RUI: Calculation of Higher Order Corrections to Positronium Energy Levels

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Positronium is a bound state of an electron and its antiparticle, a positron. As such, it forms an "exotic atom," similar in many ways to the 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 in this system. Consequently, positronium is an ideal system for testing the limits of electromagnetic bound state physics. The activities involved in calculating the positronium energy levels will be of great educational value to the undergraduate students 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 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 one MHz, and experiments are presently being developed to significantly reduce some of these uncertainties. The 2S-1S transition is of particular interest because it has the smallest natural linewidth and thus the greatest potential for improvement. The ground state hyperfine splitting is of interest because the most precise experimental results are not in accord with current theory. These transition energies and more will be calculated to a new 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.