This work details how to use the Point-Particle Effective Field Theory (PPEFT) framework to make predictions for the nuclear-size contributions to spectroscopic transitions of atoms without the overbearing large uncertainties generally associated with such effects. After a lightning review of Quantum Field Theories, Effective Field Theories and their model-building algorithms, the backbones of the PPEFT formalism are laid down by considering the low-energy effective theories of lumps. Then, by drawing an analogy between a certain type of lumps and a freely propagating point-particle we build a PPEFT for nuclei, which we gradually couple to gauge and fermionic fields. We find that the consequences of having a nucleus in our theory are captured by a set of new near-nucleus boundary conditions its action implies for the surrounding fields, set up on a Gaussian spherical boundary with arbitrary radius, $\epsilon$. Afterwards, we use this formalism to derive the effects of the finite size of the nucleus on bound-state energies in terms of Renormalization Group (RG)-invariant parameters that characterize the running of the PPEFT couplings in $\epsilon$, implied by these new boundary conditions in order to keep physical quantities independent of this fictitious scale. Surprisingly, when comparing to formulae from the literature that express these same energy shifts in terms of nuclear moments there always appear to be fewer RG-invariants than moments. By fitting these handful of parameters using experimental data we then reduce the errors in nuclear-size effect predictions for other transitions by writing them in terms of differences between spectroscopic measurements and their corresponding energy differences predicted by those bound-state Quantum Electrodynamics calculations that assume nuclei to be point-like. Finally, we apply this algorithm to the systems: ${}^4_2 {\rm He}^+$, $\mu \, {}^4_2 {\rm He}^+$, H, and $\mu$H, where we make such predictions. / Thesis / Doctor of Philosophy (PhD) / The finite size of the nucleus shifts the bound-state energy of electrons (or muons) in atoms. Although these effects had been captured through a large number of nuclear-model independent ``nuclear moments'' closely related to the extent of the nucleus in the past, they introduce large uncertainties into theoretical predictions, which hinders testing fundamental subatomic processes in spectroscopic measurements. In this work it is shown that there is a more manageable number of parameters that control these effects because the above moments always appear in specific combinations. This allows for trading these combinations for differences between experimental values and their theoretically expected ones that assume the nucleus to have no size, which is the key in making predictions for atomic transitions that do not suffer from the large nuclear errors. A large set of such predictions are made for Hydrogen and the principles are applied to its muonic cousin as well.
| Identifer | oai:union.ndltd.org:mcmaster.ca/oai:macsphere.mcmaster.ca:11375/25845 |
| Date | January 2020 |
| Creators | Zalavari, Laszlo |
| Contributors | Burgess, Clifford, Physics and Astronomy |
| Source Sets | McMaster University |
| Language | English |
| Detected Language | English |
| Type | Thesis |
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