Decaying vector dark matter as an explanation for the 3.5 keV line from galaxy clusters

We present a Vector Dark Matter (VDM) model that explains the 3.5 keV line recently observed in the XMM-Newton observatory data from galaxy clusters. In this model, dark matter is composed of two vector bosons, V and V', which couple to the photon through an effective generalized Chern-Simons coupling, g(V). V' is slightly heavier than V with a mass splitting m(V') - m(V) similar or equal to 3.5 keV. The decay of V' to V and a photon gives rise to the 3.5 keV line. The production of V and V' takes place in the early universe within the freeze-in framework through the effective gv coupling when m(V') < T < Lambda, Lambda being the cut-off above which the effective g(V) coupling is not valid. We introduce a high energy model that gives rise to the g(V) coupling at low energies. To do this, V and V' are promoted to gauge bosons of spontaneously broken new U(1)(V) and U(1)(V') gauge symmetries, respectively. The high energy sector includes milli-charged chiral fermions that lead to the g(V) coupling at low energy via triangle diagrams.