Title: Electric-Field Reconstruction for Radio Detection of Inclined Air Showers in Three Polarizations Show Chinese title

Title: 电场重构用于倾斜空气簇射的三种极化无线电探测

Abstract: Accurate reconstruction of the electric field produced by extensive air showers is essential for the radio-detection technique, as the key parameters of interest of the primary particles that generated the showers are the amplitude, polarization, frequency spectrum, and energy fluence carried by the electric field at each receiving radio antenna. Conventional electric-field reconstruction methods primarily focus on antennas with two horizontal polarizations. In this work, we introduce an analytic $\chi^2$ minimization method that is applicable to both two and three polarizations. This solution has been verified for simple and realistic antenna responses, with a particular focus on inclined air showers. Our method achieves standard deviations better than 4\% and 6\% for the estimation of the Hilbert peak envelope amplitude of the electric field and the energy fluence, respectively, with an antenna-response-dependent bias. Additionally, we have studied the dependence of the method with arrival direction showing that it has a good performance in the zenith range from 63$^\circ$ up to 80$^\circ$. This work also demonstrates that incorporating vertically polarized antennas enhances the precision of the reconstruction, leading to a more accurate and reliable electric-field estimation for inclined air showers. Show Chinese abstract

Abstract: 精确重建由广延大气簇射产生的电场对于无线电探测技术至关重要，因为由这些簇射产生的原始粒子的关键参数是每个接收无线电天线处电场携带的振幅、极化、频率谱和能量通量。传统的电场重建方法主要关注具有两种水平极化的天线。在本工作中，我们引入了一种适用于两种和三种极化的解析$\chi^2$最小化方法。该解决方案已针对简单和现实的天线响应进行了验证，特别关注倾斜的大气簇射。我们的方法在电场的希尔伯特峰值包络振幅和能量通量估计中分别实现了优于4%和6%的标准偏差，且存在与天线响应相关的偏差。此外，我们研究了该方法对到达方向的依赖性，结果表明在天顶角范围从63$^\circ$到80$^\circ$之间表现良好。这项工作还证明，将垂直极化天线纳入其中可以提高重建的精度，从而为倾斜的大气簇射提供更准确和可靠的电场估计。