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 $V^{\mathrm{\prime }}$, which couple to the photon through an effective generalized Chern-Simons coupling, $g_V$. $V^{\mathrm{\prime }}$ is slightly heavier than $V$ with a mass splitting $m_{V^{\mathrm{\prime }}}-m_V\simeq 3.5$~keV. The decay of $V^{\mathrm{\prime }}$ to $V$ and a photon gives rise to the 3.5~keV line. The production of $V$ and $V^{\mathrm{\prime }}$ takes place in the early universe within the freeze-in framework through the effective $g_V$ coupling when $m_{V^{\mathrm{\prime }}}<T<\mathrm{\Lambda }$, $\mathrm{\Lambda }$ 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 $V^{\mathrm{\prime }}$ are promoted to gauge bosons of spontaneously broken new $U(1{)}_V$ and $U(1{)}_{V^{\mathrm{\prime }}}$ 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.