Massive hidden photons as lukewarm dark matter

TL;DR

This work investigates keV–MeV mass hidden photons that couple to the Standard Model mainly through kinetic mixing with the photon as lukewarm dark matter candidates. By incorporating plasma effects on the photon self-energy, the authors show that resonant production occurs when the plasma mass satisfies $m_\gamma(T_r)=\mu$, yielding a relic abundance that is largely independent of $\mu$ and is strongly constrained by decays and stellar bounds. They derive decay rates, cosmological and gamma-ray bounds, and stellar limits, concluding that hidden photons cannot constitute the observed dark matter under kinetic mixing alone, unless another production mechanism operates. They also discuss non-renormalizable operators that could dominate production in the early Universe, potentially restoring some parameter space. Overall, the paper places stringent constraints on HP dark matter scenarios and highlights UV-dependent production pathways as possible loopholes.

Abstract

We study the possibility that a keV-MeV mass hidden photon (HP), i.e. a hidden sector U(1) gauge boson, accounts for the observed amount of dark matter. We focus on the case where the HP interacts with the standard model sector only through kinetic mixing with the photon. The relic abundance is computed including all relevant plasma effects into the photon's self-energy, which leads to a resonant yield almost independent of the HP mass. The HP can decay into three photons. Moreover, if light enough it can be copiously produced in stars. Including bounds from cosmic photon backgrounds and stellar evolution, we find that the hidden photon can only give a subdominant contribution to the dark matter. This negative conclusion may be avoided if another production mechanism besides kinetic mixing is operative.

Figures (4)

• Figure 1: Differential production rate of hidden photons for three different masses. For $\mu =10 m_e$ (right) the low temperature production through electron-positron coalescence dominates the final abundance, the resonance not being extremely peaked. Coalescence happens only for $T \lesssim 3 \mu$ because for higher temperatures the electron thermal mass is too high. Production of HPs of higher masses proceeds very much in the same way. For $\mu =m_e$ (center) coalescence is never possible, and the low temperature production suffers a ${\cal O}(\alpha)$ decrease since it is now dominated by Compton scattering and pair annihilation. The resonance is more peaked, dominating production. Finally for $\mu =m_e/3$ (left) the resonance has grown very large with respect to the low temperature production; the production rate is suppressed by the lack of ambient electrons.
• Figure 2: Plotted is the function $j = \frac{T}{m_\gamma^2} \frac{{\rm d} m_\gamma^2}{{\rm d} T}$ as a function of the temperature in units of electron mass. The resonant yield $Y_2$ is inversely proportional to $j$, see \ref{['Y2_inter']}.
• Figure 3: Bounds on hidden photons in the mass-mixing plane. HPs that reproduce the right amount of DM lie on the line $\Omega_2 h^2=0.1$ and the region above is excluded by overproduction. Above the thin dashed line HPs will interact strongly enough to reach thermal equilibrium with the standard bath. The regions labeled Sun and HB are excluded by an excessive HP luminosity in the sun respectively in horizontal branch stars in globular clusters. In the region labeled IDPB the HP decay products exceed the intergalactic diffuse photon background. This bound assumes that the HP relic density is created through the kinetic mixing as discussed in this paper. If one assumes other production mechanisms that lead to $\Omega_2 h^2=0.1$ independently of $\chi$ the bound extends all down to the light yellow region. We find no bounds above $\mu >2 m_e\simeq 1$ MeV. Also shown are regions where the HP decay could influence different cosmological epochs: pre-BBN ($\tau<1$ sec), BBN ($1$ sec$<\tau<3$ min) and post BBN ($3$ min$<\tau<10^6$ sec), CMB-unprotected ($10^6$ sec$<\tau<10^{12}$ sec), CMB decoupled until now ($10^{12}$ sec$<\tau< 4.3\times 10^{17}$ sec ). See the text for details.
• Figure 4: Cosmological constraints on a massive particle of mass $\mu$ decaying into SM particles with a lifetime $\tau$ and a relic number density $n_{\gamma'}$. Above the thick solid black line the decay products spoil successful nucleosynthesis Ellis:1990nb producing hadronic showers if $\mu \gtrsim 1$ GeV (below $\tau= 10^4$ s) and electromagnetic cascades if $\mu \gtrsim 5-30$ MeV (above $\tau=10^{4}$ s). The thick short-dashed line comes from a more recent calculation Kawasaki:2000qr. Distortions of the CMB spectrum would be noticeable above the long-dashed line Ellis:1990nb. Our predictions for hidden photons for different masses $\mu > 2m_e$ are shown as thin lines.