Some Phenomenology
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![A 1-loop diagram for muon $(g-2)_\mu$ through new vector leptons. []{data-label="fig:g-2"}](g-2.eps){width="30.00000%"}

The model contains many new sources of lepton flavor violation due to the extra scalars and fermions, and is similar to other flavor symmetry models. For example, lepton flavor violating processes in the $A_{4}$ models are studied in ref. [@Ding:2009gh].

Here we address the presence of the extra contribution to the muon anomalous magnetic moment and leptonic rare decay processes ($\mu\rightarrow e\gamma, \tau \rightarrow \mu\gamma$) due to the existence of heavy vectorlike field $l_{L+R,3}$ which does not appear in other non-Abelian discrete symmetry models. The current limit of the muon anomalous $g-2$ is [@PDG] $$\begin{aligned}
\Delta a_{\mu} = (290\pm90)\times10^{-11} \;\;,\end{aligned}$$ which is a $3.2\sigma$ deviation between SM calculations and experiment [@Jegerlehner:2009ry]. The leading contribution to the muon anomalous magnetic moment in our model is showed in Fig. \[fig:g-2\], and yields $$\begin{aligned}
\Delta a_{\mu} \approx \frac{Y_{4}Y_{S2}}{12\pi^2}\frac{m_{\mu}m_{L+R,_{3}}}{m^2_{H}}F(z) \;\;,\end{aligned}$$ where $z = \left(\frac{m_{L+R,3}}{m_{H}}\right)^{2}$. Note that we have ignored all the mixing factors in both Higgs and lepton sectors. The function $F(z)$ is defined as $$\begin{aligned}
F(z) = -\frac{3}{2(1 - z)^3}\left[3 - 4z + z^2 + 2\ln{z} \right] \;\;. \end{aligned}$$ Similar diagrams lead to rare radiative decays of $\mu \rightarrow 