Secluded Dark Composites and Remnant Binding Fields

Abstract

Dark matter may freeze-out and undergo composite assembly while decoupled from the Standard Model. In this secluded composite scenario, while individual dark matter particles may be too weakly-coupled to detect, the assembled composite can potentially be detected since its effective coupling scales with number of constituents. We examine models and observables for secluded composites, and in particular we investigate the cosmological abundance of the composite binding field, which is generated during freeze-out annihilation and secluded composite assembly. This binding field could be discovered as a new relativistic species in the early universe or through later interactions as a subdominant dark component.

Figures (7)

• Figure 1: Schematic cosmological energy densities, matching Boltzmann equation outputs, are shown as a function of the Standard Model radiation temperature $T$, for a secluded dark sector which can form composites out of equilibrium with the Standard Model. The secluded dark matter field $\chi$ annihilates solely to scalar field $\varphi$, leaving behind a residual dark matter density "$\chi,$ res". The energy densities of the symmetric dark matter, asymmetric dark matter residual, Standard Model radiation and light scalar $\varphi$ components are represented by the blue, red, orange, and green curves respectively. In the top left panel, we show the case where no DM composite forms for comparison. In all other panels, we set $m_X$ = 10 GeV, $\alpha$ = 0.1, and vary the mass of the light scalar $m_{\varphi}$ as indicated. The asymmetric residual population of $\chi$s form composites at a lower temperature, during which process the binding energy of the composites is emitted as $\varphi$. The initial residual dark matter density "$\chi$, res" is set so that matter-radiation equality is obtained at $T=0.8$ eV. The initial $\varphi$ and $\chi$ abundance are set to reflect having previously been in thermal equilibrium with the SM at high temperature.
• Figure 2: Left: Binding energy (in log scale) of two-body bound state, from Equation \ref{['eq:BE_twobody']}. Right: Number of constituents (log scale) for a strongly-bound composite state, from Equation \ref{['eq:num-const']}, assuming that the binding energy per constituent is $0.99 m_\chi$. (The actual binding energy per constituent, and the number of constituents per composite are given by Eqs. \ref{['eq:num-const']}, \ref{['eq:eff_mass']}.)
• Figure 3: Ratio of formation rate to decay rate as a function of constituent mass $m_{\chi}$ for $\alpha$ = 0.1 and $N$ = 10, where $\Gamma_{\mathrm{form}} = H(T_{\mathrm{form}})$, and the decay rate is computed using Eq. \ref{['eq:gamma_decay']}. We see that $\Gamma_{form}/\Gamma_{decay} \ll 1$, justifying the assumption that the composite decays rapidly into its ground state for composites considered in this work.
• Figure 4: $\Delta N_{\mathrm{eff}}$ at $\chi$-SM equality in $m_{\chi}$-$\alpha$ parameter space for different indicated values of $m_{\varphi}$ between 1 meV and 1 eV, for N-body composites that decay into their ground state quickly after forming. The gridded dark grey region is where $\alpha$ is below the minimum value required to form composites (absent some other attractive potential) and the solid grey region is where the composites form after matter-radiation equality. The coloured dashed lines show values for $\Bar{m}_{\chi}/m_{\chi}$, which increases as the ground state binding energy decreases. The region below the solid and dashed orange-red lines is excluded by 2$\sigma$ Planck bounds and by 2$\sigma$ projected CMB-S4 bounds on $N_{\mathrm{eff}}$ respectively. The thicker lines and darker grey region represent results for $T_{form}$ = BE/10, while the thinner lines and lighter grey region are for $T_{form}$ = BE/30; this range of formation temperatures corresponds to the uncertainty arising from Saha-type corrections to composite synthesis Gresham:2017cvl.
• Figure 5: The same as Figure \ref{['fig:Neff_vary_mphi']}, but for heavier $m_\varphi =10,\,100$ eV. Here we show the relative $\varphi-SM$ density, $\rho_{\varphi}/\rho_{SM}$ at matter-radiation ($i.e.$$\chi$-SM) equality. Here again it is assumed that the N-body composite decays into its ground state immediately after forming. The gridded dark grey region is where $\alpha$ is below the minimum value required to form composites, and the solid grey region is where the composite would form and decay after matter-radiation equality. The region below the orange-red line is where $\rho_{\varphi}/\rho_{SM}$$\geq$ 1, which is excluded by requiring matter-radiation equality occur at $T\sim$ eV. The thicker lines and darker grey region represent results for $T_{form}$ = BE/10, while the thinner lines and lighter grey region are for $T_{form}$ = BE/30; this range of formation temperatures corresponds to the uncertainty arising from Saha-type corrections to composite synthesis.