  Neutrino mixing and oscillations in quantum field theory framework had been
studied before, which shew that the Fock space of flavor states is unitarily
inequivalent to that of mass states (inequivalent vacua model). A paradox
emerges when we use these neutrino weak states to calculate the amplitude of
$W$ boson decay. The branching ratio of W(+) -> e(+) + nu_mu to W(+) -> e(+) +
nu_e is approximately at the order of O({m_i^2}/{k^2}). The existence of flavor
changing currents contradicts to the Hamiltonian we started from, and the usual
knowledge about weak processes. Also, negative energy neutrinos (or violating
the principle of energy conservation) appear in this framework. We discuss
possible reasons for the appearance of this paradox.
