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, φ, 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→μX, electron (g-2)e, K→μνμe+e-, K→μνμμ+μ-, and τ→ντμνμe+e-. We focus on the scenario where the V mass is below ∼2mμ and the φ mass runs from few MeV to 250 MeV, with V-photon mixing of the order ∼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-→μ+μ-e+e- and discuss the impact of the dark Higgs on e+e-→μ+μ-μ+μ-. Finally, we consider contributions of the V-photon mixing in the decays π0→γe+e-, η→γe+e-, ρ→πe+e-, K∗→Ke+e-, and φ(1020)→ηe+e-.