Abstract

Precision studies of simple atoms, such as hydrogen, play an essential role in tests of bound-state QED and determining fundamental constants, such as the Rydberg constant and the proton charge radius. One of the QED predictions is for the Lamb shift of hydrogenic energy levels and, in particular, of the ground state. The value of the \(1s\) Lamb shift in hydrogen and deuterium is required for an accurate determination of the Rydberg constant and the proton charge radius utilizing data from high-resolution spectroscopy of hydrogen and deuterium atoms, as well as for precision tests of bound-state QED. The dominant QED contribution to the uncertainty is due to the \({{\alpha }^{8}}m\) external-field contributions. We discuss here our recent results on the two- and three-loop contributions, which essentially reduce the theoretical uncertainty. Combined with recent calculations of Laporta on the slope of the Dirac form factor in the three-loop level, our results allow for completion of calculations of \({{\alpha }^{8}}m\) contributions to the Lamb shift of the ground state in the hydrogen atom.

中文翻译：

---

α8m 对氢中 1s 兰姆位移的完整贡献

摘要

简单原子（如氢）的精密研究在束缚态 QED 测试和确定基本常数（如里德伯常数和质子电荷半径）中起着至关重要的作用。QED 预测之一是氢能级的兰姆位移，特别是基态的兰姆位移。利用氢和氘原子的高分辨率光谱数据准确测定里德堡常数和质子电荷半径，以及对束缚态 QED。QED 对不确定性的主要贡献是由于\({{\alpha }^{8}}m\)外场贡献。我们在这里讨论我们最近关于二环和三环贡献的结果，这从本质上降低了理论不确定性。结合最近对三环水平中狄拉克形状因子斜率的拉波尔塔计算，我们的结果允许完成对兰姆位移贡献的\({{\alpha }^{8}}m\)的计算氢原子的基态。