A theory of dark matter

We propose a comprehensive theory of dark matter that explains the recent proliferation of unexpected observations in high-energy astrophysics. Cosmic ray spectra from ATIC and PAMELA require a WIMP (weakly interacting massive particle). with mass $M_{\chi }\sim 500–800\mathrm{GeV}$ that annihilates into leptons at a level well above that expected from a thermal relic. Signals from WMAP and EGRET reinforce this interpretation. Limits on $\overline{p}$ and ${\pi }^0\mathrm{\text{−}}\gamma$’s constrain the hadronic channels allowed for dark matter. Taken together, we argue these facts imply the presence of a new force in the dark sector, with a Compton wavelength $m_{\varphi }^{-1}\gtrsim 1{\mathrm{GeV}}^{-1}$. The long range allows a Sommerfeld enhancement to boost the annihilation cross section as required, without altering the weak-scale annihilation cross section during dark matter freeze-out in the early universe. If the dark matter annihilates into the new force carrier $\varphi$, its low mass can make hadronic modes kinematically inaccessible, forcing decays dominantly into leptons. If the force carrier is a non-Abelian gauge boson, the dark matter is part of a multiplet of states, and splittings between these states are naturally generated with size $\alpha m_{\varphi }\sim \mathrm{MeV}$, leading to the eXciting dark matter (XDM) scenario previously proposed to explain the positron annihilation in the galactic center observed by the INTEGRAL satellite; the light boson invoked by XDM to mediate a large inelastic scattering cross section is identified with the $\varphi$ here. Somewhat smaller splittings would also be expected, providing a natural source for the parameters of the inelastic dark matter (iDM) explanation for the DAMA annual modulation signal. Since the Sommerfeld enhancement is most significant at low velocities, early dark matter halos at redshift $\sim 10$ potentially produce observable effects on the ionization history of the universe. Because of the enhanced cross section, detection of substructure is more probable than with a conventional WIMP. Moreover, the low velocity dispersion of dwarf galaxies and Milky Way subhalos can increase the substructure annihilation signal by an additional order of magnitude or more.

Figure 1

The annihilation diagrams $\chi \chi \to \varphi \varphi$ both with (a) and without (b) the Sommerfeld enhancements.

Figure 2

Contours for the Sommerfeld enhancement factor $S$ as a function of the mass ratio $m_{\varphi }/m_{\chi }$ and the coupling constant $\lambda$, $\sigma =150\mathrm{km}/\mathrm{s}$.

Figure 3

Contours for the Sommerfeld enhancement factor $S$ as a function of the mass ratio $m_{\varphi }/m_{\chi }$ and the coupling constant $\lambda$, at a temperature $T_{\mathrm{CMB}}=m_{\chi }/20$ (the enhancement is integrated over a Boltzmann distribution with $\sigma =0.3c$).

Figure 4

Spectrum of exciting dark matter.

Figure 5

Contours for the Sommerfeld enhancement factor $S$ as a function of the mass ratio $m_{\varphi }/m_{\chi }$ and the coupling constant $\lambda$, $\sigma =10\mathrm{km}/\mathrm{s}$.

Figure 6

Contour plot of $S$ as a function of ${ϵ}_{\varphi }$ and ${ϵ}_v$. The lower right triangle corresponds to the zero-mass limit, whereas the upper left triangle is the resonance region.

Figure 7

As in Fig. 6, showing the resonance region in more detail.