Limits on the magnetic moment of sterile neutrino and two-photon neutrino decay

It is shown that the non-zero transition magnetic moment ($\mu_{tran}$) between the sterile neutrino ($\nu_{s}$) and the muon neutrino ($\nu_{\mu}$) could be effectively searched for via the Primakoff effect, in the process of $\nu_{\mu} Z \to \nu_{s}Z$ conversion in the external Coulomb field of a nucleus $Z$, with the subsequent $\nu_{s}\to \nu_{\mu} + \gamma$ decay. From the recent results of the NOMAD neutrino detector at CERN a model-independent constraint of $\mu_{tran} < (10^{-6} - 10^{-9}) \mu_{B}$ is obtained depending on the value of $\nu_{s}$ mass. For the $m_{s}\sim O(1) GeV$ region these bounds are comparable with the present experimental ones on $\nu_{\mu}$ and $\nu_{e}$ diagonal magnetic moments and are more sensitive than those on $\nu_{\tau}$ magnetic moment. From the same analysis the constraint on $\nu_{\tau}(\nu_{s})\to \nu_{\mu} +\gamma + \gamma$ decay lifetime $\tau > 2\times10^{13} sec/m_{\nu}^{7}(MeV)$ is obtained. The limit is valid for neutrino masses up to $m_{\nu}\sim O(1)GeV$.