Testing the Wigner - Weisskopf approximation by using neutral-meson - antimeson correlated states

We phenomenologically decompose the Weisskopf--Wigner approximation, as applied to the neutral flavoured meson complexes, into three pieces and propose tests for these pieces. Our tests hold for general decay amplitudes and $M^0$--$\bar M^0$ mixing parameters. We concentrate on C-odd $M^0 \bar M^0$ states and stress the importance of such tests in view of the variety of physics extracted from measurements on such complexes. Studying the feasibility of the tests confines one to the $K^0 \bar K^0$ system at present. In particular, we show that the time dependence of the correlated decay $\phi \to K^0 \bar K^0 \to 2 (\pi^+ \pi^-)$ is determined solely by the WWA and provides thus a clean test of it.