SIMPly add a dark photon

Pions of a dark sector gauge group can be strongly interacting massive particle (SIMP) matter, produced by the freeze-out $3 \to 2$ interactions, with naturally large self-interactions. We study if adding photon to set-up do it all: i) maintain thermalization visible sector, ii) resonantly enhance $3\to2$ thus allowing for perturbative pion description, and iii) provide velocity dependent self-interaction that affect small scale structure formation. For $N_f=3$ this minimal setup is marginally excluded, as required kinetic mixing too thermal equilibrium SM. Adding an extra quark opens up parameter space, -- perhaps somewhat surprisingly we find all bounds satisfied masses $m_\pi \sim 250-600\,$MeV. Dropping requirement iii), viable reproduced charges $\alpha_d = 0.01-1$ mass \geq 30$ MeV. Late time annihilations are non-negligible making SIMP bit WIMPy.