Effective field theories for collective excitations of atomic nuclei

TL;DR

This paper reviews how effective field theories provide a systematic, symmetry-based framework to describe low-energy collective excitations in atomic nuclei, enabling precise calculations with quantified uncertainties.

Contribution

It introduces an effective field theory approach to nuclear collective modes, clarifying their structure and allowing systematic improvements and uncertainty quantification.

Findings

Effective field theories accurately describe nuclear spectra and transition rates.

Predictions for neutrinoless double beta decay matrix elements include quantified uncertainties.

Comparison with traditional models and ab initio methods highlights the approach's advantages.

Abstract

Collective modes emerge as the relevant degrees of freedom that govern low-energy excitations of atomic nuclei. These modes - rotations, pairing rotations, and vibrations - are separated in energy from non-collective excitations, making it possible to describe them in the framework of effective field theory. Rotations and pairing rotations are the remnants of Nambu-Goldstone modes from the emergent breaking of rotational symmetry and phase symmetries in finite deformed and finite superfluid nuclei, respectively. The symmetry breaking severely constrains the structure of low-energy Lagrangians and thereby clarifies what is essential and simplifies the description. The approach via effective field theories exposes the essence of nuclear collective excitations and is defined with a breakdown scale in mind. This permits one to make systematic improvements and to estimate and quantify uncertainties. Effective field theories of collective excitations have been used to compute spectra, transition rates, and other matrix elements of interest. In particular, predictions of the nuclear matrix element for neutrinoless double beta decay then come with quantified uncertainties. This review summarizes these results and also compares the approach via effective field theories to well-known models and ab initio computations.