Stable bi-frequency spinor modes as Dark Matter candidates

TL;DR

This work analyzes nonlinear spinor fields with scalar self-interaction, showing that bi-frequency solitary waves arise generically in models such as the Soler equation and the Dirac--Klein--Gordon system. It develops a linear stability framework via radial reduction, linking bi-frequency stability to one-frequency stability through SU(1,1) symmetry in key configurations, and provides detailed numerical spectra in (3+1)D indicating broad stability windows. The findings suggest that dynamically stable bi-frequency spinor states could serve as Dark Matter storages, with the DKG system reducing to NLD in the heavy-boson limit, supporting the physical relevance of the results. Together, these contributions advance the understanding of spinor solitons and their potential DM phenomenology while offering concrete criteria for stability across parameter ranges.

Abstract

We show that spinor systems with scalar self-interaction, such as the Dirac--Klein--Gordon system with Yukawa coupling or the Soler model, generically have bi-frequency solitary wave solutions. We develop the approach to stability properties of such waves and use the radial reduction to show that indeed the (linear) stability is available for a wide range of parameters. We show that only bi-frequency modes can be dynamically stable and suggest that stable bi-frequency modes can serve as storages of the Dark Matter. The approach is based on linear stability results of one-frequency solitary waves in (3+1)D Soler model, which we obtain as a by-product.

Figures (3)

• Figure 1: Imaginary (top) and real (bottom) parts of the spectrum for $\ell=0,\,1$ (left) and $\ell=2$ (right) as functions of $\omega\in(0.1,1)$.
• Figure 2: Spectrum for $\ell=3$ (left) and $\ell=4$ (right). Dashed black lines refer to quadruplets of eigenvalues with $\mathop{\rm{R e}}\nolimits\lambda\ne 0$ bifurcating from the thresholds $\pm\mathrm{i}(1-\omega)$ (possibly a numerical artifact).
• Figure 3: Value $\omega_p$ of the pitchfork bifurcation for perturbations from $\mathscr{X}_{\ell,m}$.