Darker matter generating from the dark

TL;DR

This work investigates a two-step freeze-in framework where dark matter resides in a darker hidden sector that is itself generated from a feebly connected hidden sector. It provides a concrete two-$U(1)$ extension of the Standard Model, develops a coupled Boltzmann formalism for the evolution of multiple hidden sectors, and demonstrates that dark matter from the second hidden sector can constitute nearly all of the observed relic density while exhibiting velocity-dependent self-interactions. A key result is that a dark photon in the second hidden sector, with ultraweak couplings, can decay to $e^+e^-$ and potentially explain the galactic 511 keV line in concordance with various density profiles. The framework yields a coherent, testable scenario for dark matter with strong internal dynamics and distinctive indirect-detection signatures, motivating further exploration of multi-hidden-sector cosmology and associated constraints.

Abstract

The non-detection of dark matter may be attributed to the dark matter residing in a darker hidden sector. We explore the possibility that a hidden sector produced through the freeze-in mechanism, can further generate an even more hidden sector via an additional freeze-in process. Such a two-step freeze-in process produces dark matter coupled weaker-than-ultraweakly to the standard model particles, and is thus referred to as the "darker matter". To illustrate the two-step freeze-in process, we study a model featuring two $U(1)$ hidden sectors. The first $U(1)$ sector is directly coupled to the standard model with feeble interactions, while the second $U(1)$ sector is directly coupled to the first $U(1)$ sector and thus only indirectly to the standard model, rendering it darker. Remarkably, darker matter candidates residing in the second darker $U(1)$ sector, generated from the two-step freeze-in process, can account for almost the entire observed dark matter relic density. The darker matter, interacted with standard model particles through ultraweak couplings, can exhibit velocity-dependent self-interacting cross-sections, which potentially provides an explanation for addressing problems associated with cosmic small-scale structures. Additionally, the dark photon darker matter residing in the darker hidden sector can be responsible for the galactic 511 keV photon signal, consistent with various dark matter density profiles.

Figures (6)

• Figure 1: A graphic illustration of a general two-$U(1)$ model we discuss. The $U(1)_{1}^{\prime}$ hidden sector connects to the SM and the second hidden sector $U(1)_{2}^{\prime}$ via kinetic mixing characterized by parameters $\delta_{1}$ and $\delta_{2}$. Thus $U(1)_{2}^{\prime}$ couples to the SM indirectly and with the strength proportional to $\delta_1\times \delta_2$. $U(1)_{1}^{\prime}$ sector particles are produced via freeze-in processes from SM particles while $U(1)_{2}^{\prime}$ particles are produced via freeze-in mostly from the $U(1)_{1}^{\prime}$ sector. Each $U(1)$ hidden sector possesses a different temperature $T_{h1},T_{h2}$ respectively, related to the visible sector temperature $T_{v}$ through functions $\eta(T_{h1})= T_{v}/T_{h1}$ and $\zeta(T_{h1})= T_{h2}/T_{h1}$. The dark matter candidates are a combination of $\chi_{1},\chi_{2},\gamma_{2}^{\prime}$, and $\chi_{2},\gamma_{2}^{\prime}$ from the $U(1)_{2}^{\prime}$ sector are the darker matter candidates. The dark photon $\gamma^\prime_2$ from the $U(1)_2$ sector may potentially account for the galactic 511 keV signal.
• Figure 2: [Color online] An exhibition of the evolution of a dark $U(1)_1$ sector and a darker $U(1)_2$ sector, for models $y$ (left) and $z$ (right). The upper panels for the two plots show the evolution of the comoving number densities of all dark particles in two $U(1)$ hidden sectors, and the lower panels of the two plots present the interaction rates of hidden sector interactions compared with the Hubble parameter. The red horizontal dash line denotes the observed dark matter relic density for fermion darker matter in the upper panels, and the purple horizontal dash line denotes the observed dark matter relic density for the dark photon darker matter in the upper panels. Thus the darker matter $\chi_2$ and $\gamma^\prime_{2}$ originating from the darker hidden sector are respectively the major component of the dark matter for models $y$ and $z$. In the lower panels, interaction rates for the most important interactions within the hidden sectors as well as the Hubble expansion rate versus temperature are presented.
• Figure 3: The hidden sector temperature evolutions of the $U(1)_1$ and $U(1)_2$ sectors for models $x,y,z$ are shown. The $U(1)_1$ hidden sector, being directly connected to the SM, thermalized with the visible Universe first; while the $U(1)_2$ hidden sector, which is only indirectly coupled to the SM and features a weaker-than-ultraweak connection, thermalized later compared to the $U(1)_1$ sector.
• Figure 4: [Color online] An exhibition $\langle\sigma_{T}v_{r}\rangle/m_{\chi}$ for the self-interacting darker matter $\chi_2$ as a function of the averaged relative velocity $\langle v_{r} \rangle$ for model $y$. Data points with error bars from measurements are colored as: LSB galaxies (blue), dwarf galaxies (red), and clusters (yellow). The diagonal gray lines correspond to constant values $\sigma/m_{\chi}$ = 0.1, 1 and 10 ${\rm cm^{2}/g}$, respectively.
• Figure 5: [color online] A display of current experimental constraints (colored regions) on the kinetic mixing parameter. We also include the constraint from 511 keV signal discussed in Section \ref{['Sec:SN-FIPs']} (the region in red) Calore:2021lih. This constraint is valid for a dark photon that can decay only into $e^+e^-$. Benchmark models $a$ and $b$ fall into this category, thus we choose parameters outside this red region. In benchmark models $c$-$g$, the dark photon $\gamma_1^\prime$ can also decay into dark matter, allowing this constraint to be circumvented. Hence, we can safely choose parameter values within the red region.