Study of WIMP annihilations into a pair of on-shell scalar mediators

In this article, we focus on new scalar $\varphi$ mediated scalar/vectorial weakly interacting massive particles (WIMPs) with $\varphi$’s mass slightly below the WIMP mass. To explain the Galactic center 1–3 GeV gamma-ray excess, here we consider the case that a WIMP pair predominantly annihilates into an on-shell $\varphi \varphi$ pair with $\varphi$ mainly decaying to $\tau \overline{\tau }$. The masses of WIMPs are in a range about 14–22 GeV, and the annihilations of WIMPs are phase space suppressed today. In this annihilation scheme, the couplings of the $\varphi$-standard model (SM) particles are almost arbitrarily small, and the WIMP-nucleus spin-independent scattering can be tolerant by the present dark matter (DM) direct detections. A scalar mediator-Higgs field mixing is introduced, which is small and available. The lower limit on the couplings of the $\varphi$-SM particles set by the thermal equilibrium in the early Universe is derived, and this constraint is above the neutrino background for scalar DM in direct detections. The WIMPs may be detectable at the upgraded DM direct detection experiment in the next few years, and the exotic decay $h\to \varphi \varphi$, the production of $\varphi$ may be observable at the future high-luminosity $e^{+}{e}^{-}$ collider.

Figure 1

The process of $S{S}^{*}\to \varphi \varphi$.

Figure 2

The thermally averaged annihilation cross section of WIMPs with masses in the range 14–22 GeV. The solid-dotted curves are the results of $⟨{\sigma }_{ann}{v}_r{⟩}_f$, with the lower one, the upper one corresponding to the case of $\xi =0.994$, $\xi =0.998$, respectively. The dash-dotted curves are the results of $⟨{\sigma }_{ann}{v}_r{⟩}_0$, with the upper one, the lower one for the case of $\xi =0.994$, $\xi =0.998$, respectively.

Figure 3

The SI elastic cross section ${\sigma }_{\mathrm{el}}$ of WIMPs in a mass range 10–30 GeV. The solid curves from top to bottom are the upper limit set by LUX [3], the upper limit set by XENON1T [4], the lower limit set by the thermal equilibrium, the lower detection limit set by the neutrino background [62], respectively. The filled area is the allowed region of the elastic cross section in the potential mass range $m_S\sim 14–22\mathrm{GeV}$ of concern.

Figure 4

The main production processes of $\varphi$ at $e^{+}{e}^{-}$ collider.

Figure 5

The production cross section of $\varphi$ at the $e^{+}{e}^{-}$ collider with $m_{\varphi }=20\mathrm{GeV}$ and $\sqrt{s}$ varying in a range of 150–500 GeV. The solid curves, the dashed curves and the dash dotted curves are the production cross sections of the $\varphi$ strahlung, $WW$ fusion, and $ZZ$ fusion, respectively. In each type of curve, the upper one, the lower one are for the case of ${\sin }^2\theta ={10}^{-3}$, ${\sin }^2\theta =6.1\times {10}^{-4}/m_S^3$, respectively.

Figure 6

The $\varphi$ production cross section as a function of $m_{\varphi }$ with $m_{\varphi }$ varying in a range of 14–22 GeV at $\sqrt{s}=250\mathrm{GeV}$. The solid curves, the dashed curves and the dash dotted curves are the production cross sections of the $\varphi$ strahlung, $WW$ fusion, and $ZZ$ fusion, respectively. In each type curve, the upper one, the lower one are for the case of ${\sin }^2\theta ={10}^{-3}$, ${\sin }^2\theta =6.1\times {10}^{-4}/m_S^3$, respectively.

Figure 7

The production cross section of $\varphi$ as a function of $\sqrt{s}$ in the $\varphi$ strahlung process at $e^{+}{e}^{-}$ collider. The value ${\sin }^2\theta ={10}^{-3}$ is taken here, and $\sqrt{s}$ varies in a range of 115–200 GeV. The solid curve and the dashed curve are for the case of $m_{\varphi }=14\mathrm{GeV}$ and $m_{\varphi }=22\mathrm{GeV}$, respectively.