In this note we discuss subtleties associated with the efficiency corrections for measurements of off-diagonal cumulants and factorial moments for a situation when one deals with overlapping sets of particles, such as correlations between numbers of protons and positively charged particles. In particular, we discuss the situation commonly encountered in heavy-ion experiments, where first all charges are reconstructed and then protons are selected from these charges by an additional particle identification procedure. We present the efficiency correction formulas for the case when the detection efficiencies follow a binomial distribution.

中文翻译：

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重叠粒子集的阶乘矩和累积量的效率校正

在本说明中，我们讨论了与非对角累积量的测量效率校正相关的细微差别，以及当人们处理一组重叠粒子时的质子矩，例如质子数和带正电粒子之间的相关性。特别是，我们讨论了重离子实验中经常遇到的情况，首先重构所有电荷，然后通过附加的粒子识别程序从这些电荷中选择质子。我们提出了当检测效率遵循二项式分布时的效率校正公式。