The solar-neutrino detectors GALLEX and SAGE were calibrated by electron-neutrino flux from the $^{37}$Ar and $^{51}$Cr calibration sources. A deficit in the measured neutrino flux was recorded by counting the number of neutrino-induced conversions of the $^{71}$Ga nuclei to $^{71}$Ge nuclei. This deficit was coined ``gallium anomaly'' and it has lead to speculations about beyond-the-standard-model physics in the form of eV-mass sterile neutrinos. Notably, this anomaly has already defied final solution for more than 20 years. Here we reassess the statistical significance of this anomaly and improve the related statistical approaches by treating the neutrino experiments as repeated Bernoulli trials taking into account the fact that the number of the detected $^{71}$Ge nuclei is quite small, thus calling for a Bayesian statistical approach. In addition, we take into account the systematic errors of the experiments, their correlations, theoretical uncertainties and the number of background solar-neutrino events as a Poisson-distributed random variable. To compare with the previously reported statistical significances of the anomaly we convert the posterior intervals of our Bayesian approach to standard deviations $σ$ of the frequentist approach. We find that our approach reduces the statistical significance of the anomaly by $0.8\,σ$ for all the adopted theoretical approaches. This renders the gallium anomaly a statistically weakly supported concept. Furthermore, the implications of our approach go far beyond the gallium anomaly since the results of many rare-events experiments should be reassessed for their limited number of recorded events.
Istituto Nazionale di Fisica Nucleare (INFN), Sezione di Torino（意大利国家核物理研究所都灵分部）；Institute of High Energy Physics, Chinese Academy of Sciences（中国科学院高能物理研究所）；School of Physical Sciences, University of Chinese Academy of Sciences（中国科学院大学物理科学学院）
The effect of nuclear recoil on neutrino oscillations: Toward understanding of short baseline anomalies
Università del Salento（萨伦托大学）；INFN Sezione di Lecce（意大利国家核物理研究所莱切分部）；Institute of Nanotechnology of the National Research Council of Italy, CNR-NANOTEC, Lecce Central Unit（意大利国家研究委员会纳米技术研究所莱切中央单元）
最近，巴克桑无菌跃迁实验（BEST）的结果证实了镓异常--在SAGE和GALLEX校准时缺乏电子中微子$ν_e$--统计显著性超过5 $\,σ$。这一结果与镓异常的解释是一致的，即电子中微子振荡成无菌中微子，$ν_s$。在这个解释范围内，BEST实验本身在中微子领域所有先前的异常结果中为不育中微子提供了最强有力的证据。我们结合镓实验的结果与搜索无菌中微子在反应堆反中微子实验（假设CPT守恒的$3+1$中微子部门）。虽然“镓”在模型参数空间中的最佳拟合点（无菌中微子质量平方$m_{ν_s}^2\approx 1.25\,$ eV $^2$，无菌电子中微子混合$\sin^22θ\approx 0.34$）被排除在这些搜索之外，但部分最受欢迎的2 $\,σ$区域与$m^2_{ν_s}>5\,$ eV $^2$是一致的。值得注意的是，NEUTRINO-4实验异常结果所宣扬的区域与BEST实验的区域重叠：联合分析的最佳拟合点是$\sin^22θ\approx 0.38$、$m_{ν_s}^2\approx7.3\,$ eV $^2$，有利区域将由KATRIN实验探索。对BEST结果的无菌中微子解释不仅意味着粒子物理学标准模型的扩展，而且意味着对标准宇宙模型和太阳模型的重大修改，或者对抑制早期宇宙和太阳中无菌中微子产生所需的无菌扇区进行特定修改。
