The Lepton Flavor Changing Decays and One-loop Muon Anomalous Magnetic Moment in the Extended Mirror Twin Higgs Models

Mirror Twin Higgs(MTH) models always contain heavy gauge bosons and extra Higgses. Besides, to accommodate tiny neutrino masses via seesaw mechanism, new heavy neutrinos can also be introduced in MTH extension models. Such new particles and interactions may lead to new contributions to the lepton flavor violating (LFV) processes, including $\ell_i \to \ell_jγ$ and $\ell_i \to \ell_j\ell_k\ell_l$. We find that current experimental data can stringently constrain the parameter spaces and certain LFV processes can possibly be tested by the next generation colliders. One-loop contributions of the new particles to the muon anomalous magnetic momentumare also calculated. Such contributions can still not solve the discrepancy between the experiments and the prediction of the standard model.

💡 Research Summary

The paper investigates lepton‑flavor‑violating (LFV) processes and the muon anomalous magnetic moment (g‑2) within an extended Mirror Twin Higgs (MTH) framework. In the minimal MTH scenario the Standard Model (SM) is duplicated in a twin sector related by a Z₂ symmetry; this protects the Higgs mass from quadratic divergences but introduces a hidden sector that is difficult to probe directly at colliders. To generate realistic neutrino masses the authors introduce heavy neutrinos of two types: (i) twin neutrinos (ν̃) that mix with the SM neutrinos via a small angle θ (or equivalently a mixing matrix element Ṽ_ν), and (ii) right‑handed neutrinos (ν_R) that couple to a new charged scalar H^± through a Yukawa coupling y_νR. The model also contains the usual SM gauge bosons (W^±, Z) and their twin counterparts, as well as additional charged Higgs bosons whose masses are taken in the range 100–1000 GeV, while the heavy neutrinos have masses m_{ν̃}≈1 GeV and m_{ν_R}=0.5–5 TeV.

The authors first write down the LFV interaction Lagrangian. The mixing term (Eq. 2) yields a coupling of W^± to a linear combination of ν and ν̃, while the Yukawa term (Eq. 3) provides a coupling of H^± to charged leptons and ν_R. These interactions generate LFV transitions at one‑loop order. The radiative decays ℓ_i→ℓ_jγ are computed using the standard electromagnetic current decomposition; the gauge‑invariant form factor F_2(0) is extracted from the loop amplitude. The amplitude is expressed in terms of Passarino‑Veltman three‑point functions C_ij, with separate contributions from the W–ν̃ loop (proportional to |Ṽ_ν|^2) and the H^±–ν_R loop (proportional to |y_νR|^2). The decay width is Γ(ℓ_i→ℓ_jγ)=m_i^5/(4π)·|M|^2, and the branching ratio is obtained by normalising to the dominant SM decay ℓ_i→ℓ_jνν̄, giving BR≈48π^2 G_F^2 |M|^2.

A detailed numerical scan shows that the current experimental bound on μ→eγ (BR<4.2×10^−13) translates into |Ṽ_ν|≲2×10^−3 and |y_νR|≲4.6×10^−3 for the benchmark masses (m_{H^±}=300 GeV, m_{ν̃}=1 GeV, m_{ν_R}=1 TeV). The branching ratios rise monotonically with the couplings, while the dependence on the heavy masses is milder; increasing m_{H^±} or m_{ν_R} slightly suppresses the rates, but the effect is modest within the explored range. The authors plot the allowed regions in the (Ṽ_ν, y_νR) plane that would lead to observable signals at upcoming experiments such as MEG II and Mu3e. Similar analyses are performed for τ→eγ and τ→μγ, taking into account the larger total τ width (including hadronic modes). The resulting τ LFV branching ratios are roughly a factor of five smaller than the muon case, still below present limits but potentially reachable at future high‑luminosity B‑factories or FCC‑ee.

The three‑body decays ℓ_i→ℓ_jℓ_kℓ_l (e.g., μ→3e, τ→3μ) are also evaluated. They receive contributions from photon‑penguin diagrams (essentially the same loop functions as the radiative decays) and from box diagrams involving the heavy neutrinos and H^±. The predicted rates are typically one to two orders of magnitude beneath current experimental bounds, indicating that next‑generation searches could start probing the parameter space, especially in the τ sector where the limits are weaker.

Finally, the paper addresses the muon anomalous magnetic moment. The same loops that generate LFV also contribute to Δa_μ. The authors derive Δa_μ≈(m_μ^2/8π^2)