Loopy Constraints on Leptophilic Dark Matter and Internal Bremsstrahlung

A sharp and spatially extended peak in an astrophysical gamma ray spectrum would provide very strong evidence for the existence of dark matter (DM), given that there are no known astrophysical processes that could mimic such a signal. From the particle physics perspective, perhaps the simplest explanation for a gamma ray peak is internal bremsstrahlung in DM annihilation through a charged t-channel mediator eta close in mass to the DM particle chi. Since DM annihilation to quarks is already tightly constrained in this scenario, we focus here on the leptophilic case. We compute the electromagnetic anapole and dipole moments that DM acquires at 1-loop, and we find an interesting enhancement of these moments if the DM particle and the mediator are close in mass. We constrain the DM anapole and dipole moments using direct detection data, and then translate these limits into bounds on the DM annihilation cross section. Our bounds are highly competitive with those from astrophysical gamma ray searches. In the second part of the paper, we derive complementary constraints on internal bremsstrahlung in DM annihilation using LEP mono-photon data, measurements of the anomalous magnetic moments of the electron and the muon, and searches for lepton flavor violation. We also comment on the impact of the internal bremsstrahlung scenario on the hyperfine splitting of true muonium.