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. Secondly, 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,We focus in the scenario where the V mass is below ∼ 2mµ and the φ mass runs from few MeV till 250 MeV, with V-photon mixing of the order ∼ O(10 −3 ).

We examine theoretical features of U(1) X extensions of the Standard Model whose quantum anomalies are canceled per generation. Similarly to other versions, the theory consists of a Two-Higgs-Doublet Model plus a scalar singlet embedded into the SM ⊗ U(1) X gauge group, and introduces small modifications to the Z-boson interactions. These changes can be minimized by exclusively charging right-handed fermions under the new Abelian symmetry, and are compensated by the neutral X-boson exchange. Nonuniversality of fermion couplings can also be achieved by requiring one single X-charged family. In general, X gauge bosons can be separated into A and Z subsets, distinguished by the presence of axial-vector components in the Z exchange. A physics, in particular the dark photons case, is commonly simpler to constrain and therefore favored by experimental tests. Finally, the model can be UV completed both by stable χ fermions or by right-handed neutrinos. The prior case may provide cold WIMPs in the theory.

We consider in the 3-3-1 model with heavy leptons the box contributions to the mass difference in K and B neutral mesons induced by neutral (pseudo)scalars, exotic charged quarks, singly and doubly charged scalar and gauge bosons. In particular, we include the effects of a real scalar with mass near 125 GeV but with non-diagonal couplings to quarks. We show that, as in the tree level case, there are ranges of the parameters in which these contributions can be enough suppressed by negative interference among several amplitudes. Hence, in this model these ∆F = 2 processes may be dominated by the standard model contributions. In addition, our results are valid in the minimal 3-3-1 model without the sextet.

We consider experimental constraints in the MeV region in order to determine the parameter space for the U(1) X extension of the Standard Model, presented in the first part of our work. In particular, we focus on the model UV-completed by cold WIMPs. We conclude that the electron anomalous magnetic moment and the neutrino trident production provide the most stringent bounds to g 2 X ∼ 10 −6 in the mass interval below the di-muon threshold. By allowing the axial-vector coupling of the dark gauge boson Z , the interference effect with the SM gauge bosons may reduce the bounds coming from the neutrino trident production. At the same time, such coupling allows a region of the parameter space already favored both by the relic abundance and by the discrepancy between experimental result and theoretical prediction for the muon anomalous magnetic moment. We emphasize that light-Z interactions, non-universal for the two first lepton families, necessarily create a difference in the proton charge radius measured in the Lamb shift of the e-hydrogen and µ-hydrogen. Finally, we determine the effects of the new gauge boson on the forward-backward asymmetry in e + e − →f f , f = µ, τ , and on the leptonic decays M → jν j l + l − , where M = π, K, D, D s , B and j, l = e, µ.

, where the new degrees of freedom have the same standard electric charges, additional Yukawa interactions may create decay channels into the SM sector. Furthermore, motivated by a general consequence of the Goldstone theorem, a method of diagonalization by parts is introduced in the Scalar sector and provides a clarification on the definition of mass eigenstates. In summary, we develop the most complete set of terms allowed by the symmetry group and resolve their definitive pieces in order to justify the model description present in the literature.