Nuclear physics from an expansion around the unitarity limit

U Van Kolck

doi:10.1088/1742-6596/966/1/012014

Abstract

Many features of the structure of nuclei can be understood in the unitarity limit, where the two-nucleon S waves have bound states at zero energy. In this limit, the only dimensionful parameter, which is needed for proper renormalization of the relevant effective field theory, is set by the triton binding energy. While the complexity of some many-body systems may stem from a profusion of distinct scales, this one three-body scale is sufficient to generate rich structures already in few-body systems due to the anomalous breaking of continuous to discrete scale invariance. I discuss how the spectra of light nuclei arise from a controlled, perturbative expansion around the unitarity limit. I also present some implications of discrete scale invariance for nuclear matter.

Highlights

What is essential in the physics of nuclei? Somehow a perfect plate of rigatoni alla genovese at La Colombaia on the beach in Ischia seemed to me the ideal occasion to ponder this question
In the last quarter of a century, the field-theoretical roots of this program have been revived by the use of effective field theory (EFT), in the form of Chiral EFT, the generalization of Chiral Perturbation Theory to systems with A ≥ 2 nucleons
I will argue that a good starting point is the limit where the A = 2 system is at unitarity and a single momentum scale Λ appears through the 3BF that ensures renormalizability for A ≥ 3 systems

Summary

Introduction

What is essential in the physics of nuclei? Somehow a perfect plate of rigatoni alla genovese at La Colombaia on the beach in Ischia seemed to me the ideal occasion to ponder this question. In most reports we do not even find leading-order (LO) results, because they are supposed to be so poor This was not the original goal of the EFT program. LO is supposed to provide an overall description of most low-energy observables —to represent the essential physics. I will argue that a good starting point is the limit where the A = 2 system is at unitarity and a single momentum scale Λ appears through the 3BF that ensures renormalizability for A ≥ 3 systems. This scale arises from the anomalous breaking of scale symmetry down to a residual discrete scale invariance (DSI), which determines the essential features of spectra and reactions. Our emphasis shifts from an accurate description of the NN system to an approximate description of three-, four- and hopefully more-nucleon bound states

Why two-body unitarity?

Conclusion