In the positron-electron annihilation process, finite deviations from the standard calculation based on the Fermi's Golden rule are suggested in recent theoretical work. This paper describes an experimental test of the predictions of this theoretical work by searching for events with two photons from positron annihilation of energy larger than the electron rest mass ($511\,{\rm keV}$). The positrons came from a ${\rm {}^{22}Na}$ source, tagging the third photon from the spontaneous emission of ${\rm {}^{22}{Ne}^*}$ de-exitation to suppress backgrounds. Using the collected sample of $1.06\times 10^{7}$ positron-electron annihilations, triple coincidence photon events in the signal enhanced energy regions are examined. The observed number of events in two signal regions, $N^{\rm SR1}_{\rm obs}=0$ and $N^{\rm SR2}_{\rm obs}=0$ are, within a current precision, consistent with the expected number of events, $N^{\rm SR1}_{\rm exp}=0.86\pm0.08({\rm stat.})^{+1.85}_{-0.81}({\rm syst.})$ and $N^{\rm SR2}_{\rm exp}=0.37\pm 0.05({\rm stat.})^{+0.80}_{-0.29}({\rm syst.})$ from Fermi's golden rule respectively. Based on the $P^{(d)}$ modeling, the 90% CL lower limit on the photon wave packet size is obtained.

中文翻译：

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寻找正电子湮灭中费米黄金法则的修正项

在正电子-电子湮灭过程中，最近的理论工作提出了与基于费米黄金法则的标准计算的有限偏差。本文描述了通过搜索来自正电子湮灭能量大于电子静止质量 ($511\,{\rm keV}$) 的两个光子的事件，对该理论工作的预测进行的实验测试。正电子来自 ${\rm {}^{22}Na}$ 源，标记来自 ${\rm {}^{22}{Ne}^*}$ 去激发的自发发射的第三个光子抑制背景。使用收集的 $1.06\times 10^{7}$ 正电子-电子湮灭样本，检查信号增强能量区域中的三重巧合光子事件。在两个信号区域观察到的事件数 $N^{\rm SR1}_{\rm obs}=0$ 和 $N^{\rm SR2}_{\rm obs}=0$ 是，在当前精度内，与预期事件数一致，$N^{\rm SR1}_{\rm exp}=0.86\pm0.08({\rm stat.})^{+1.85}_{-0.81 }({\rm syst.})$ 和 $N^{\rm SR2}_{\rm exp}=0.37\pm 0.05({\rm stat.})^{+0.80}_{-0.29}({ \rm syst.})$ 分别来自费米的黄金法则。基于$P^{(d)}$建模，获得了光子波包大小的90%CL下限。