Composite dark matter with forbidden annihilation

A dark matter model based on QCD-like SU(N_c) gauge theory with electroweakly interacting dark quarks is discussed. Assuming the dark quark mass m is smaller than the dynamical scale Λ_d ~ 4πf_d, the main component of the dark matter is the lightest G-parity odd dark pion associated with chiral symmetry breaking in the dark sector. We show that nonzero dark quark mass induces the universal mass contribution to both G-parity odd and even pions, and their masses tend to be degenerate. As a result, dark pion annihilation into heavier G-parity even dark pion also affects the dark matter relic abundance. Thus, our setup naturally accommodates forbidden dark matter scenario and realizes heavy dark matter whose mass is $\mathcal{O}$ \( \mathcal{O} \) (1–100) TeV, which is different from conventional electroweakly interacting dark matter such as minimal dark matter. We also discuss CP-violation from the θ-term in the dark gauge sector and find that the predicted size of the electron electric dipole moment can be as large as ∼ 10⁻³² e cm.