Dipole moments of charged leptons in the THDM-III with Textures

We study the magnetic and weak magnetic dipole moments of charged leptons in the framework of the Two Higgs Doublet Model type III (THDM-III) with four zero textures. We first analyze the possibility that the discrepancy between the experimental measurements and the theoretical prediction of the muon anomalous magnetic dipole moment ($a_{\mu}$) in the Standard Model (SM) can be explained in the context of the model and then find values for the parameters of the THDM-III: neutral and charged Higgs boson masses ($m_{H}$, $m_{H^{\pm}}$), mixing angles ($\alpha, {\beta}$), CP-violating angles $\theta_1,\,\theta_2$ and an additional parameter arising from the mass matrix ($\gamma_f$), for which a correspondence between theory and experiment is possible. We use $a_{\mu}^{THDM-III}$ and current low energy processes $K-\bar{K}$ mixing, $B_s^0\to\mu\bar\mu$, $\tau\to\mu\mu\bar\mu$, $\mu\to e e \bar e$, $\tau\to \mu\gamma$, $\tau\to e\gamma$, $\mu\to e \gamma$, $b\to s\gamma$, $B\to D (D^*) \tau\nu$ and the rare higgs decay $h\to\tau\mu$ in order to determine the allowed parameter space of THDM-III and from these we give a prediction for the magnetic and weak magnetic dipole moment of charged leptons, in particular of the $\tau$ lepton. The obtained magnetic dipole moment of the $\tau$ lepton is of the order of $\mathcal{O}(10^{-8}-10^{-7})$ and the weak magnetic is of the order $\mathcal{O}(10^{-10}-10^{-7})$.