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The Circular Electron Positron Collider (CEPC) was proposed by the Chinese particle physics scientists as a future Higgs factory and $W/Z$ factory. It will produced more than $10^{12}$$Z$ bosons by operating at a center-of-mass energy around 91.2 GeV in two years. In this study, the measurement of the relative decay widths of $Z$ bosons decaying to $b$ quarks $(R_b)$, $c$ quarks $(R_c)$ and light quarks $(R_{uds})$ in hadronic $Z$ decays are studied on CEPC Monte Carlo (MC) samples. By using a template method, $R_b$, $R_c$ and $R_{uds}$ can be fitted from reconstructed data as the fractions of MC templates with different flavors. The distribution of a sensitive variable, $b$-tagging probability, is used as the template, because of its high performance in discriminating different flavors. Based on the expected statistics of $10^{12}$$Z$ bosons at CEPC, the statistical uncertainty is estimated to be approximately $10^{-6}$ by using the template method, which means that the measurement will no longer be limited by the statistics. Systematic errors arise directly from the difference in the $b$-tagging probability distribution between real data and template MC samples. By considering the bias of input variables used for $b$-tagging probability computing, the quantitative effect for each kind of input variable is investigated by using an ensemble test procedure.

The Circular Electron Position Collider (CEPC) is a future $Z$ and Higgs bosons factory, which targets precision electroweak and Higgs measurements. The simulation, reconstruction, analysis chain has been established at CEPC. The detector design parameters were optimized according to several performances of key physical objects. The physics potential has been studied for the detector geometry CEPC_v1.