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 $\Lambda_d \sim 4\pi f_d$, 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 ${\cal O}(1$-$100)~{\rm TeV}$, which is different from conventional electroweakly interacting dark matter such as minimal dark matter. We also discuss CP-violation from $\theta$-term in the dark gauge sector and find that the predicted size of electron electric dipole moment can be as large as $\sim 10^{-32}~e~{\rm cm}$.