ is calculate through the light-cone approach. The higher-order QCD and relativistic corrections in the amplitude of γ *→ J/ψ γ ∗ → J / ψ and the large logarithms of mZ²/mc² m Z 2 / m c 2 that appear in the amplitude of Z→ J/ψ + γ * Z → J / ψ + γ ∗ are resummed in our calculation. Besides, the non-fragmentation amplitude is calculated based on the NRQCD factorization, and the next-to-leading order QCD and relativistic corrections are included. The obtained branching fraction for this Z decay channel is 8.66 +1.48 -0.69× 10⁻¹¹. 8 . 66 - 0.69 + 1.48 × 10 - 11 .