NMSSM interpretation of the Galactic Center excess

We explore models for the GeV Galactic Center excess (GCE) observed by the Fermi Telescope, focusing on $\chi \chi \to f\overline{f}$ annihilation processes in the $Z_3$ next-to-minimal supersymmetric standard model (NMSSM). We begin by examining the requirements for a simplified model [parametrized by the couplings and masses of dark matter (DM) and mediator particles] to reproduce the GCE via $\chi \chi \to f\overline{f}$, while simultaneously thermally producing the observed relic abundance. We apply the results of our simplified model to the $Z_3$ NMSSM for singlino/Higgsino (S/H) or bino/Higgsino (B/H) DM. In the case of S/H DM, we find that the DM must be very close to a pseudoscalar resonance to be viable, and large $\tan \beta$ and positive values of $\mu$ are preferred for evading direct detection constraints while simultaneously obtaining the observed Higgs mass. In the case of B/H DM, by contrast, the situation is much less tuned: annihilation generally occurs off resonance, and for large $\tan \beta$, direct detection constraints are easily satisfied by choosing $\mu$ sufficiently large and negative. The B/H model generally has a light, largely MSSM-like pseudoscalar with no accompanying charged Higgs, which could be searched for at the LHC.

Figure 1

Upper panels: Couplings $y_{abb}$ and $y_{a\chi \chi }$ required to obtain relic density and GCE through resonant annihilation as a function of $m_a/m_{\chi }$. The left and right panels should be read as a pair, with blue (solid) and red (dashed) curves in the left panel coupling to the similarly denoted curves in the right panel. In the left panel, either blue (solid) curve can be matched with the single blue (solid) curve in the right panel, and likewise either red (dashed) curve in the right panel can be matched with the single red (dashed) curve in the left panel to obtain both the observed relic abundance and the GCE. Lower panels: Allowing $m_a/m_{\chi }$ to float, the allowed couplings $y_{abb}$ and $y_{a\chi \chi }$ to obtain both the relic abundance and the GCE are shown, obtained using analytic results (left panel) and the full numerical scan (right panel). The blue (solid) and red (dashed) curves in the left panel correspond to the similarly denoted curves in the top two panels. One can see broad agreement between the analytic results and the output of the scan.

Figure 2

Left panel: $\lambda$ as a function of $\mu$ needed to set the relic density via annihilation through the $Z$. The relic abundance thus fixes an upper bound on the Higgsino fraction. Right panel: Blue (dashed) curves denote the value of $\lambda$ needed to obtain the GCE in the $\mu$ versus pseudoscalar mass $m_a$ plane. The red (solid) curve traces out where the Higgsino fraction is such that one obtains the correct relic abundance via annihilation through the $Z$ alone. As one can see, annihilation must occur very close to resonance to achieve the GCE under these conditions.

Figure 3

Results of a numerical scan with micrOMEGAs, fixing $m_h\sim 125\mathrm{GeV}$, $t_{\beta }=40$, $A_{\kappa }=-250\mathrm{GeV}$, and $A_{\lambda }$ to remove mixing between the SM-like and singlet Higgses. The green band shows the region of parameter space fitting the GCE: $0.5<10^{26}{\mathrm{cm}}^3/\mathrm{s}\times \sigma v{|}_{v\to 0}<4$; the blue region shows the observed relic abundance; and the red shows the excluded LUX region. We have fixed $\kappa$ to accommodate particular values of the DM mass. Upper panels: $m_{\chi }\sim 37\pm 0.5\mathrm{GeV}$. Lower panels: $m_{\chi }\sim 42\pm 0.5\mathrm{GeV}$. Consistent with the analytic results shown in Fig. 2, the green strips are centered around $m_a=2m_{\chi }$, and as $\lambda /\mu$ (controlling the Higgsino fraction) decreases, the green strips converge closer to resonant annihilation. The blue relic density strip breaks away from the green GCE line when annihilation through the $Z$ becomes important.

Figure 4

Left panel: Contours of the direct detection cross section (in units of $10^{-45}{\mathrm{cm}}^2$) in the $\lambda -\mu$ plane, taking the analytic expressions in Eq. (3.15) and $\tan \beta =1$. Right panel: Contours of $\lambda$ needed to obtain the Galactic Center excess. Comparing with the left-hand plot, we can see that the annihilation must occur very close to resonance.

Figure 5

Left panel: Contours fixing the $s$-wave annihilation cross section of bino/Higgsino DM to $2.3\times 10^{-26}{\mathrm{cm}}^3/\mathrm{s}$ for various choices of $\kappa$ as a function of $\mu$ and $m_A$. The dot-dashed lines show the constraints from requiring that the scattering cross section in direct detection experiments be smaller than $10^{-45}{\mathrm{cm}}^2$ (below and to the right is allowed). Right panel: Contours fixing the $s$-wave annihilation cross section of bino/Higgsino DM to $2.3\times 10^{-26}{\mathrm{cm}}^3/\mathrm{s}$ for various choices of $\kappa$ as a function of $m_a$ and $m_A$.

Figure 6

Results of a numerical scan with $M_1=35\mathrm{GeV}$ $\mu =-600\mathrm{GeV}$, $m_A=600\mathrm{GeV}$, $t_{\beta }=20$, $\lambda =0.05$, $122\mathrm{GeV}<m_h<128\mathrm{GeV}$, GCE: $0.5<10^{26}{\mathrm{cm}}^3/\mathrm{s}\times \sigma v{|}_{v\to 0}<4$, $0.1118<\mathrm{\Omega }{h}^2<0.128$. The green and blue regions show the parameter space consistent with the GCE and observed relic density. The black dashed lines show the contours for constant pseudoscalar mass $m_a$. Notice that as $\kappa$ increases, the regions with the correct relic abundance pull slightly away from resonance, as expected from our analytical results. The red region is excluded by $A\to {\tau }^{+}{\tau }^{-}$ searches at the LHC, while the purple exclusion comes from modification of SM Higgs rates due to the presence of the open $h\to aa$ channel.