Examination of unitarity condition (positive definiteness of expression for transition probabilities) at three neutrino oscillations in vacuum

Abstract

This work has shown that at strict fulfilment of condition $Δm^2_{1 3} = Δm^2_{1 2} + Δm^2_{2 3}$ the expression for probability of $ν_e \to ν_e$ transitions $P_{ν_e \to ν_e}(t)$ is positively defined at every values of $θ$ and $β$ while at any arbitrarily small deviation from this condition it becomes negative. In order to make this expression for probability transitions positively defined, it is necessary to put a limitation on angle mixing $β$ at fixed value of $θ= 32.45^o$ (i.e. the value for $β$ must be $β\le 15^o ÷17^o$).