Improved analysis of double $$J/\psi $$ production in Z-boson decay

Abstract

AbstractIn this paper, we present an improved calculation for the decay rate of the rare Z-boson decay into $$J/\psi + J/\psi .$$ J / ψ + J / ψ . This decay is dominated by the photon fragmentation mechanism, i.e., the transition $$Z\rightarrow J/\psi + \gamma ^{*}$$ Z → J / ψ + γ ∗ followed by the fragmentation $$\gamma ^{*}\rightarrow J/\psi .$$ γ ∗ → J / ψ . In our calculation, the amplitude of $$\gamma ^{*}\rightarrow J/\psi $$ γ ∗ → J / ψ is extracted from the measured value of $$\Gamma (J/\psi \rightarrow e^+ e^-),$$ Γ ( J / ψ → e + e - ) , and the amplitude of $$Z\rightarrow J/\psi + \gamma ^{*}$$ Z → J / ψ + γ ∗ is calculate through the light-cone approach. The higher-order QCD and relativistic corrections in the amplitude of $$\gamma ^{*}\rightarrow J/\psi $$ γ ∗ → J / ψ and the large logarithms of $$m_{_Z}^2/m_c^2$$ m Z 2 / m c 2 that appear in the amplitude of $$Z\rightarrow J/\psi + \gamma ^{*}$$ 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 $$8.66 ^{+1.48} _{-0.69}\times 10^{-11}.$$ 8 . 66 - 0.69 + 1.48 × 10 - 11 .