RUI: Calculation of Higher Order Corrections to Positronium Energy Levels

正电子是由电子及其反粒子--正电子组成的束缚系统。因此，它形成了一种“奇异原子”，在许多方面与氢和氦等传统的简单原子相似，但由于其独特的组成和湮灭的倾向而不同，它以高能光子的形式转化为纯粹的电磁能量。正电子素的许多性质，如能级和寿命，都可以通过高精度的实验获得。由于强相互作用和弱相互作用的影响可以忽略不计，用束缚态量子电动力学(QED)的方法也可以从理论上高精度地计算正电子素的性质。因此，对于测试QED束缚态物理的极限，以及在如此高的精度下探索理论和实验之间一致或不一致的后果，正电子是一个理想的系统。计算正电子能级所涉及的活动将对参与这项工作的富兰克林和马歇尔学院的本科生具有重大的教育价值。学生将学习比本科水平更高级的理论方法和计算技术。他们将通过进行研究，通过在专业会议上展示他们的结果，以及通过在研究期刊上作为合著者发表他们的工作来获得宝贵的经验。已经测量了低激发态(n=1和n=2)的正电子能级，其不确定度约为1 MHz，目前正在开发和进行实验，以显著减少其中一些不确定度。1S-2S转换特别令人感兴趣，因为它具有最小的自然线宽，因此改进潜力最大。这些跃迁能量和更多的能量将被计算到一个新的更高的精度水平。计算将基于低能有效量子场理论NRQED(非相对论QED)，该理论为研究正电子等非相对论原子提供了一个自然而有效的框架。这一奖项反映了NSF的法定使命，并通过使用基金会的智力优势和更广泛的影响审查标准进行评估，被认为值得支持。

Positronium is the bound system consisting of the electron and its antiparticle, the positron. As such, it forms an “exotic atom”, similar in many ways to 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 levels and lifetimes, are accessible to high-precision experiments. Positronium properties can also be calculated theoretically to high precision using the methods of bound-state Quantum Electrodynamics (QED) because strong and weak interaction effects are negligible. Consequently, positronium is an ideal system for testing the limits of QED bound state physics and for exploring the consequences of agreement or disagreement between theory and experiment at this high level of precision. The activities involved in calculating the positronium energy levels will be of great educational value to the undergraduate students at Franklin & Marshall College involved as collaborators in that work. The students will learn theoretical methods and techniques of calculation more advanced than those usually encountered at the undergraduate level. They will gain valuable experience by doing the research, by presenting their results at professional meetings, and by publishing their work as co-authors in research journals. Positronium energy levels of low-lying states (n=1 and n=2) have been measured with uncertainties of roughly 1 MHz, and experiments are presently being developed and performed to significantly reduce some of these uncertainties. The 1S-2S transition is of particular interest because it has the smallest natural line-width and thus the greatest potential for improvement. These transition energies and more will be calculated to a new and higher level of precision. The calculations will be based on the low-energy effective quantum field theory NRQED (Non-Relativistic QED), which provides a natural and efficient framework for the study of non-relativistic atoms such as positronium.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.