Theory of Light Hydrogenlike Bound States: Multiloop Corrections in Muonic and Electronic Atoms and Ions

基础研究的一个领域是研究类氢原子和外来原子（原子中一个粒子如电子被另一个粒子如介子取代）的能级。实验越来越精确，在越来越强的层次上检验理论。这为我们对这些系统的物理理解提供了一个测试。这个项目将计算理论和实验之间存在差异的系统的能级。本研究所获得的理论结果将应用于即将到来的关于介子和电子原子和离子的实验结果的分析。这种分析将得到更精确的基本物理常数，特别是质子半径，以及氘核和α粒子的半径。这些值将在计量学和核物理学中得到应用。新的理论表达式将用于新的CODATA分析基本物理常数。从基础研究到消费电子产品，每个科学课堂以及科学和工程的许多领域都使用基本常数的CODATA编译。参与这项研究的研究生和本科生将获得研究、计算机、解决问题和演讲技巧。研究生的研究活动有望导致博士论文。这个项目将促进国际合作，因为计划与外国科学家合作。拟议的研究结果将发表在经过评审的期刊上，将在国内和国际会议和讲习班上提出，并将用于研究生课程的教学。类氢束缚态的高精度量子电动力学是一个活跃的理论研究领域，其动力来自于惊人的实验进展和智力挑战。尽管在光、类氢束缚态理论方面取得了重大进展，但在这个项目中仍有许多具有挑战性的问题需要解决。寻找从理论上解释介子氢实验得到的质子电荷半径值与氢光谱学和电子-质子散射得到的质子电荷半径值之间的差异是主要目标之一。不管质子电荷半径的争议将如何解决，为了与当前和即将到来的实验结果相匹配，一个广泛的关于光介子原子和离子（介子氢、介子氘和介子氦离子）能量分裂的研究项目正在进行。在本研究中，非相对论性和相对论性量子电动力学的方法将应用于松散结合的两粒子系统。该研究的理论结果与其他作者的理论结果以及过去和正在进行的实验结果将使许多基本物理常数的更精确值的确定成为可能：质子电荷半径、里德伯常数、电子-介子和电子-质子质量比等。

An area of fundamental research is the study of the energy levels of hydrogen-like atoms and exotic atoms (atoms where one particle such as an electron is replaced by another such as a muon). Experiments have become more and more accurate, testing the theory at a stronger and stronger level. This supplies a test of our understanding of the physics of these systems. This project will calculate energy levels for systems where there have been discrepancies between theory and experiment. The theoretical results obtained in this research will find applications in the analysis of the forthcoming experimental results on muonic and electronic atoms and ions. This analysis will result in more precise values of the fundamental physical constants, especially the proton radius, as well as radii of the deuteron and alpha particles. These values will find applications in metrology and nuclear physics. New theoretical expressions will be used in the new CODATA analysis of the fundamental physical constants. In its turn CODATA compilations of the fundamental constants are used in every science classroom, and in numerous fields of science and engineering, from fundamental research to consumer electronics. Graduate and undergraduate students participating in this research will acquire research, computer, problem solving, and presentation skills. Research activity of a graduate student is expected to lead to a PhD thesis. This project will promote international collaboration, as collaboration with foreign scientists is planned. The results of the proposed research will be published in refereed journals, will be presented at domestic and international conferences and workshops, and will be used in teaching graduate courses.High precision quantum electrodynamics of hydrogenlike bound states is an active field of theoretical research, motivated both by spectacular experimental progress and the intellectual challenge. Despite significant progress in the theory of light, hydrogenlike bound states, there are a number of challenging problems in this field that are addressed in this project. Search for a theoretical explanation of the discrepancy between the value of the proton charge radius obtained from the experiment with muonic hydrogen and the proton charge radius derived from hydrogen spectroscopy and electron-proton scattering is one of the main objectives. Irrespective of the way the proton charge radius controversy will be resolved, an extensive program of research on energy splittings in light muonic atoms and ions (muonic hydrogen, muonic deuterium, and muonic helium ions) is in order to match current and forthcoming experimental results. Methods of nonrelativistic and relativistic quantum electrodynamics will be applied to loosely bound two-particle systems in the proposed research. Theoretical results of the proposed research together with the theoretical results of other authors and with the results of the past and ongoing experiments would allow the determination of more precise values for many fundamental physical constants: the proton charge radius, the Rydberg constant, electron-muon and electron-proton mass ratios, etc.