Flavor State of the Neutrino: Conditions for a Consistent Definition

Similar to Blasone et al. Phys. Rev. D 72 (2005) 013003 by examining the expectation value of the flavor charge under the normalized flavor state of the neutrino, we demonstrate that the introduction of the flavor state is consistent with the flavor charge only when the conditions, i.e. (A) |p|=0 (the low energy case), or |p|/m_i≫1 (the relativistic case) and (B) the flavor state should be defined of the Pontecorvo form |ν_e〉=cosθ|ν₁〉+sinθ|ν₂〉 or equivalently except a global phase, are satisfied. The root of the issue lies in the structure of the flavor charge operator. The diagonalization of the flavor charge operator with the integer eigenvalue can be realized through the Bogoliubov–Valatin transformation when condition A is satisfied. The eigenstate of the diagonalized flavor charge is of the Pontecorvo form under condition B.