Impact of a resonance on thermal targets for invisible dark photon searches

Dark photons in the MeV to GeV mass range are important targets for experimental searches. We consider the case where dark photons $A^{\prime }$ decay invisibly to hidden dark matter $X$ through $A^{\prime }\to XX$. For generic masses, proposed accelerator searches are projected to probe the thermal target region of parameter space, where the $X$ particles annihilate through $XX\to A^{\prime }\to \mathrm{SM}$ in the early universe and freeze out with the correct relic density. However, if $m_{A^{\prime }}\approx 2m_X$, dark matter annihilation is resonantly enhanced, shifting the thermal target region to weaker couplings. For $\sim 10\%$ degeneracies, we find that the annihilation cross section is generically enhanced by 4 (2) orders of magnitude for scalar (pseudo-Dirac) dark matter. For such moderate degeneracies, the thermal target region drops to weak couplings beyond the reach of all proposed accelerator experiments in the scalar case and becomes extremely challenging in the pseudo-Dirac case. Proposed direct detection experiments can probe moderate degeneracies in the scalar case. For greater degeneracies, the effect of the resonance can be even more significant, and both scalar and pseudo-Dirac cases are beyond the reach of all proposed accelerator and direct detection experiments. For scalar dark matter, we find an absolute minimum that sets the ultimate experimental sensitivity required to probe the entire thermal target parameter space, but for pseudo-Dirac fermions, we find no such thermal target floor.

Figure 1

Thermal targets and accelerator search experiments. Solid black contours: Thermal target contours in dark photon parameter space $(m_{A^{\prime }},{\kappa }^2)$ for ${\alpha }_X=0.5$ in the nondegenerate cases with $m_{A^{\prime }}=3m_X$ and ${\epsilon }_R\equiv (m_{A^{\prime }}^2-4m_X^2)/(4m_X^2)=0.3$, and in the degenerate cases with ${\epsilon }_R={10}^{-n}$, where $n=1,2,\dots 6$. In the scalar case (top) the thermal relic contours reach a floor near ${\epsilon }_R={10}^{-6}$, where the thermal relic abundance requirement becomes inconsistent with the requirement that the dark photon decay is dominantly invisible. The ${\epsilon }_R={10}^{-5}$ contour is displayed in this plot, but is close enough to the ${\epsilon }_R={10}^{-6}$ contour that they appear to overlap. In the pseudo-Dirac case (bottom) the thermal relic contours extend to arbitrarily low values of ${\kappa }^2$ with appropriate choice of ${\epsilon }_R$, but we display only a small number of contours to avoid clutter. In the bottom left panel, the mass splitting is $\mathrm{\Delta }=0.1m_X$, and these models evade direct detection bounds. In the bottom right panel, $\mathrm{\Delta }=0$, which illustrates the effect of decreasing $\mathrm{\Delta }$ on the thermal target regions. Dotted black contours: Thermal target contours for $m_{A^{\prime }}=3m_X$ from relativistic treatments of freeze-out for the scalar [33] and pseudo-Dirac [11] cases. Gray shaded: Regions excluded by current bounds (see text). Dashed contours: Projected reaches of proposed dark photon and dark matter accelerator searches (see text).

Figure 2

Thermal targets and direct detection search experiments. Solid black contours: Thermal target contours as in Fig. 1, but in the direct detection parameter space $(m_X,{\overline{\sigma }}_e)$, where ${\overline{\sigma }}_e=(16\pi {\mu }_{X,e}^2\alpha {\kappa }^2{\alpha }_X)/(m_{A^{\prime }}^2+{\alpha }^2{m}_e^2{)}^2$ (see text). In the scalar case (left) a resonantly annihilating thermal relic may still be within reach of future nuclear recoil experiments. In the right panel we show only the lines for Majorana DM-nuclear scattering, with $m_T=0.936\mathrm{GeV}$; the thermal targets for DM-electron scattering scale approximately with the target mass squared, placing them far out of reach of current and proposed experiments. Dotted black contours: Relativistic thermal relic contours, as in Fig. 1. Gray shaded: Regions excluded by current bounds (see text). Colored contours: Projected reaches of proposed direct detection experiments (see text).