Enhancing dark matter annihilation rates with dark bremsstrahlung

Many dark matter interaction types lead to annihilation processes which suffer from $p$-wave suppression or helicity suppression, rendering them subdominant to unsuppressed $s$-wave processes. We demonstrate that the natural inclusion of dark initial state radiation can open an unsuppressed $s$-wave annihilation channel and, thus, provide the dominant dark matter annihilation process for particular interaction types. We illustrate this effect with the bremsstrahlung of a dark spin-0 or dark spin-1 particle from fermionic dark matter, $\overline{\chi }\chi \to \overline{f}f\varphi$ or $\overline{f}f{Z}^{\prime }$. The dark initial state radiation process, despite having a 3-body final state, proceeds at the same order in the new physics scale $\mathrm{\Lambda }$ as the annihilation to the 2-body final state $\overline{\chi }\chi \to \overline{f}f$. This opens an unsuppressed $s$ wave at lower order in $\mathrm{\Lambda }$ than the well-studied lifting of helicity suppression via Standard Model final state radiation or virtual internal bremsstrahlung. This dark bremsstrahlung process should influence LHC and indirect detection searches for dark matter.

Figure 1

Dark vector (left) and dark scalar (right) ISR. Note in both cases that there is also an additional diagram for emission from the other initial state DM.

Figure 2

$s$-wave process for DM annihilation to pseudoscalars, $\overline{\chi }\chi \to \varphi \varphi \varphi$. Note that there are a total of six diagrams that contribute.

Figure 3

Comparison of the $s$-wave cross sections for the pseudoscalar ISR (pink) and 3-body $\varphi \varphi \varphi$ (black) annihilation processes for $m_{\varphi }$, $\mathrm{\Lambda }$ and $g_{\varphi }$ as labeled, and $m_f=0$. Note the largest value shown for $m_{\chi }$ corresponds to $m_{\chi }\sim \sqrt{4\pi }\mathrm{\Lambda }$, where the validity of the EFT within the perturbative regime is satisfied.

Figure 4

$s$-wave process for DM annihilation to dark vectors. Note there is also a contribution from the $u$-channel diagram.

Figure 5

Comparison of the $s$-wave cross sections for Dirac DM annihilating via the dark vector ISR process (cyan) and the 2-body $Z^{\prime }{Z}^{\prime }$ process (purple), for $m_{Z^{\prime }}$, $\mathrm{\Lambda }$ and $g_{Z^{\prime }}$ as labeled, and $m_f=0$. Note the largest value shown for $m_{\chi }$ corresponds approximately to the largest value permitted within a gauge-invariant and perturbative framework, without other new physics appearing.