A toy Monte Carlo simulation for the transverse polarization of high-energy electron beams

Transversely-polarized beams are heuristic to the mechanism of CP violation and explore new physics. Besides, the transverse-polarization monitoring is a key point for the beam energy calibration by the resonant depolarization technique. In the article, the transverse polarization measurement of a high-energy electron beam is performed by Monte Carlo simulation on the circular electron-positron collider. The principle based on the Compton back-scattering combining a deflection magnetic field is discussed in detail. The physical presentation of the analyzing power is used to fit the asymmetric distribution of scattered electrons, which is proportional to the transverse polarization. Furthermore, we develop an efficient algorithm that obtain this analyzing power function and use different strategies to measure the transverse polarization for cross-check. Our measurement method is theoretically suitable with a statistical error 1% within few tens of seconds in Z pole on the circular electron-positron collider. The total systematic uncertainties are controlled to be about 0.6% related to the magnetic field, the drift distance, the laser polarization, the beam energy spread and the related uncertainties of a position sensitive detector.