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In this paper, we will present analytic formulas to express one-loop contributions to lepton flavor violating decays $e_b\to e_a γ$, which are also relevant to the anomalous dipole magnetic moments of charged leptons $e_a$. These formulas were computed in the unitary gauge, using the well-known Passarino-Veltman notations. We also show that our results are consistent with those calculated previously in the 't Hooft-Veltman gauge, or in the limit of zero lepton masses. At the one-loop level, we show that the appearance of fermion-scalar-vector type diagrams in the unitary gauge will violate the Ward Identity relating to an external photon. As a result, the validation of the Ward Identity guarantees that the photon always couples with two identical particles in an arbitrary triple coupling vertex containing a photon., The version accepted to Nuclear Physics B

The significance of new physics appearing in the loop-induced decays of neutral Higgs bosons into pairs of dibosons γγ and Zγ will be discussed in the framework of the 3-3-1 models based on a recent work [H. Okada, N. Okada, Y. Orikasa, and K. Yagyu, Phys. Rev. D 94, 015002 (2016)], where the Higgs sector becomes effectively the same as that in the two Higgs doublet models (2HDM) after the first symmetry breaking from SU(3)L scale into the electroweak scale. For large SU(3)L scale v3≃10 TeV, dominant one-loop contributions to the two decay amplitudes arise from only the single charged Higgs boson predicted by the 2HDM, leading to that experimental constraint on the signal strength μγγ331 of the Standard Model-like Higgs boson decay h→γγ will result in a strict upper bound on the signal strength μZγ331 of the decay h→Zγ. For a particular model with lower v3 around 3 TeV, contributions from heavy charged gauge and Higgs bosons may have the same order, therefore may give strong destructive or constructive correlations. As a by-product, a deviation from the SM prediction |μγγ331−1|≤0.04 still allows |μZγ331−1| to reach values near 0.1. We also show that there exists an CP-even neutral Higgs boson h30 predicted by the 3-3-1 models, but beyond the 2HDM, has an interesting property that the branching ratio Br(h30→γγ) is very sensitive to the parameter β used to distinguish different 3-3-1 models.

The significance of new physics appearing in the loop-induced decays of neutral Higgs bosons into pairs of dibosons $����$ and $Z��$ will be discussed in the framework of the 3-3-1 models based on a recent work~\cite{Okada:2016whh}, where the Higgs sector becomes effectively the same as that in the two Higgs doublet models (2HDM) after the first symmetry breaking from $SU(3)_L$ scale into the electroweak scale. For large $SU(3)_L$ scale $v_3\simeq10$ TeV, dominant one-loop contributions to the two decay amplitudes arise from only the single charged Higgs boson predicted by the 2HDM, leading to that experimental constraint on the signal strength $��^{331}_{����}$ of the Standard Model-like Higgs boson decay $h\rightarrow ����$ will result in a strict upper bound on the signal strength $��^{331}_{Z��}$ of the decay $h\rightarrow\, Z��$. For a particular model with lower $v_3$ around 3 TeV, contributions from heavy charged gauge and Higgs bosons may have the same order, therefore may give strong destructive or constructive correlations. As a by-product, a deviation from the SM prediction $|��^{331}_{����}-1| \le 0.04$ still allows $|��^{331}_{Z��}-1|$ to reach values near 0.1. We also show that there exists an $CP$-even neutral Higgs boson $h^0_3$ predicted by the 3-3-1 models, but beyond the 2HDM, has an interesting property that the branching ratio Br$(h^0_3\rightarrow ����)$ is very sensitive to the parameter $��$ used to distinguish different 3-3-1 models., Version accepted for publication in PRD