Slightly massive photon

We study a renormalizable field-theory model of a slightly massive photon compatible with experiment. Such a model can be built only by spontaneous breaking of electromagnetic gauge symmetry which is triggered by a charged Higgs field with a tiny charge $Q_{\chi }$ in units of the proton charge. A physical-Higgs-boson mass $m_h$ must obey an inequality $Q_{\chi }$ $m_h$≲${10}^{\mathrm{-}20}$ MeV. If $m_h$ is smaller than 10 keV or so, a mass-independent upper limit is imposed on $Q_{\chi }$ by astrophysics as $Q_{\chi }$ ${<10\mathrm{}}^{\mathrm{-}7}$. Since this Higgs boson is almost decoupled from all known particles, there are very few physical consequences.