Thermal Relics in Hidden Sectors

TL;DR

This work investigates hidden-sector dark matter, focusing on the WIMPless framework where $m_X/g_X^2$ remains comparable to the SM WIMP ratio, yielding the correct thermal relic density despite diverse masses and couplings. The authors perform a model-independent analysis of BBN and CMB constraints allowing a temperature mismatch between sectors, and demonstrate that substantial hidden sectors are compatible if the hidden sector is sufficiently colder after reheating (quantified by $\xi_{RH}$). They then present a concrete 1-generation flavor-free MSSM-like hidden model with a stable hidden stau $X$ and compute the relic density by numerically solving the Boltzmann equation, showing that viable relic densities arise for $m_X$ spanning keV to TeV with $m_X \propto g_X^2$, and that connecting sectors do not generally overturn these results. The findings imply that WIMPless DM generalizes the WIMP paradigm to a nine-order mass range, linking collider- and astrophysical-era signals across a broad parameter space and motivating further exploration of small-scale structure, kinetic decoupling, and potential observational constraints such as Lyman-$\alpha$ data. Overall, the paper provides a robust framework showing hidden-sector thermal relics can naturally account for dark matter while remaining consistent with cosmological bounds.

Abstract

Dark matter may be hidden, with no standard model gauge interactions. At the same time, in WIMPless models with hidden matter masses proportional to hidden gauge couplings squared, the hidden dark matter's thermal relic density may naturally be in the right range, preserving the key quantitative virtue of WIMPs. We consider this possibility in detail. We first determine model-independent constraints on hidden sectors from Big Bang nucleosynthesis and the cosmic microwave background. Contrary to conventional wisdom, large hidden sectors are easily accommodated. A flavour-free version of the standard model is allowed if the hidden sector is just 30% colder than the observable sector after reheating. Alternatively, if the hidden sector contains a 1-generation version of the standard model with characteristic mass scale below 1 MeV, even identical reheating temperatures are allowed. We then analyze hidden sector freezeout in detail for a concrete model, solving the Boltzmann equation numerically and understanding the results from both observable and hidden sector points of view. We find that WIMPless dark matter indeed obtains the correct relic density for masses in the range keV < m_X < TeV. The upper bound results from the requirement of perturbativity, and the lower bound assumes that the observable and hidden sectors reheat to the same temperature and is raised to the MeV scale if the hidden sector is 10 times colder. WIMPless dark matter therefore generalizes the WIMP paradigm to the largest mass range possible for viable thermal relics and provides a unified framework for exploring dark matter signals across nine orders of magnitude in dark matter mass.

Figures (8)

• Figure 1: Bounds from BBN in the $(g^{h\, \text{BBN}}_{\text{light}}, g^{h\, \text{BBN}}_{\text{heavy}})$ plane, where $g^{h\, \text{BBN}}_{\text{light}}$ and $g^{h\, \text{BBN}}_{\text{heavy}}$ are the hidden degrees of freedom with masses $m < T^h_{\text{BBN}}$ and $T^h_{\text{BBN}} < m < T^h_{\text{RH}}$, respectively, for $\xi_{\text{RH}} \equiv T^h_{\text{RH}}/T_{\text{RH}} = 0.5$, 0.7, 0.8, 1.0 (from top to bottom). The regions above the contours are excluded. We assume that the observable sector reheats to a temperature above the mass of all MSSM particles. The values of $(g^{h\, \text{BBN}}_{\text{light}}, g^{h\, \text{BBN}}_{\text{heavy}})$ are marked for four example hidden sectors: (A) 1-generation and (B) 3-generation flavor-free versions of the MSSM with $T^h_{\text{BBN}} < m_X < T^h_{\text{RH}}$, and (C) 1-generation and (D) 3-generation flavor-free versions of the MSSM with $m_X < T^h_{\text{BBN}}/2$ (see Sec. \ref{['sec:concrete']}).
• Figure 2: As in Fig. \ref{['fig:gstar']}, but for bounds from the CMB in the $(g^{h\, \text{CMB}}_{\text{light}}, g^{h\, \text{CMB}}_{\text{heavy}})$ plane, where $g^{h\, \text{CMB}}_{\text{light}}$ and $g^{h\, \text{CMB}}_{\text{heavy}}$ are the hidden effective degrees of freedom with masses $m < T^h_{\text{CMB}}$ and $T^h_{\text{CMB}} < m < T^h_{\text{RH}}$, respectively. The values of $(g^{h\, \text{CMB}}_{\text{light}}, g^{h\, \text{CMB}}_{\text{heavy}})$ are given for four example hidden sectors: (C$^\prime$) 1-generation and (D$^\prime$) 3-generation flavor-free versions of the MSSM with $T^h_{\text{CMB}} < m_X < T^h_{\text{RH}}$, and (C$^{\prime\prime}$) 1-generation and (D$^{\prime\prime}$) 3-generation flavor-free versions of the MSSM with $m_X < T^h_{\text{CMB}}/2$ (see Sec. \ref{['sec:concrete']}).
• Figure 3: Evolution of $\xi = T^h/T$, the ratio of hidden to observable temperatures, for $m_X = 1~\text{GeV}$, 1 MeV, 1 keV and 1 eV, assuming $T_{\text{RH}}=50~\text{TeV}$, $\xi_{\text{RH}}=0.8$, and a hidden sector that is the 1-generation flavor-free version of the MSSM. For other $\xi_{\text{RH}}$, these curves are simply re-scaled by $\xi_{\text{RH}} / 0.8$. All supersymmetric particles in the observable sector are assumed to have mass around 1 TeV.
• Figure 4: $Y(x)$, the $\tilde{\tau}^h_R$ number density per comoving volume, as a function of $x \equiv m_X/T$, for $m_X = 1~\text{MeV}$, $g_X = 5.57 \cdot 10^{-4}$, and various ratios of hidden sector to visible sector reheating temperature $\xi_{\text{RH}} = 0.8$, 0.5 and 0.3 (from top to bottom).
• Figure 5: As in Fig. \ref{['fig:freezeout_xi']}, but now plotted in terms of the hidden sector parameters $Y^h(x^h)$.