NSF Award
2308792
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.<br/> <br/>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.<br/><br/>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.
