Emission of Nambu-Goldstone bosons from the semilocal string network

TL;DR

The paper addresses the emission of massless Nambu-Goldstone bosons from a semilocal string network formed after breaking $SU(2)_{\\rm global} \\times U(1)_{\\rm gauge}$ to $U(1)_{\\rm global}$. It uses 3D lattice simulations in fat-string and physical-string regimes to show the network reaches a scaling regime and emits NG bosons with a spectrum peaked at the horizon scale, $k_{\\rm peak} \\sim \\alpha/\\ell_H$, with the comoving density $a^3 n_{\\rm NG}$ growing roughly as $a$ and $n_{\\rm NG} \\propto H$. The authors show that if NG bosons acquire mass by soft-breaking, they can form very light pseudo-NG dark matter with relic density $\\Omega_{NG} h^2 \\sim 0.2 (m_{NG}/10^{-13} \\mathrm{eV})^{1/2} (v/10^{14} \\mathrm{GeV})^{2}$, constraining viable regions. The results indicate potential suppression or modification of the gravitational-wave spectrum and provide a novel production channel for ultra-light dark matter, motivating further studies of GW signatures and related string configurations such as Z-strings.

Abstract

Semilocal cosmic string is a line-like non-topological soliton associated with the breakdown of the $SU(2)_{\rm global} \times U(1)_{\rm gauge}$ symmetry to the $U(1)_{\rm global}$ symmetry. The broken phase has two massless Nambu-Goldstone (NG) modes as dynamical fields, and they can be emitted by semilocal strings. In this paper, we numerically show that such NG bosons are copiously produced with the evolution of the semilocal string network in the early universe. Our numerical analysis shows that the spectrum of produced particles has a peak at low momenta corresponding to the horizon scale. If the emitted NG bosons acquire mass due to soft-breaking terms, they can take the role of dark matter. This scenario typically predicts very light pseudo NG boson dark matter.

Figures (6)

• Figure 1: Snapshots of the semilocal string network for the fat string regime. Time evolves from left to right.
• Figure 2: Time evolution of the mean string separation for the semilocal string (red) and the Abelian-Higgs string (blue) in the fat/physical string regime (top/bottom panel). We have taken $\lambda = 0.025$ and $q = 1$ ($\beta = 0.05$). The solid curve and shaded region represent respectively the mean value and 1-$\sigma$ error with 10 independent simulations.
• Figure 3: Time evolution of the comoving number density of two NG modes for the fat/physical string regime in the top/bottom panel. The solid curve and shaded region represent respectively the mean value and 1-$\sigma$ error with 10 independent simulations. The dashed line is the linear fitting line, $Av\tau + B$ with $(A,B) = (0.6,-150)$ (top), $(0.6,-7.5)$ (bottom). We have taken $\lambda = 0.025$ and $q = 1$ ($\beta = 0.05$).
• Figure 4: Evolution of the spectrum of NG modes in the fat string case for $v\tau = 29$-$1045$ with the interval $v\Delta \tau = 64$. Time evolves from bottom to top and the thick black line corresponds to the final time.
• Figure 5: Spectra of the comoving number density for two NG modes, $\vartheta$ (solid red) and $\theta_-$ (solid blue), and the radial mode, $\varphi_r$ (dashed magenta), at the final time of the simulation in the fat/physical string regime (top/bottom panel). The solid curve and shaded region represent respectively the mean value and 1-$\sigma$ error with 10 independent simulations.