RUI: Calculation of Higher Order Corrections to Positronium Energy Levels

正电子是由电子和它的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，如能级和寿命，都可以通过高精度的实验得到。由于强相互作用和弱相互作用可以忽略不计，所以利用束缚态量子电动力学（QED）的方法也可以从理论上计算出正电子的性质。因此，正电子是一种理想的系统，用于测试QED束缚态物理的极限，并用于探索在这种高精度水平上理论和实验之间的一致或不一致的后果。计算正电子能级的活动对作为合作者参与这项工作的富兰克林马歇尔学院的本科生具有很大的教育价值。学生将学习比通常在本科阶段遇到的更高级的理论方法和计算技术。他们将通过做研究，在专业会议上展示他们的成果，以及在研究期刊上作为共同作者发表他们的工作，获得宝贵的经验。低洼态（n=1和n=2）的正电子能级测量的不确定度约为1兆赫，目前正在开发和进行实验，以显着降低这些不确定度。1S-2S转换特别有趣，因为它具有最小的自然线宽，因此具有最大的改进潜力。这些跃迁能量和更多的能量将被计算到一个新的和更高的精度水平。计算将基于低能量有效量子场论NRQED (Non-Relativistic QED)，该理论为正电子等非相对论性原子的研究提供了一个自然而有效的框架。该奖项反映了美国国家科学基金会的法定使命，并通过使用基金会的知识价值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.