Renormalizable model for the Galactic Center gamma-ray excess from dark matter annihilation

Evidence for an excess of gamma rays with $\mathcal{\text{O}}(\mathrm{GeV})$ energy coming from the center of our galaxy has been steadily accumulating over the past several years. Recent studies of the excess in data from the Fermi telescope have cast doubt on an explanation for the excess arising from unknown astrophysical sources. A potential source of the excess is the annihilation of dark matter into standard model final states, giving rise to gamma ray production. The spectrum of the excess is well fit by 30 GeV dark matter annihilating into a pair of $b$ quarks with a cross section of the same order of magnitude as expected for a thermal relic. Simple models that can lead to this annihilation channel for dark matter are in strong tension with null results from direct detection experiments. We construct a renormalizable model where dark matter-standard model interactions are mediated by a pseudoscalar that mixes with the $CP$-odd component of a pair of Higgs doublets, allowing for the gamma ray excess to be explained while suppressing the direct detection signal. We consider implications for this scenario from Higgs decays, rare $B$ meson decays and monojet searches and also comment on some difficulties that any dark matter model explaining the gamma ray excess via direct annihilation into quarks will encounter.

Figure 1

Regions of mixing angle $\theta$ vs $m_a$ that are ruled out or suggested by various measurements. We have fixed $m_{H,H^{\pm }}\simeq m_A=800\mathrm{GeV}$, $\tan \beta =40$, $\alpha =\beta -\pi /2$, and $y_{\chi }=0.5$. The area that gives an annihilation cross section of $⟨\sigma v_{\text{rel}}⟩=1–5\times 10^{-26}{\mathrm{cm}}^3/\mathrm{s}$ as indicated by fits to the gamma ray excess is between the solid black lines (shaded in green). The shaded purple region above the solid purple line is in $2\sigma$ conflict with the LHCb measurement of $B_s\to {\mu }^{+}{\mu }^{-}$. The darker red region with the solid outline is ruled out by $h\to b\overline{b}$ constraints on the $h\to 4b$ signal. The larger, lighter red region with a solid outline is ruled out from the indirect limit $\mathrm{Br}(h\to aa)<0.22$ coming from fits to Higgs properties, assuming SM Higgs production. The dashed red line shows the area that could be probed by limiting $\mathrm{Br}(h\to aa\to 2b2\mu )\lesssim 10^{-4}$. The blue region labeled LUX is in conflict with the limit ${\sigma }_{\text{SI}}<8\times 10^{-46}{\mathrm{cm}}^2$ while the area above the blue dashed line leads to ${\sigma }_{\text{SI}}>10^{-49}{\mathrm{cm}}^2$, potentially accessible at the next generation of direct detection experiments. The orange region shows the area ruled out by a mono-$b$-jet search at 8 TeV with $20{\mathrm{fb}}^{-1}$ of data. See text for details.

Figure 2

Diagrams that (with the crossed top diagram) lead to spin-independent DM-nucleon scattering. The $b$ quarks in the top diagram can also be replaced by $d$ and $s$ quarks.