Anapole dark matter annihilation into photons

In models of anapole dark matter (DM), the DM candidate is a Majorana fermion whose primary interaction with standard model (SM) particles is through an anapole coupling to off-shell photons. As such, at tree-level, anapole DM undergoes p-wave annihilation into SM charged fermions via a virtual photon. But, generally, Majorana fermions are polarizable, coupling to two real photons. This fact admits the possibility that anapole DM can annihilate into two photons in an s-wave process. Using an explicit model, we compute both the tree-level and diphoton contributions to the anapole DM annihilation cross section. Depending on model parameters, the s-wave process can either rival or be dwarfed by the p-wave contribution to the total annihilation cross section. Subjecting the model to astrophysical upper bounds on the s-wave annihilation mode, we rule out the model with large s-wave annihilation.

Figure 1

Feynman diagram representing the annihilation of two Majorana fermions into charged SM fermions.

Figure 2

Feynman diagrams relevant for the computation of the anapole moment of the Majorana fermion. In our computations, we consider both directions of fermion flow in the loop.

Figure 3

Feynman diagrams relevant for s-wave Majorana fermion annihilation into two photons. In our computations, we consider both directions of fermion flow in the loop.

Figure 4

The anapole moment and DM mass which reproduce the observed relic DM density. The dashed (blue) line employs only p-wave annihilation; the dotted (red) line employs only s-wave annihilation; and the solid (black) line employs both s- and p-wave processes. We assume $m_{\varphi }=10m_{\chi }$ and $m_{\chi }=10m_f$.

Figure 5

The (black) solid curve shows the lower bound on $m_f$ for case (i.b) as set by the constraints on s-wave DM annihilation into photons. The (blue) dashed curve shows the assumed mass ratio $m_f=10m_{\chi }$ used in Sec. 3.

Figure 6

The (black) solid curve shows the lower bound on $m_f$ for case (ii) as set by the constraints on s-wave DM annihilation into photons. The (blue) dashed curve shows the assumed mass ratio $m_f=100m_{\chi }$ used in Sec. 3.