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Neutrino mixing and oscillations in quantum field theory framework had beenstudied before, which shew that the Fock space of flavor states is unitarilyinequivalent to that of mass states (inequivalent vacua model). A paradoxemerges 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 flavorchanging currents contradicts to the Hamiltonian we started from, and the usualknowledge about weak processes. Also, negative energy neutrinos (or violatingthe principle of energy conservation) appear in this framework. We discusspossible reasons for the appearance of this paradox.Comment: 15 pages, revised version: oscillation effect is separate

A paradox on quantum field theory of neutrino mixing and oscillations