AI 中文总结
本文推导了含本底不确定性的计数实验的发现显著性近似表达式，纳入高阶渐近修正，经对比验证其在低事例产额下的有效性，可用于评估实验灵敏度及优化截断选择。
AI 中文摘要
在粒子物理学中，新信号过程的寻找通常基于观测服从泊松分布的事例数，其均值包含本底贡献，若信号存在则还包含假设信号的贡献。发现显著性可表示为仅含本底假设的p值导出的等效标准差数目。为表征实验灵敏度，可报告名义信号强度下发现显著性的中位数。本文推导了两种情况下中位数显著性的近似表达式：一是本底事例数的预期值已知，二是本底率不确定但受泊松控制测量约束。这些公式基于使用轮廓似然比的检验统计量，中位数显著性通过Asimov数据集近似。同时，基于Barndorff-Nielsen r*统计量的高阶渐近修正被纳入观测和预期发现显著性中。将所得表达式的有效性与蒙特卡罗结果及粒子物理中常用的其他预期显著性公式进行比较，发现高阶修正在事例产额较小时能提供有意义的改进。这些结果对准确评估计划实验的灵敏度，以及选择确定信号和本底预期事例数的最优截断至关重要。
英文摘要
In Particle Physics, a search for a new signal process is often based on observing a Poisson-distributed number of events, whose mean contains contributions from background and, if it exists, the hypothesised signal. The discovery significance can be expressed as an equivalent number of standard deviations derived from the $p$-value of the background-only hypothesis. To characterise the experimental sensitivity, one may report the median, assuming a nominal signal strength, of the discovery significance. In this paper, approximate expressions for the median significance are derived both when the expected number of background events is known and when the background rate is uncertain but constrained by a Poisson control measurement. The formulae are based on a test statistic using the profile likelihood ratio, and the median significance is approximated using the Asimov data set. Higher-order asymptotic corrections, based on the Barndorff-Nielsen $r^\ast$ statistic, are incorporated for both the observed and expected discovery significance. The validity of the resulting expressions is compared with Monte Carlo results and with other formulae for expected significance often used in particle physics. The higher-order corrections are found to provide meaningful improvements at small event yields. The results are important for obtaining an accurate assessment of the sensitivity of a planned experiment and for the optimal choice of cuts that determine the expected numbers of signal and background events.
Comments13 pages, 6 figures
