Nuclear Structure of Bound States of Asymmetric Dark Matter

TL;DR

This paper systematically analyzes the properties of bound states of asymmetric dark matter, called nuggets, using relativistic mean field theory to describe their profiles, binding energies, and regimes of behavior across different sizes and force parameters.

Contribution

It introduces a comprehensive relativistic mean field approach to compute nugget properties across various regimes, extending beyond previous non-relativistic models.

Findings

Identification of three regimes of nugget behavior: non-relativistic, relativistic Coulomb-like, and saturation.

Analytical descriptions for each regime of nugget properties.

Numerical confirmation of analytical models and transition behaviors between regimes.

Abstract

Models of Asymmetric Dark Matter (ADM) with a sufficiently attractive and long-range force gives rise to stable bound objects, analogous to nuclei in the Standard Model, called nuggets. We study the properties of these nuggets and compute their profiles and binding energies. Our approach, applicable to both elementary and composite fermionic ADM, utilizes relativistic mean field theory, and allows a more systematic computation of nugget properties, over a wider range of sizes and force mediator masses, compared to previous literature. We identify three separate regimes of nugget property behavior corresponding to (1) non-relativistic and (2) relativistic constituents in a Coulomb-like limit, and (3) saturation in an anti-Coulomb limit when the nuggets are large compared to the force range. We provide analytical descriptions for nuggets in each regime. Through numerical calculations, we are able to confirm our analytic descriptions and also obtain smooth transitions for the nugget profiles between all three regimes. We also find that over a wide range of parameter space, the binding energy in the saturation limit is an ${\cal O}(1)$ fraction of the constituent's mass, significantly larger than expectations in the non-relativistic case. In a companion paper, we apply our results to synthesis of ADM nuggets in the early Universe.