Note on the field theory of neutrino mixing

Abstract

The possibility of constructing the Hilbert space of definite flavor neutrino states, especially a one-flavor neutrino state, is investigated in the theory with flavor-mixing mass terms in the Lagrangian. Reviewing the work of Blasone and Vitiello in detail, we clarify that even if we construct the Hilbert space of a definite flavor neutrino, the oscillation probabilities of neutrinos derived according to the usual way include arbitrary mass parameters. We examine the structure of the flavor neutrino propagator and show that the physical poles of the propagator coincide with mass eigenvalues of the mass matrix in the Lagrangian irrespective of such arbitrary parameters. This gives a possible way of escaping the arbitrariness.