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

Abstract

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

10 pages, 2 figures

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