Vector fermion-portal dark matter: Direct detection and Galactic Center gamma-ray excess

We investigate a neutral gauge boson $X_{\mu }$ that originates from a hidden $U(1)$ extension of the standard model as the particle dark matter candidate. Vector dark matter interacts with the standard model fermions through heavy fermion mediators. The interactions give rise to a $t$-channel annihilation cross section in the $XX\to f\overline{f}$ process, which dominates the thermal relic abundance during thermal freeze-out and produces measurable gamma-ray flux in the galactic halo. For a light vector dark matter, if it predominantly couples to the third-generation fermions, this model could explain the excess of gamma rays from the Galactic Center. We show that vector dark matter with a mass of $\sim 20–40\mathrm{GeV}$ and which annihilates into the $b\overline{b}$ and $\tau \overline{\tau }$ final states provides an excellent description of the observed gamma-ray excess. The parameter space aimed at explaining the gamma-ray excess could also provide the correct thermal relic density and is compatible with the constraints from electroweak precision data, Higgs invisible decay, and collider searches. We show the dark matter couplings to the nucleon from the fermion portal interactions are loop suppressed, and only contribute to the spin-dependent cross section. Therefore vector dark matter could easily escape the stringent constraints from the direct-detection experiments.

Figure 1

(a) The relic density contours for several scalar couplings $g_{\varphi }{c}_{\phi }{s}_{\phi }$ in the dark matter mass $m_X$ vs $g_{Xb}$ plane in the quark-portal model. At the same time, we fix $m_{b^{\prime }}=900\mathrm{GeV}$ and $m_S=500\mathrm{GeV}$. (b) The relic density contours for several mediator masses $m_{{\tau }^{\prime }}$ in the dark matter mass $m_X$ vs $g_{X\tau }$ plane in the lepton-portal model. Here we take $g_{\varphi }{c}_{\phi }{s}_{\phi }=0.05$ and $m_S=500\mathrm{GeV}$.

Figure 2

The relic density contours in the fermion-portal model. (a) The contours of the $(m_X,g_{X\tau })$ plane for several $g_{Xb}$ couplings. (b) The contours of the $(g_{Xb},g_{X\tau })$ plane for several dark matter masses $m_X$. Here the mediator masses are fixed to be $m_{b^{\prime }}=900\mathrm{GeV}$, $m_{{\tau }^{\prime }}=250\mathrm{GeV}$, and the scalar parameters are chosen to be $g_{\varphi }{c}_{\phi }{s}_{\phi }=0.05$ and $m_S=500\mathrm{GeV}$.

Figure 3

The one-loop effective trilinear vertex ${\mathrm{\Gamma }}^{\mu \nu \rho }$ between vector dark matter and the photon or the $Z$ boson. The fermions that appear in the loop are the SM fermions $f$ and corresponding mediators $F$. Here the mediators are the ${\tau }^{\prime }$, the $b^{\prime }$, and the $t^{\prime }$. In Feynman diagram (a), $F$ attaches to the photon and the $Z$ boson, while $f$ attaches to the photon and the $Z$ boson in (b).

Figure 4

One-loop Feynman diagrams (a)–(c) show vector dark matter scattering off the gluon in direct detection. The fermions that appear in the loop are the SM fermions $f$ and corresponding mediators $F$. Here the mediator $F$ can only be the $b^{\prime }$ and the $t^{\prime }$.

Figure 5

The allowed parameter spaces at the 90% confidence level from the exclusion limits of the spin-independent cross section. (a) The allowed regions of the coupling $g_{\varphi }{c}_{\phi }{s}_{\phi }$ vs the dark matter mass $m_X$ plane, for three different values of the scalar masses, in the lepton-portal model. (b) The allowed regions of the coupling $g_{\varphi }{c}_{\phi }{s}_{\phi }$ vs the dark matter mass $m_X$ plane, for three different values of the couplings $g_{Xb}$, in the quark-portal model. We choose $m_S=500\mathrm{GeV}$ and $m_{b^{\prime }}=900\mathrm{GeV}$ to fix the box-diagram contributions in the quark-portal model. The allowed region in the fermion-portal model is the same as the one in (b).

Figure 6

The allowed parameter spaces at the 90% confidence level from the exclusion limits of the spin-dependent cross section. (a) The allowed regions of the $(m_X,g_{X\tau })$ plane for several mediator masses in the lepton-portal model. (b) The $(m_X,g_{Xb})$ plane for several mediator masses in the quark-portal model.

Figure 7

The allowed regions of the $(g_{Xb},g_{X\tau })$ plane at the 90% confidence level from the exclusion limits of the spin-dependent cross section in the fermion-portal model. Here we take the benchmark points $m_{\tilde{b}}=m_{\tilde{t}}=900\mathrm{GeV}$, $m_{\tilde{\tau }}=250\mathrm{GeV}$ in (a), and $m_{\tilde{\tau }}=500\mathrm{GeV}$ in (b).

Figure 8

(left) The allowed regions of the $(m_S,s_{\phi })$ plane at 68%, 90%, and 95% confidence levels. (right) The allowed parameter space as a function of $m_X$ and $g_{\varphi }{c}_{\phi }{s}_{\phi }$ for three values of the mixing angle $s_{\phi }$.

Figure 9

(left) The excluded regions on the parameter space $(m_{b^{\prime }},m_X)$ from LHC searches on the bottom pair plus missing transverse energy final states with $20.1{\mathrm{fb}}^{-1}$ luminosity at 8 TeV. (right) The excluded regions on the parameter space $(m_{t^{\prime }},m_X)$ from LHC searches on the hadronic top pair plus missing transverse energy final states with $20.3{\mathrm{fb}}^{-1}$ luminosity at 8 TeV.

Figure 10

Data of the gamma-ray flux observed in the inner galaxy, taken from Ref. [11]. The curves are the best-fit spectra for several relative weight $R$, which parametrize the combination of the $b\overline{b}$ and $\tau \overline{\tau }$ final states. For each curve, the flux is calculated with an angular direction 5° from the Galactic Center, and a generalized NFW profile is used.

Figure 11

(left) The contours of the dark matter mass and annihilation cross section required to fit the gamma-ray spectrum at the 68%, 90%, and 95% confidence levels, for a variety of the relative weight $R$. (right) The regions of the annihilation cross section at the 95% confidence level vs the best fit of the dark matter mass, compared to the allowed region by the requirement of the correct relic density.

Figure 12

(a) The regions of the $(m_X,g_{Xb})$ plane in the quark-portal model, for the 35.9 GeV dark matter that gives the best fit of the quark-portal dark matter. Both the regions (light blue) allowed by the gamma-ray excess and the contour (red line) that gives the correct relic density are shown. We also display the region excluded by the direct searches at the LHC. (b) The regions of the $(m_X,g_{X\tau })$ plane in the lepton-portal model, for the 6.9 GeV dark matter that gives the best fit of the lepton-portal dark matter. Both the regions (light blue) allowed by the gamma-ray excess and the contour (red line) that gives the correct relic density are shown.

Figure 13

The regions (light blue) allowed by the gamma-ray excess and the contour (red line) that gives the correct relic density in the fermion-portal model. The vector dark matter mass is taken as 30 GeV, which corresponds to the best fit from the combination of 80% $b\overline{b}$ and 20% $\tau \overline{\tau }$. (left) The $(m_X,g_{Xb})$ plane. (right) The $(m_X,g_{X\tau })$ plane. We also display the region excluded by the direct searches at the LHC on the left panel.

Figure 14

Similar to what is shown in Fig. 13, but for a dark matter with mass 25 GeV. We also show the excluded region from the direct-detection experiments.