Abstract
The secluded dark matter resides within a hidden sector and self-annihilates into lighter mediators which subsequently decay to the Standard Model (SM) particles. Depending on the coupling strength of the mediator to the SM, the hidden sector can be kinetically decoupled from the SM bath when the temperature drops below the mediator’s mass, and the dark matter annihilation cross section at freeze-out is thus possible to be boosted above the conventional value of weak interacting massive particles. We present a comprehensive study on thermodynamic evolution of the hidden sector from the first principle, using the simplest secluded vector dark matter model. Motivated by the observation of Galactic center gamma-ray excess, we take two mass sets ∼ mathcal{O} (80 GeV) for the dark matter and mediator as examples to illustrate the thermodynamics. The coupled Boltzmann moment equations for number densities and temperature evolutions of the hidden sector are numerically solved. The formalism can be easily extended to a general secluded dark matter model. We show that a long-lived mediator can result in a boosted dark matter annihilation cross section to account for the relic abundance. We further show the parameter space which provides a good fit to the Galactic center excess data and is compatible with the current bounds and LUX-ZEPLIN projected sensitivity. We find that the future observations of dwarf spheroidal galaxies offer promising reach to probe the most relic allowed parameter space relevant to the boosted dark matter annihilation cross section.
Highlights
Matter becomes nonrelativistic, its comoving number density is exponentially depleted through Boltzmann suppression and keeps the thermal equilibrium with the bath until freeze-out
To have a thorough understanding about the thermodynamics of the secluded dark matter from the first principle, we will study the simplest secluded vector dark matter model, taken as an example in which the vector dark matter and the mediator within the hidden sector are in thermal equilibrium with each other before freeze-out, but may be kinetically decoupled from the Standard Model (SM) bath at temperature T ∼ mX,S, depending on the couplings to the SM, where mX and mS are the masses of the DM and hidden scalar, respectively
Using the secluded vector dark matter model, we have presented a comprehensive study on thermodynamic evolutions of the hidden sector particles from the first principle
Summary
The simplest secluded vector dark matter can be made of the abelian gauge bosons, Xμ’s, which get the mass from the vacuum expectation value (VEV) of the hidden complex scalar field ΦS due to the spontaneously dark gauge symmetry UX (1) breaking, where the Z2 symmetry, Xμ → −Xμ and ΦS → Φ∗S, is imposed to stabilize the dark matter [17]. In the right panel of figure 1, the S particles with the width corresponding to α = 1 × 10−5 or 1 × 10−6 can be in thermal equilibrium with the bath when mX /T 0.4 or 3 (with mX =80 GeV) (see section 5(iv), where a more precise estimation is given). For the hidden scalar with a much smaller mixing angle α = 5 × 10−7 or 1 × 10−7, because the ratio of the Hubble cooling rate to heating rate, ∼ 2HnS(TS)TS/ ΓSneSq(T ) T , is much larger than 1 due to the fact that nS(TS)TS neSq(T )T for the nonrelativistic S (see figures 4 and 5), where nS(TS) is the number density of S at its temperature TS, and neSq(T ) is the equilibrium number density of S at the corresponding bath temperature T , the hidden scalar starts to undergo out-of-equilibrium decay at the cosmological time the S lifetime, (2H)−1 Γ−S 1.
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