The orbital period of a compact binary system decays mainly due to quadrupole gravitational radiation, which agrees with the observation to within 1%. Other types of radiation such as ultralight scalar or pseudoscalar radiation and massive vector boson radiation also contribute to the decay of the orbital period as long as the mass of the emitted particle is less than the orbital frequency of the compact binary system. We obtain an expression of the energy loss due to the radiation of the massive vector field from the neutron star–neutron star and neutron star–white dwarf binaries. Because of the large chemical potential of the degenerate electrons, neutron stars (NSs) have large muon charge. We derive the energy loss due to U(1)Lμ−Lτ gauge boson radiation from the binaries. For the radiation of the vector boson, the mass is restricted by MZ′<Ω≃10−19 eV, which are the orbital frequencies of the compact star binaries. Using the formula of orbital period decay, we obtain constraints on the coupling constant of the gauge boson in the gauged Lμ−Lτ theory for the four compact binary systems. For vector gauge boson muon coupling, we find that for MZ′<10−19 eV, the constraint on the coupling constant is g