Vectorlike lepton imprints at lepton $g-2$ measurements and $e^+e^-$ colliders

A fermion can be chiral or vectorlike with respect to a given symmetry, depending on its coupling to the corresponding gauge boson. Vectorlike fermions have a distinct property that their left-handed and right-handed components behave in the same way under the gauge symmetry. In this paper, we investigate an extension of the standard model with an $SU(2)$ doublet of vectorlike leptons and two complex scalars. The new physics effects on the lepton anomalous magnetic moment, as well as the electron and muon pair production processes at $e^+e^-$ colliders are analyzed. Taking into account the updated measurement results of the electron and muon $g-2$, the LEP and the LHC data, the viable parameter space of the model is identified. We also examine the prospect of testing the model using $μ^+μ^-$ signals from electron-position annihilation at the Future Circular Collider (FCC-ee). The analysis shows that the FCC-ee will be able to exclude a significant part of the parameter space, pinpointing exiguous viable regions to be tested in the future due to its high precision.

💡 Research Summary

The paper proposes a minimal extension of the Standard Model (SM) that adds an SU(2)ₗ doublet of vector‑like leptons (L = (N, E)ᵀ) together with two complex scalar singlets, χ and ϕ. The scalar ϕ belongs to a hidden sector and acquires a non‑zero vacuum expectation value (VEV), while χ does not develop a VEV and couples to the SM leptons and the vector‑like leptons through exotic Yukawa interactions yℓ L ℓ_R χ (ℓ = e, μ, τ). A Z₂ symmetry is imposed under which SM fields and ϕ are even, whereas L and χ are odd. Consequently, there is no tree‑level mixing between SM leptons and the new vector‑like states, avoiding dangerous flavor‑changing neutral currents.

The scalar potential contains a term r ϕ χ² that splits the masses of the real and imaginary components of χ, denoted χ_r and χ_i. Their masses are m²_{χ_r}=m’²_χ−2r⟨ϕ⟩, m²_{χ_i}=m’²_χ+2r⟨ϕ⟩, with m’²_χ containing the usual quadratic and quartic contributions. For r > 0, χ_r is lighter and, being Z₂‑odd, becomes a stable particle that can serve as a dark‑matter candidate.

The new particles contribute to the anomalous magnetic moments of charged leptons at one loop. The contribution reads Δa_NP^ℓ = (y_ℓ² m_ℓ²)/(32π² m_{χ_r}²)