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 m${}_Z^2$/m${}_c^2$ 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${}_{-0.69}^{+1.48}$ × 10${}^{-11}$.