Lepton Flavor Violating Z Decays in the Zee Model

We calculate lepton flavor violating (LFV) Z decays Z \to {{e_i^\pm}}e_j^\mp (i, j = e, \mu, \tau ; i\neq j) in the Zee model keeping in view the radiative leptonic decays e_i\to e_j\gamma (i = \mu, \tau ; j = e, \mu ; i\neq j), \mu decay and anomalous muon magnetic moment (\mu AMM). We investigate three different cases of Zee f_{ij} coupling (A) f_{e\mu}^2 = f_{\mu\tau}^2= f_{\tau e}^2, (B) f_{e\mu}^2 \gg f_{\tau e}^2 \gg f_{\mu\tau}^2, and (C) f_{\mu\tau}^2 \gg f_{e\mu}^2 \gg f_{\tau e}^2 subject to the neutrino phenomenology. Interestingly, we find that, although the case (C) satisfies the large excess value of \mu AMM, however, it is unable to explain the solar neutrino experimental result, whereas the case (B) satisfies the bi-maximal neutrino mixing scenario, but confronts with the result of \mu AMM experiment. We also find that among all the three cases, only the case (C) gives rise to largest contribution to the ratio B(Z\to e^\pm\tau^\mp)/B(Z\to \mu^\pm \mu^\mp) \simeq {10}^{-8} which is still two order less than the accessible value to be probed by the future linear colliders, whereas for the other two cases, this ratio is too low to be observed even in the near future for all possible LFV Z decay modes.