Conclusion

$\quad$ In summary, we have calculated the transition radiation of a neutrino induced by its toroid dipole moment in the framework of quantum theory. Since the TDM of a neutrino is nonzero in the massless limit [4,5], the corresponding TR energy is also nonzero and equals $S\simeq 2.26\times10^{-40}$ keV for $\tau_{\nu_e}=e\sqrt{2}G_F/\pi^2$.  In addition the TDM is the weak-electromagnetic characteristic which both Dirac and Majorana neutrinos posses, therefore the transition radiation induced by TDM exist indepedently on the nature of the neutrino and its mass.

It is highly plausible that we will stand face-to-face with the dramatic circumstances if either the Dirac neutrinos possess negligible masses and their magnetic moments are also small, or if all neutrinos have a Majorana nature. Then the unique electromagnetic characteristic of such neutrinos will be the toroid moment and we will be forced to seek for some exotic effects generated by it. For instance, if the neutrino is a massless particle then measurement of the transition radiation can be used as a tool to distinguish the nature of the neutrino (since the Dirac TDM is half of the Majorana one and as the energy intensity is proportional to the square of the TDM (8), the TR of Dirac neutrino is 1/4 of the Majorana one).

It is interesting to note that TR energy of the order of $10^{-40}$ keV for a neutrino with TDM corresponds to the TR energy of a neutrino with anomalous magnetic moment $\mu_\nu\sim10^{-15}\mu_B$ for $m_\nu=1$ eV [12]. Such TR of neutrinos induced by their TDMs may have interesting implications for astrophysics as well as the early Universe. However, the conclusions about the magnitude of these effects requires further investigation.