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 $\Delta m_{13}^2=\Delta m_{12}^2+\Delta m_{23}^2$ the expression for probability of ${\nu }_e\to {\nu }_e$ transitions $P_{{\nu }_e\to {\nu }_e}(t)$ is positively defined at every values of $\theta$ and $\beta$ 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 $\beta$ at fixed value of $\theta =32.45^o$ (i.e. the value for $\beta$ must be $\beta \le 15^o÷17^o$).

Comments: 13 pages, 11 figures