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作为这项工作合作者的富兰克林和马歇尔学院的本科生具有很大的教育价值。学生将学习比本科水平更高级的理论方法和计算技术。他们将通过做研究，通过准备和发表演讲描述他们的结果，并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。利用有效量子场论非相对论QED(NRQED)，可以高精度地计算正电子的能级。NRQED适合于这项工作，因为与电子静止能量相比，正电子等原子系统的典型能量和动量都很小。分歧将使用维度正则化来处理。在NRQED中，能级可以用电子-正电子-电子-正电子四点格林函数的极点位置来确定，其数值将用束缚态微扰理论来计算。反冲修正对于氢等原子来说很小，但在正电子中却很大，这将成为这项工作的主要焦点。反冲修正的计算将使用最近在较低近似级数下测试正电子的“部分积分”恒等式和相关方法来执行。改进的实验结果和更高的精度理论将结合在一起，使束缚态QED成为迄今为止最严格的测试之一。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 this 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 preparing and giving presentations describing their results, and by publishing their work as co-authors in research journals. Positronium energy levels will be calculated to high precision using the effective quantum field theory Non-Relativistic QED (NRQED). NRQED is appropriate for this work because the energies and momenta typical of atomic systems such as positronium are small compared to the electron rest energy. Divergences will be dealt with using dimensional regularization. Energy levels can be found as the positions of the poles of the electron-positron to electron-positron four-point Green's function and their values will be calculated using bound-state perturbation theory in NRQED. Recoil corrections, which are small for atoms such as hydrogen, are large in positronium and will form a major focus of this work. Calculations of recoil corrections will be performed using the "integration by parts" identities and related methods that have recently been tested for positronium at a lower order of approximation. Improved experimental results and higher precision theory will combine to give bound-state QED one of its most stringent tests to date.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.