RUI: Calculation of the Positronium Hyperfine Interval

正电子是电子和它的反粒子正电子的结合态。因此，它形成了一种“奇异原子”，在许多方面与传统的简单原子（如氢和氦）相似，但不同之处在于它独特的组成和它的湮灭倾向，它以高能光子的形式转化为纯电磁能量。正电子的许多特性，如能级差和寿命，都可以通过高精度的实验获得。从理论上也可以计算出正电子的性质，精度很高。因此，正电子是测试电磁束缚态物理极限的理想系统。正电子超精细分裂——最低能态的自旋为1和自旋为0之间的间隔——是人们最感兴趣的，因为这种分裂的理论和实验之间存在着长期存在的差异（大约是实验不确定性的四倍）。目前的建议是将正电子超细区间的计算提高到一个更高的水平。完成后，这项工作的结果将有助于解决或锐化正电子的超精细差异。这项理论工作是及时的，因为位于加州大学河滨分校和东京大学的两个实验小组正在开发改进的超精细间隔的实验测量方法。改进的实验结果和更高精度的理论相结合，将共同为束缚态量子电动力学（QED）提供迄今为止最严格的测试之一。这个项目的一个重要方面是培养本科生合作者在这个领域的科学调查的技术和过程。整个项目包括许多不同的部分，这些部分将成为小型学生团队的理想项目。学生们将在工作的各个方面进行合作，包括计算技术和工具的开发、计算本身、在科学会议上的展示和出版。由于强相互作用和弱相互作用可以忽略不计，因此用束缚态量子电动力学（QED）的方法可以从理论上计算出正电子的性质。通过完成对超精细区间的所有三回修正，正电子子超精细区间的计算精度将比以前更高。这将需要有效的场论方法的应用，特别是非相对论QED (NRQED)，在三环阶。完成后，这项工作的结果将有助于解决或锐化正电子的超精细差异。

Positronium is the bound state of the electron and its antiparticle, the positron. As such, it forms an "exotic atom", similar in many ways to the traditional simple atoms such as hydrogen and helium, but different because of its unique composition and because of its tendency to annihilate, transforming into pure electromagnetic energy in the form of high-energy photons. Many properties of positronium, such as energy level differences and lifetimes, are accessible to high-precision experiments. Positronium properties can also be calculated theoretically to high precision. Consequently, positronium is an ideal system for testing the limits of electromagnetic bound state physics. The positronium hyperfine splitting--the interval between the spin-1 and spin-0 variants of the lowest energy state--is of prime interest because there is a long-standing difference (of about four times the experimental uncertainty) between theory and experiment for this splitting. The current proposal is to calculate the positronium hyperfine interval to a higher level. When complete, the result of this work will help to resolve or sharpen the positronium hyperfine discrepancy. This theoretical work is timely because two experimental groups, based at the University of California, Riverside and at the University of Tokyo, are developing improved experimental measurements of the hyperfine interval. The combination of improved experimental results and higher precision theory will work together to give bound-state Quantum Electrodynamics (QED) one of its most stringent tests to date. An important aspect of this project will be the training of undergraduate student collaborators in the techniques and processes of scientific investigation in this field. The overall project involves a number of distinct parts that will make ideal projects for small teams of students. The students will cooperate in all aspects of the work including the development of calculational techniques and tools, the calculations themselves, presentation at scientific meetings, and publication. Positronium properties will be calculated theoretically to high precision using the methods of bound-state Quantum Electrodynamics (QED) because strong and weak interaction effects are negligible. The positronium hyperfine interval will be calculated to a higher level of precision than heretofore by completing all three-loop corrections to the hyperfine interval. This will require an application of effective field theory methods, specifically Non-Relativistic QED (NRQED), at the three-loop order. When complete, the result of this work will help to resolve or sharpen the positronium hyperfine discrepancy.