Over a century after Rutherford’s discovery of the nucleus, a complete theoretical understanding of the full range of nuclear phenomena remains elusive. To achieve this feat, physicists seek to solve the nuclear many-body problem, treating nuclear systems as quantum systems of protons and neutrons interacting according to the laws of nuclear physics. Naively, Quantum Chromodynamics (QCD) could provide a solution, as it is the sector of the Standard Model which deals with strong (and hence nuclear) interactions. However, the nonperturbative nature of QCD at the energy scales associated with nuclear physics means this is impossible in practice. Therefore, many different approaches have been proposed to model nuclear interactions and thus “solve” the nuclear many-body problem. Such models often require a trade-off between firm theoretical grounding versus wide applicability across the nuclear many-body landscape. Methods to limit the severity of this tradeoff and obtain a “best of both worlds” situation would greatly assist nuclear physicists, particularly in the study of exotic nuclear systems such as neutron star matter or super-heavy elements.
In this talk, we propose a method based on effective field theory (EFT). This technique is used in quantum field theory to approximate a Lagrangian by averaging out its high-energy behaviour to leave behind a simpler “effective Lagrangian” that remains accurate at low energies. We apply EFT to a one-meson exchange model of nuclear interactions. In doing so, we demonstrate that a popular approach to the nuclear many-body problem, the Skyrme energy density functional, can be partially derived as the low-energy effective field theory of our one-meson exchange model. The Skyrme functional is popular amongst nuclear physicists due to its relative simplicity and wide applicability across the nuclear landscape. However, it has many parameters, and these can only be phenomenologically fitted to experiment with little reference to theoretical grounding. Via EFT, we derive linear relations on these parameters and suggest simple constraints on their values. The results in the poorly-understood isovector spin-orbit sector are especially promising. These results suggest that effective field theory can be used to introduce theoretical grounding into models which are otherwise largely phenomenological. The next stage is to apply EFT to nuclear Lagrangians arising in the modern relativistic mean field theories, as well as study the consequences of higher-order loop expansions on the effective field theory with an eye to more complex nuclear phenomena such as saturation.