分段缪子探测器的广义似然模型
A generalized likelihood model for segmented muon counters
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中文总结 AI 辅助
本研究开发了纳入探测器效率不足等因素的统一统计框架，推导了缪子LDF重建所需的精确似然表达式及近似形式，其性能良好且适用范围广。
中文摘要 AI 辅助
广延空气簇射的缪子成分测量可约束宇宙射线的质量成分以及加速器无法达到的超高能区强相互作用过程。为此，广泛采用具有二进制读出的分段探测器阵列，它们采样簇射核心不同距离处的缪子密度，以重建缪子横向分布函数（LDF）。每个探测器的响应由被激活的段数$k$表示，其概率分布构成将观测结果与预期缪子含量关联的似然函数。信号堆积、探测器效率不足、边缘截断缪子以及背景信号会影响该分布，忽略这些因素会导致重建结果出现偏差。现有分析模型虽包含了堆积效应，但其余部分均假设探测器响应为理想状态。本研究开发了一个统一统计框架，通过一组具有物理解释的参数纳入探测器效率不足、边缘截断缪子及背景效应。我们推导了用于缪子LDF重建的探测器响应和似然函数的精确表达式，同时给出了保留精确分布主要统计特性的简单二项式近似。专用蒙特卡罗模拟用于评估分析处理所依据假设的影响，结果显示在考虑的参数范围内该影响可忽略不计；模拟还表明，精确和近似似然函数在估计量偏差和置信区间覆盖方面表现相近。尽管本框架由皮埃尔·奥格天文台的地下缪子探测器所启发，但它更广泛适用于通过被激活段数推断粒子含量的具有二进制读出的分段粒子探测器。
英文摘要
Measurements of the muonic component of extensive air showers constrain cosmic-ray mass composition and hadronic interactions at energies beyond those accessible at accelerators. Arrays of segmented detectors with binary readout are widely used for this purpose: they sample the muon density at different distances from the shower core to reconstruct the muon lateral distribution function (LDF). Each detector response is summarized by the number of activated segments, $k$, whose probability distribution provides the likelihood relating the observation to the expected muon content. Signal pile-up, detector inefficiency, corner-clipping muons, and background signals shape this distribution, and neglecting them can bias the reconstruction. Existing analytical models include pile-up but otherwise assume an ideal detector response. In this work, we develop a unified statistical framework that incorporates inefficiency, corner clipping, and background through a small set of physically interpretable parameters. We derive exact expressions for the detector response and the likelihood required for muon-LDF reconstruction, together with a simple binomial approximation that preserves the main statistical properties of the exact distribution. Dedicated Monte Carlo simulations are used to assess the impact of the assumptions underlying the analytical treatment and show that it is negligible over the parameter range considered. They also show that the exact and approximate likelihoods yield similar performance in terms of estimator bias and confidence-interval coverage. Although motivated by the Underground Muon Detector of the Pierre Auger Observatory, the framework applies more broadly to segmented particle detectors with binary readout in which particle content is inferred from the number of activated segments.
发表机构
- Instituto de Tecnología en Detección y Astropartículas (CNEA, CONICET, UNSAM)（探测与高能天体粒子技术研究所）
- Karlsruhe Institute of Technology（卡尔斯鲁厄理工学院）
- Instituto Galego de Física de Altas Enerxías（加利西亚高能物理研究所）
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