Indirect detection constraints on s- and t-channel simplified models of dark matter

Recent Fermi-LAT observations of dwarf spheroidal galaxies in the Milky Way have placed strong limits on the gamma-ray flux from dark matter annihilation. In order to produce the strongest limit on the dark matter annihilation cross section, the observations of each dwarf galaxy have typically been “stacked” in a joint-likelihood analysis, utilizing optical observations to constrain the dark matter density profile in each dwarf. These limits have typically been computed only for singular annihilation final states, such as $b\overline{b}$ or ${\tau }^{+}{\tau }^{-}$. In this paper, we generalize this approach by producing an independent joint-likelihood analysis to set constraints on models where the dark matter particle annihilates to multiple final-state fermions. We interpret these results in the context of the most popular simplified models, including those with s- and t-channel dark matter annihilation through scalar and vector mediators. We present our results as constraints on the minimum dark matter mass and the mediator sector parameters. Additionally, we compare our simplified model results to those of effective field theory contact interactions in the high-mass limit.

Figure 1

Gamma-ray spectrum from DM annihilation into various channels for a 100 GeV DM particle.

Figure 2

A comparison of the annihilation cross-section upper limits obtained using this work and the spectrum calculated by PPPC, compared to the Fermi-LAT Collaboration analysis [23] for the case of “standard” DM annihilations into $b\overline{b}$ (top) and ${\tau }^{+}{\tau }^{-}$ (bottom) final states as a function of the DM mass and assuming a 95% confidence upper limit set at $\mathrm{\Delta }LG(\mathcal{L})=2.71/2$.

Figure 3

Stages in the analysis of the joint-likelihood limits on the annihilation of particle dark matter. First, the limit is shown in an intermediate state, as a joint-likelihood analysis calculated independently in each spectral bin, with $J$ factors for each dwarf that are allowed to float independently in each spectral (top left). Second, a dark matter mass and annihilation pathway is fixed (100 GeV DM annihilating to a $b\overline{b}$ final state), and the $J$ factor for each dwarf is forced to be consistent over each spectral bin (bottom left). Finally, the combined limits are calculated by summing the $\mathrm{LG}(\mathcal{L})$ scan in each energy bin to produce a limit on the dark matter cross section (right).

Figure 4

The lower bound on the DM mass (GeV) for annihilations into $b\overline{b}$, ${\tau }^{+}{\tau }^{-}$, and invisible particles for $⟨\sigma v{⟩}_{\mathrm{tot}}=⟨\sigma v{⟩}_{\mathrm{Th}}$. In the left figure, the photon spectrum is generated with PPPC; while in the right figure, the photon spectrum is generated with DarkSUSY.

Figure 5

The lower bound on the effective coupling (GeV) of DM to $b$ quarks for annihilations into $b\overline{b}$, ${\tau }^{+}{\tau }^{-}$, and invisible particles for $⟨\sigma v{⟩}_{\mathrm{tot}}=⟨\sigma v{⟩}_{\mathrm{Th}}$. In the left figure, the photon spectrum is generated with PPPC. In the right figure, the photon spectrum is generated with DarkSUSY.

Figure 6

The lower bound on the effective coupling (GeV) of DM to $\tau$ leptons for annihilations into $b\overline{b}$, ${\tau }^{+}{\tau }^{-}$, and invisible particles for $⟨\sigma v{⟩}_{\mathrm{tot}}=⟨\sigma v{⟩}_{\mathrm{Th}}$. In the left figure, the photon spectrum is generated with PPPC. In the right figure, the photon spectrum is generated with DarkSUSY.

Figure 7

Diagrams for DM annihilation in simplified models with a vector mediator (upper left), a scalar mediator (upper right), and a t-channel mediator (lower).

Figure 8

Upper bound on the allowed DM-mediator coupling ($g_f$) as a function of mediator mass for DM annihilation to pure $b$’s (upper left), pure $\tau$’s (upper right), and the 30/70 mixed cases (lower) for $g_{\chi }=1$ in the vector mediator simplified model.

Figure 9

Upper bounds on DM-mediator coupling as a function of mediator mass for a vector mediator model compared with assumptions from effective operator D5 ($\overline{\chi }{\gamma }^{\mu }\chi f{\gamma }_{\mu }f$) with $g_{\chi }=1$ and $m_{\chi }=150\mathrm{GeV}$ (left) and 950 GeV (right).

Figure 10

Upper bounds on the allowed DM coupling to final states $bb$ (left) and $\tau \tau$ (right) in the t-channel mediator simplified model.

Figure 11

Upper bounds on the allowed DM coupling vs mediator mass for a t-channel simplified model where DM annihilates to 70% $\tau$’s and 30% $b$’s. The left plot has the bounds on the parameters related to the $b$ interaction with DM, and the right plot is the same for $\tau$ interactions.

Figure 12

Upper bounds on the allowed DM coupling vs mediator mass for a t-channel simplified model where DM annihilates to 30% $\tau$’s and 70% $b$’s. The left plot has the bounds on the parameters related to the $b$ interaction with DM, and the right plot is the same for $\tau$ interactions.

Figure 13

Upper bounds on the allowed DM coupling to final states of down-type quarks (left) and leptons (right) in the t-channel mediator simplified model.