Testing Real WIMPs with CTAO

Abstract

We forecast the reach of the upcoming Cherenkov Telescope Array Observatory (CTAO) to the full set of real representations within the paradigm of minimal dark matter. We employ effective field theory techniques to compute the annihilation cross section and photon spectrum that results when fermionic dark matter is the neutral component of an arbitrary odd and real representation of SU(2), including the Sommerfeld enhancement, next-to-leading log resummation of the relevant electroweak effects, and the contribution from bound states. We also compute the corresponding signals for scalar dark matter, with the exception of the bound state contribution. Results are presented for all real representations from the $\sim$3 TeV triplet (or wino), a $\mathbf{3}$ of SU(2), to the $\sim$300 TeV tredecuplet, a $\mathbf{13}$ of SU(2) that is at the threshold of the unitarity bound. Using these results, we forecast that with 500 hrs of Galactic Center observations and assuming background systematics are controlled at the level of ${\cal O}(1\%)$, then should no signal emerge, CTAO could exclude all representations up to the $\mathbf{11}$ of SU(2) in even the most conservative models for the dark-matter density in the inner galaxy, in both the fermionic and scalar dark matter cases. Assuming the default CTAO configuration, the tredecuplet will marginally escape exclusion, although we outline steps that CTAO could take to test even this scenario. In summary, CTAO appears poised to make a definitive statement on whether real WIMPs constitute the dark matter of our universe.

Figures (13)

• Figure 1: Line cross-sections for all real multiplets as a function of the DM mass. The blue band shows the NLL prediction with associated uncertainties, whereas the dashed orange curve corresponds to the Sommerfeld enhanced tree-level prediction. The gray shaded area shows the predicted range for the thermal mass Bottaro:2021snnBottaro:2023wjv.
• Figure 2: The spectrum of the septuplet ($\mathbf{7}$) and tredecuplet ($\mathbf{13}$) for three masses around their central thermal value. The CTAO forecasts in this work will only assume sensitivity up to 200 TeV photons and therefore we do not show the tredecuplet spectrum up to the energies where one would resolve its line-like feature. The definition of the spectrum is provided in Eq. \ref{['eq:spectra']} and the results here have been smeared by the CTAO energy resolution.
• Figure 3: A comparison of various DM density profiles to a cored Einasto distribution. (Left) We show the DM density computed for three profiles, our default Einasto (black, including in dashed the impact of a 2 kpc core), and the Thelma (orange) and Romulus (purple) profiles that bracket the range of densities found in FIRE-2 simulations Hopkins:2017ycnMcKeown:2021sob. The gray band corresponds to the uncertainty band on the Milky Way DM density profile proposed in Ref. Hussein:2025xwm. All profiles are aligned to a local density of $\rho = 0.39$ GeV/cm$^3$ at 8.5 kpc. (Right) The average $J$-factor in our ROI for these same profiles. We now show how the Einasto DM flux decreases as the core radius increases. Comparing this to the alternative profiles, we find that Thelma maps to a $\simeq$1.6 kpc core, whereas the lower edge of the band from Ref. Hussein:2025xwm corresponds closely to our chosen 2 kpc exclusion.
• Figure 4: The expected background flux from misidentified charged cosmic-rays and astrophysical diffuse emission in our ROI. See text for details.
• Figure 5: The projected reach of CTAO to real WIMPs assuming 500 hrs of inner galaxy observations. The sensitivity is quantified with how much the inner galaxy $J$-factor would need to be reduced for the scenario to avoid exclusion, which we quantify with an increasing core radius $r_c$. Results are shown for the contribution of the line and endpoint spectrum (red, Line), together with the sensitivity gained when adding the continuum (blue, Cnt.) and bound states (orange, BS). For a given representation the spectrum and cross section are fixed up to the uncertainty on the thermal mass. The points correspond to the central mass prediction, whereas the error bars correspond to the strongest and weakest constraints obtained across the entire thermal mass window. As discussed in Sec. \ref{['ssec:Rho']}, we adopt a 2 kpc core to set a lower limit on the amount of DM in the inner galaxy (see also Fig. \ref{['fig:DM-Comparison']}): core sizes above this value are deemed excluded. The results show that CTAO is poised to test all real WIMPs with the exception of possibly the tredecuplet, although as discussed in the text there are paths to probe this scenario also.