Restrained dark U(1)(d) at low energies

We investigate a spontaneously broken U(1)(d) gauge symmetry with a muon-specific dark Higgs. Our first goal is to verify how the presence of a new dark Higgs,., and a dark gauge boson, V, can simultaneously face the anomalies from the muon magnetic moment and the proton charge radius. Second, by assuming that V must decay to an electron-positron pair, we explore the corresponding parameter space determined with the low-energy constraints coming from K -> mu X, electron (g-2)(e), K -> mu nu(mu)e(+)e(-), K ->mu nu(mu)mu(+)mu(-), and tau -> nu(tau)mu nu(mu)e(+)e(-). We focus on the scenario where the V mass is below similar to 2m(mu) and the phi mass runs from few MeV to 250 MeV, with V-photon mixing of the order similar to O(10(-3)). Among weak process at low energies, we check the influence of the new light vector on kaon decays as well as on the scattering e(+)e(-) -> mu(+)mu(-)e(+)e(-) and discuss the impact of the dark Higgs on e(+)e(-) -> mu(+)mu(-)mu(+)mu(-). Finally, we consider contributions of the V-photon mixing in the decays pi(0) -> gamma e(+)e(-),eta -> e(+)e(-), rho -> pi e(+)e(-), K* -> Ke(+)e(-), and phi(1020) -> eta e(+)e(-).