Energy-Momentum Tensor and Energy Levels of Loosely Bound States

The simplest atoms, those composed of only two elementary particles, are optimal systems for testing fundamental theories of physics in high precision experiments because they avoid additional complications which arise in three-, four- or many-body systems. Testing laws of nature with these “simplest atoms” requires making experimental measurements of observable properties with a high level of precision, followed by detailed comparison with correspondingly exhaustive calculations using fundamental theoretical principles. This project addresses several theoretical challenges in this field, including calculations of the precise energies of stationary states of muonium and positronium as well as calculations of various mechanical properties of loosely bound states in quantum electrodynamics. Results will be useful in the search for new physics beyond the Standard Model as well as for comparisons with processes in nuclear and particle physics, including the physics of heavy charmonia and pentaquarks. The results of this research also will be used in teaching graduate courses. The project will develop methods for calculation of high order three-loop spin-independent corrections to energy levels of muonium and positronium in high precision quantum electrodynamics. With the help of these methods, all hard three-loop spin-independent corrections to the energy levels in muonium and positronium will be calculated. A second goal of the project is the calculation of the two-loop electron mass as a matrix element of the trace of the energy-momentum tensor (including both the anomalous and non-anomalous terms). A third focus of the project is research on the properties of one-loop matrix elements of the energy-momentum tensor trace in loosely bound multiscale states, like those in muonic hydrogen. Research on the properties of the energy-momentum tensor of bound states has the potential to provide a new perspective on the calculation of radiative corrections to the energy levels of hydrogen, muonium and 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.