Right-handed Neutrino Fields are Real Spinors

The ansatz that the right-handed neutrino fields are real spinors is proposed in this letter. We naturally explain why the right-handed neutrinos don't feel the electroweak interactions and why there is neutrino mixing. It is found that the Majorana representation of Dirac equation is uniquely permitted in our scenario. With this ansatz, we predict that: 1. there are at least four species of neutrinos; 2. the mass matrix of neutrinos must be traceless; 3. there is CP violation in the lepton sector. The difference between our scenario and the Zee model is discussed also.