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

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

2007-07-30

arxiv.org/abs/0707.4427v1

Physics

High Energy Physics

High Energy Physics - Phenomenology

13 pages, 11 figures

Scientific paper

This work has shown that at strict fulfilment of condition $\Delta m^2_{1 3} = \Delta m^2_{1 2} + \Delta m^2_{2 3}$ 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 $\beta \le 15^o \div 17^o$).

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