Point-Particle Effective Field Theory and the Helium Ion

Abstract

This thesis develops a new class of effective field theories to treat systems with localized relics of high energy physics (e.g., nuclei in atomic systems), which ultimately act as point- like sources for the light fields of interest. In contrast to previous efforts to treat this problem, our Point-Particle Effective Field Theory identifies the low-energy degrees of freedom of the point-like relic in position space, resulting in a theory where the heavy source is described by a first-quantized coordinate, while the light fields are still fully second-quantized. This more efficiently prunes out the excess degrees of freedom inherited from the high-energy physics, and leads to a simpler treatment of the remaining fields. We find the internal physics of the heavy object to be fully encoded in a near-source boundary condition on the modefunctions of the light field. We show how this program allows a consistent treatment of ambiguous potentials generated by the source, with emphasis on the infamous inverse-square potential, and address its consequences for non-relativistic scalar, relativistic scalar, and Dirac fermionic light fields. Finally, we apply our results to the 4He+ ion, where large errors from nuclear modelling present an obstruction to precision tests of the Standard Model. It is found through our boundary condition that nuclear effects perturb energy levels through fewer independent parameters than previously thought. Using this observation, we introduce (and implement) a scheme to make predictions for future spectroscopic experiments that avoid altogether the necessarily large errors from nuclear theory.