We study the interactions between strongly interacting massive particle dark matter and the Standard Model via a massive vector boson that is kinetically mixed with the hypercharge gauge boson. The relic abundance is set by 3-to-2 self-interactions of the dark matter, while the interactions with the vector mediator enable kinetic equilibrium between the dark and visible sectors. We show that a wide range of parameters is phenomenologically viable and can be probed in various ways. Astrophysical and cosmological constraints are evaded due to the p-wave nature of dark matter annihilation into visible particles, while direct detection methods using electron recoils can be sensitive to parts of the parameter space. In addition, we propose performing spectroscopy of the strongly coupled dark sector at e+e- colliders, where the energy of a mono-photon can track the resonance structure of the dark sector. Alternatively, some resonances may decay back into Standard Model leptons or jets, realizing `hidden valley' phenomenology at the LHC and ILC in a concrete fashion.

35 pages, 8 figures; v2: matches published version; v3: fixed typos in Eqs. (4.15), (6.7) and (6.9), results unchanged