Tev-scale thermal WIMPs: Unitarity and its consequences

We reexamine unitarity bounds on the annihilation cross section of thermal weakly interacting massive particle (WIMP) dark matter. For high-mass pointlike dark matter, it is generic to form WIMP bound states, which, together with Sommerfeld enhancement, affects the relic abundance. We show that these effects lower the unitarity bound from 139 TeV to below 100 TeV for non-self-conjugate dark matter and from 195 TeV (the oft-quoted value of 340 TeV assumes ${\mathrm{\Omega }}_{\mathrm{DM}}{h}^2=1$) to 140 TeV for the self-conjugate case. For composite dark matter, for which the unitarity limit on the radius was thought to be mass independent, we show that the largest allowed mass is 1 PeV. In addition, we find important new effects for annihilation in the late universe. For example, while the production of high-energy light fermions in WIMP annihilation is suppressed by helicity, we show that bound-state formation changes this. Coupled with rapidly improving experimental sensitivity to TeV-range gamma rays, cosmic rays, and neutrinos, our results give new hope to attack the thermal-WIMP mass range from the high-mass end.

Figure 1

Effects on freeze-out due to the Sommerfeld effect alone and the additional effects of bound-state formation. The inset shows the qualitative behavior at the time of deviation from the thermal DM abundance. Note in particular, that the DM depletion due to bound-state formation (green lines) sets in at later times than the Sommerfeld enhanced freeze-out. In particular in the case indicated by the dot-dashed green line, where the smaller bound-state annihilation rate of ${\mathrm{\Gamma }}_{\mathrm{ann}}\approx {10}^{-7}{M}_{\mathrm{DM}}$ leads to a belated annihilation. This is a direct consequence of the branching ratio introduced in Eq. (3).

Figure 2

The green solid line indicates the mass and representation at which the relic density for a parametric WIMP is equal to the observed DM density, including bound-state formation. The blue dashed line shows the same prediction with only Sommerfeld enhancement taken into account. The largest representation compatible with unitarity and the DM abundance is $R=12$.

Figure 3

The green solid line shows the predicted relic density under the assumption that the s-wave cross section saturates the full unitarity bound, for a self-conjugate DM candidate. The green dashed line is the same for the non-self-conjugate case. The red line shows this prediction when bound-state formation is neglected.

Figure 4

Comparison of the early universe and late-time annihilation cross sections allowed by unitarity and experimental constraints. Since the cross section contains the $1/v_{\mathrm{rel}}$ factor from the Sommerfeld and bound-state formation effects, the unitarity bounds on the maximally allowed cross section strongly differ between the early universe in (a) and late time annihilation in (b). Today, the annihilation cross section can be significantly enhanced.

Figure 5

Gamma-ray spectra from a $SU(2)$ DM candidate with $R=5$ and a mass of 14 TeV. The energy resolution is taken to be 10%, corresponding to the Fermi LAT experiment. For the flux a J-factor of the galactic center region $R_3$ of $13.9\times 10^{22}{\mathrm{GeV}}^2{\mathrm{cm}}^{-5}$ was assumed. The large separation of monochromatic signals in their energy makes experimental searches for them highly complementary.

Figure 6

Spin-zero bound-state annihilation to two gauge bosons ($\gamma$, Z, W), where the last requires that the internal line be a charged state of the $\chi$ multiplet.

Figure 7

Spin-one bound-state annihilation to two fermions via a gauge boson ($\gamma$, Z). $SU(2{)}_L$ symmetry dictates a democratic distribution of fermionic final states.

Figure 8

The predicted spin-independent cross section, under the assumption that DM relic abundance is satisfied. Red dots show the exact results for the $R=\{3,4,5\}$ representations. Superposed are the latest limits of the XENON1T experiment from Ref. [75].

Figure 9

The allowed parameter space for the simplest dark atoms (white area). The zero-temperature unitarity bound coincides with the full unitarity bound we derive only in the strong coupling regime. Geometrical annihilation (i.e., ${\ell }_{\max }\gg 1$) only takes place in the regime where $M_{\mathcal{Q}}\gg \mathrm{\Lambda }$. The values of ${\ell }_{\max }$ are indicated by dashed lines.

Figure 10

The cross section for self-annihilation of dark atoms at late times. Superposed are limits of the HAWC experiment from Ref. [85], assuming complete annihilation to neutrino final states. At the large annihilation energies electroweak corrections lead to gamma-ray emission, which is constrained by the HAWC experiment.