AI 中文总结
研究基于玩具推力分布的模板参数提取的统计验证，开发推理框架并测试三种提取策略，通过伪实验量化性能，结果表明多项似然表现优，插值减离散化效应，模型不匹配有偏差，提供比较估计器等的受控框架。
AI 中文摘要
一个统计上可靠的参数提取程序应独立于其最终应用的物理和探测器模型进行验证。开发并测试了一个基于模板的推理框架，使用受控玩具推力分布作为未来FCC-ee事件形状研究的方法基准。该模型包含类似双喷注和三喷注的事件成分，其相对贡献由一个连续控制参数决定。比较了三种提取策略：离散的Pearson型\(\chi^2\)距离、离散多项负对数似然估计器和基于线性插值模板的似然估计器。通过对包含200 - 2000个事件的样本进行10000次伪实验来量化其性能。还研究了离网格恢复、直方图分箱变化、模板统计变化以及基于修正动量涂抹的模型不匹配测试。多项似然始终优于这里使用的简单不相关Pearson型基线。对于输入参数0.30，正确模板分数从200个事件时的\(0.467\pm0.005\)增加到2000个事件时的\(0.934\pm0.002\)。插值减少了离网格离散化效应，在测试配置中最大绝对平均偏差约为0.003。然而，模型不匹配会产生可测量的偏差，表明仅名义闭合不足以建立稳健性。本研究未确定物理强耦合常数。它提供了一个用于比较估计器、量化统计分辨率以及在应用于实际部分子淋浴模拟、强子化模型、探测器效应和FCC-ee数据之前诊断模型依赖性的受控框架。
英文摘要
A statistically reliable parameter-extraction procedure should be validated independently of the physical and detector models to which it will eventually be applied. A template-based inference framework is developed and tested using controlled toy thrust distributions as a methodological benchmark for future FCC-ee event-shape studies. The model contains two-jet-like and three-jet-like event components whose relative contribution is governed by a continuous control parameter. Three extraction strategies are compared: a discrete Pearson-type $χ^2$ distance, a discrete multinomial negative-log-likelihood estimator, and a likelihood estimator based on linearly interpolated templates. Their performance is quantified with 10,000 pseudo-experiments for samples containing 200--2000 events. Off-grid recovery, histogram-binning variations, template-statistics variations, and a model-mismatch test based on modified momentum smearing are also studied. The multinomial likelihood consistently outperforms the simple uncorrelated Pearson-type baseline used here. For an input parameter of 0.30, the correct-template fraction increases from $0.467\pm0.005$ for 200 events to $0.934\pm0.002$ for 2000 events. Interpolation reduces off-grid discretization effects, with a maximum absolute mean bias of approximately 0.003 in the tested configuration. Model mismatch nevertheless produces measurable biases, demonstrating that nominal closure alone is insufficient to establish robustness. This study does not determine the physical strong coupling constant. It provides a controlled framework for comparing estimators, quantifying statistical resolution, and diagnosing model dependence before application to realistic parton-shower simulations, hadronization models, detector effects, and FCC-ee data.
Comments13 pages, 7 figures, 1 table. Supplementary analysis code and numerical outputs are included as ancillary files
