Spin portal to dark matter

In this work, we study the possibility that dark matter fields transform in the $(1,0)\oplus (0,1)$ representation of the homogeneous Lorentz group. In an effective theory approach, we study the lowest-dimension interacting terms of dark matter with standard model fields, assuming that dark matter fields transform as singlets under the standard model gauge group. There are three dimension-four operators, two of them yielding a Higgs portal to dark matter. The third operator couples the photon and $Z^0$ fields to the higher multipoles of dark matter, yielding a spin portal to dark matter. For low mass dark matter ($D$), the decays $Z^0\to \overline{D}D$ and $H\to \overline{D}D$ are kinematically allowed and contribute to the invisible widths of the $Z^0$ and $H$ bosons. We use experimental results on these invisible widths to constrain the values of the low-energy constants $g_t$ (for the spin portal) and $g_s$, $g_p$ (for the Higgs portal) for this mass region. We calculate the dark matter relic density in our formalism and, using the above constraints, we find that consistency with the experimental value requires dark matter to have a mass $M>43\mathrm{GeV}$ in the case of the spin portal and $M>62\mathrm{GeV}$ for the Higgs portal. For higher mass dark matter ($M>M_H/2$), we calculate the velocity averaged cross section for the annihilation of dark matter into $\overline{b}b$ and ${\tau }^{+}{\tau }^{-}$ and compare with the upper bounds recently reported by Fermi-LAT and DES Collaborations, finding that both portals yield results consistent with the reported upper bounds. Finally, we study direct detection by elastic scattering on nuclei. The Higgs portal yields results consistent with the upper bounds reported recently by the XENON Collaboration. The spin portal can also accommodate this data but requires higher values of the dark matter mass or smaller values of the corresponding coupling.

Figure 1

Feynman rules from the leading terms in the effective theory.

Figure 2

Parameter space for $g_t$, $g_s$ and $g_p$ consistent $\mathrm{\Gamma }(Z\to \overline{D}D)<{\mathrm{\Gamma }}_Z^{\mathrm{inv}}=1.4\pm 1.5\mathrm{MeV}$ and $\mathrm{\Gamma }(H\to \overline{D}D)<{\mathrm{\Gamma }}_H^{\mathrm{inv}}=1.14\pm 0.04\mathrm{MeV}$ for $M<M_Z/2$. Solid lines correspond to the central values of the invisible decay widths.

Figure 3

Feynman diagrams for $\overline{D}D\to \overline{f}f$.

Figure 4

Feynman diagrams for $\overline{D}D\to \gamma \gamma$.

Figure 5

Individual contributions of the spin portal ($g_t=g$, $g_s=g_p=0$) and the Higgs portal ($g_t=0$, $g_s=g_p=g$) to $⟨\sigma v_r⟩$. Similar results are obtained in the second case when varying independently $g_s$ or $g_p$.

Figure 6

Solution of the Boltzman equation for the spin portal (left) and Higgs portal (right). Similar results are obtained in the later case when varying independently $g_s$ and $g_p$. The solid line corresponds to $Y_{\mathrm{eq}}(x)$.

Figure 7

Values of the couplings consistent with the measured dark matter relic density, ${\mathrm{\Omega }}_{\mathrm{DM}}^{\exp }{h}^2=0.1186\pm 0.0020$ (solid line), as a function of $M$. The shadowed region in the left panel corresponds to the values consistent with the $Z^0$ invisible width, $\mathrm{\Gamma }(Z^0\to \overline{D}D)<{\mathrm{\Gamma }}_Z^{\mathrm{inv}}=1.4\pm 1.5\mathrm{MeV}$, for the spin portal. These constraints exclude masses below 43 GeV for the spin portal. The shadowed region in the right panel are the values consistent with the constraint $\mathrm{\Gamma }(H\to \overline{D}D)<{\mathrm{\Gamma }}_H^{\mathrm{inv}}=1.14\pm 0.04\mathrm{MeV}$ for the spin portal. Masses below 62 GeV are excluded for this portal.

Figure 8

Velocity averaged cross section for dark matter annihilation into ${\tau }^{+}{\tau }^{-}$ (left) and $\overline{b}b$ (right) and comparison with Fermilat-DES upper bounds, for different values of $g_s$ (Higgs portal). The spin portal yields contributions even smaller and are consistent with these upper bounds.

Figure 9

Observable ${\sigma }_p$ as a function of the dark matter mass for the Higgs ($g_t=0$, left panel) and spin ($g_s=0$, right panel) portals, compared with the XENON1T upper bounds [49].