Eur. Phys. J. C (2024) 84: 544
https://doi.org/10.1140/epjc/s10052-024-12887-3

Regular Article - Theoretical Physics

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

¹ Department of Physics, Chongqing Key Laboratory for Strongly Coupled Physics, Chongqing University, 401331, Chongqing, People’s Republic of China
² Department of Physics, Chongqing University of Science and Technology, 401331, Chongqing, People’s Republic of China

^c zhengxc@cqu.edu.cn

Received: 12 April 2024
Accepted: 2 May 2024
Published online: 29 May 2024

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 $\mathrm{\Gamma }(J/\psi \to e^{+}{e}^{-}),$ 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 $8.{66}_{-0.69}^{+1.48}\times {10}^{-11}.$