Lepton flavor violating signals driven by CP symmetry of order 4

CP4 3HDM is a curious version of the three-Higgs-doublet model built upon a CP symmetry of order 4 (dubbed CP4). When extended to fermions, CP4 leads to unusually tight correlations between the scalar and Yukawa sectors and induces tree-level flavor changing neutral couplings. Still, viable scenarios exist, in which quark flavor changing signals remain within experimental limits. In this work, we extend CP4 to the lepton sector and investigate whether the lepton-Higgs couplings and lepton flavor violating (LFV) signals can also be kept under control. We consider two classes of LFV processes: tree-level lepton decays of the 125 GeV Higgs boson and one-loop radiative decay $μ\rightarrow eγ$. For each CP4-invariant lepton Yukawa scenario, we perform a focused Yukawa sector scan that uses physical lepton properties as input and suppresses LFV effects. We identify a promising CP4 3HDM scenario compatible with the present-day experimental constraints, show that it can accommodate the recent CMS hint of a 146 GeV scalar decaying to $eμ$, and argue that this interpretation can be tested at future colliders.

💡 Research Summary

The paper investigates lepton‑flavour‑violating (LFV) phenomena in a three‑Higgs‑doublet model (3HDM) that is invariant under a generalized CP transformation of order four (CP4). While CP4 has already been studied in the scalar sector and, more recently, in the quark Yukawa sector, this work extends the symmetry to the charged‑lepton sector and examines whether the resulting LFV effects can be compatible with current experimental bounds.

The authors first review the CP4‑3HDM scalar potential, which consists of a CP4‑invariant part V₀ and a CP‑odd part V₁. The vacuum expectation values are parametrised by two angles β and ψ, and a Higgs basis rotation isolates a single doublet with a non‑zero vev. Misalignment between the SM‑like Higgs boson h_SM and the vacuum direction is described by four mixing angles (ϵ, α, γ₁, γ₂); ϵ plays the role of the usual β–α in 2HDM and controls the h_SM couplings to gauge bosons.

In the lepton Yukawa sector, CP4 invariance restricts the three Yukawa matrices Γ₁, Γ₂, Γ₃ to three non‑trivial textures, labelled B₁, B₂ and B₃ (case A is trivial and yields no LFV). After electroweak symmetry breaking the charged‑lepton mass matrix M_e is a linear combination of Γ₁, Γ₂, Γ₃ weighted by β, ψ. Diagonalisation with unitary matrices V_L and V_R yields the physical masses and the PMNS matrix (θ₁₂≈33.6°, θ₂₃≈46.9°, θ₁₃≈8.5°, δ≈210°). The off‑diagonal couplings of the non‑SM Higgs doublets Φ₂ and Φ₃ to leptons are encoded in matrices N₂ and N₃, which are functions of the chosen texture but independent of ψ.

The physical neutral and charged Higgs bosons are obtained by diagonalising the 5×5 neutral and 2×2 charged scalar mass matrices. Their couplings to leptons are expressed through matrices Y_k (neutral) and Z_k (charged). For the SM‑like Higgs the coupling matrix Y contains a diagonal piece proportional to the lepton masses (scaled by cos ϵ) and off‑diagonal pieces proportional to sin ϵ multiplied by linear combinations of N₂ and N₃ with coefficients set by α, γ₁, γ₂. Consequently, tree‑level LFV decays h_SM→ℓ_iℓ_j (i≠j) are directly linked to the chosen Yukawa texture and the scalar mixing angles.

The authors also compute the one‑loop contribution to the radiative decay μ→eγ, which receives diagrams with neutral Higgs exchange and with charged Higgs exchange. Using the standard loop functions for multi‑Higgs doublet models, they evaluate the amplitudes A_L and A_R and compare the resulting branching ratio with the MEG II limit Br(μ→eγ)<1.5×10⁻¹³.

A two‑stage numerical scan is performed. First, the scalar sector is sampled over v, β, ψ, the SM‑like Higgs mass, the four mixing angles, the charged‑Higgs masses and the combination λ₈₉ = √