Positronium is the bound state of the electron and its antiparticle, the 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 level differences and lifetimes, are accessible to high-precision experiments. Positronium properties can also be calculated theoretically to high precision. Consequently, positronium is an ideal system for testing the limits of electromagnetic bound state physics. The positronium hyperfine splitting--the interval between the spin-1 and spin-0 variants of the lowest energy state--is of prime interest because there is a long-standing difference (of about four times the experimental uncertainty) between theory and experiment for this splitting. The current proposal is to calculate the positronium hyperfine interval to a higher level. When complete, the result of this work will help to resolve or sharpen the positronium hyperfine discrepancy. This theoretical work is timely because two experimental groups, based at the University of California, Riverside and at the University of Tokyo, are developing improved experimental measurements of the hyperfine interval. The combination of improved experimental results and higher precision theory will work together to give bound-state Quantum Electrodynamics (QED) one of its most stringent tests to date. An important aspect of this project will be the training of undergraduate student collaborators in the techniques and processes of scientific investigation in this field. The overall project involves a number of distinct parts that will make ideal projects for small teams of students. The students will cooperate in all aspects of the work including the development of calculational techniques and tools, the calculations themselves, presentation at scientific meetings, and publication.
Positronium properties will be calculated theoretically to high precision using the methods of bound-state Quantum Electrodynamics (QED) because strong and weak interaction effects are negligible. The positronium hyperfine interval will be calculated to a higher level of precision than heretofore by completing all three-loop corrections to the hyperfine interval. This will require an application of effective field theory methods, specifically Non-Relativistic QED (NRQED), at the three-loop order. When complete, the result of this work will help to resolve or sharpen the positronium hyperfine discrepancy.
