RUI: Calculation of Higher Order Corrections to Positronium Energy Levels

正电子素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，但由于其独特的组成和湮灭倾向而不同，转化为高能光子形式的纯电磁能。 正电子素的许多性质，如能级和寿命，都可以通过高精度实验获得。 正电子素的性质也可以用束缚态量子电动力学（QED）的方法在理论上进行高精度的计算，因为强弱相互作用的影响可以忽略不计。 因此，正电子素是一个理想的系统，可以用来测试QED束缚态物理的极限，并探索在这种高精度下理论和实验之间一致或不一致的后果。 参与计算正电子素能级的活动对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。 学生将学习理论方法和计算技术比通常在本科阶段遇到的更先进。 他们将通过做研究，通过准备和介绍他们的结果，并通过在研究期刊上发表他们的工作作为合著者获得宝贵的经验。正电子素能级将使用有效量子场论非相对论QED（NRQED）进行高精度计算。 NRQED适合于这项工作，因为原子系统（如正电子素）的典型能量和动量与电子静止能量相比很小。 发散将使用维数正则化来处理。 在NRQED中，能级可以作为电子-正电子到电子-正电子四点绿色函数的极点的位置，并且它们的值将使用束缚态微扰理论来计算。 反冲修正，这是小的原子，如氢，是大的正电子素，将形成一个主要的重点，这项工作。 反冲修正的计算将使用“部分积分”恒等式和最近在较低阶近似下对正电子偶素进行测试的相关方法进行。 改进的实验结果和更高精度的理论将联合收割机结合起来，使束缚态QED成为迄今为止最严格的测试之一。该奖项反映了NSF的法定使命，并被认为值得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来支持。

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.