Selection Rule for Enhanced Dark Matter Annihilation

We point out a selection rule for enhancement (suppression) of odd (even) partial waves of dark matter coannihilation or annihilation using the Sommerfeld effect. Using this, the usually velocity-suppressed $p$-wave annihilation can dominate the annihilation signals in the present Universe. The selection mechanism is a manifestation of the exchange symmetry of identical incoming particles, and generic for multistate DM with off-diagonal long-range interactions. As a consequence, the relic and late-time annihilation rates are parametrically different and a distinctive phenomenology, with large but strongly velocity-dependent annihilation rates, is predicted.

Figure 1

Sommerfeld factors for $s$-wave and $p$-wave coannihilation or annihilation processes at velocities $v$. At smaller velocities the $p$-wave coannihilation or annihilation processes are strongly enhanced but $s$-wave coannihilation is suppressed. The $\sim 1/v^3$ rise of $S_p$ at intermediate velocities predicts that $⟨\sigma v⟩\simeq S_p⟨\sigma v{⟩}_p$ peaks for $v$ at the edge of the saturation plateau at low $v$. Typical DM velocities in different sources or epochs are annotated. See text for details of the model.

Figure 2

Sommerfeld enhancement of $p$-wave annihilation, for DM of mass $m_{\chi }$ interacting via a mediator of mass $m_{\rho }$ with dark fine-structure constant $\alpha$. The Sommerfeld factor is large for $\alpha \gtrsim \mathrm{few}\times {10}^{-3}$ and $m_{\rho }/m_{\chi }\lesssim \mathrm{few}\times {10}^{-2}$, using $v={10}^{-3}$ and $\mathrm{\Delta }/m_{\chi }={10}^{-3}$ as representative values.

Figure 3

$p$-wave DM annihilation rates in different astrophysical sources and source-specific constraints from indirect detection searches. The annihilation rates have a signature nonmonotonic $v$ dependence over and above the resonances; e.g., for $m_{\chi }>4\mathrm{TeV}$ the galactic annihilation rate (solid line) exceeds that in clusters (dashed line) and dwarf galaxies (dot-dashed line). In DM mass ranges shown by gray vertical bands a 100% branching ratio to ${\mu }^{+}{\mu }^{-}$ is ruled out.