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. This decay is dominated by the photon fragmentation mechanism, i.e., the transition Z→ J/ψ + γ* followed by the fragmentation γ*→ J/ψ. In our calculation, the amplitude of γ*→ J/ψ is extracted from the measured value of Γ(J/ψ → e⁺ e⁻), and the amplitude of 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 and the large logarithms of mZ²/mc² that appear in the amplitude of 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.