Unitarity triangle test of the extra factor of two in particle oscillation phases

There are claims in the literature that in neutrino oscillations and oscillations of neutral kaons and B-mesons the oscillation phase differs from the standard one by a factor of two. We reconsider the arguments leading to this extra factor and investigate, in particular, the non-relativistic regime. We actually find that the very same arguments lead to an ambiguous phase and that the extra factor of two is a special case. We demonstrate that the unitarity triangle (UT) fit in the Standard Model with three families is a suitable means to discriminate between the standard oscillation phase and the phase with an extra factor of two. If $K_L - K_S$ and $B_{dH} - B_{dL}$ mass differences are extracted from the $K^0 - \bar K^0$ and $B_d^0 - \bar B_d^0$ data, respectively, with the extra factor of two in the oscillation phases, then the UT fit becomes significantly worse in comparison with the standard fit and the extra factor of two is disfavoured by the existing data at the level of more than 3 $\sigma$.