Refined applications of the collapse of the wave function

Abstract

In a two-part system the "collapse of the wavefunction" of one part can put the other part in a state which would be difficult or impossible to achieve otherwise, in particular one sensitive to small effects in the `collapse' interaction. We present some applications to the very symmeteric and experimentally accessible situations of the decays $\phi(1020)\to K^oK^o$, $\psi(3770)\to D^oD^o$, or $\Upsilon(4s)\to B^oB^o$, involving the internal state of the two-state $K^o$, $D^o$ or $B^o$ mesons. The "collapse of the wavefunction" occasioned by a decay of one member of the pair (`away side') fixes the state vector of that side's two-state system. Bose-Einstein statistics then determines the state of the recoiling meson (`near side'), whose evolution can then be followed further. In particular the statistics requirement dictates that the `away side' and `near side' internal states must be orthogonal at the time of the "collapse". Thus a CP violation in the `away side', decay implies a complementary CP impurity on the `near side', which can be detected in the further evolution. The CP violaion so manifested is necessarily direct CP violation, since neither the mass matrix nor time evolution was involved in the "collapse". A parametrization of the direct CP violation is given and various manifestations are presented. Certain rates or combination of rates are identified which are nonzero only if there is direct CP violation. The very explicit and detailed use made of "collapse of the wavefunction" makes the procedure interesting with respect to the fundamentals of quantum mechanics. We note an experimental consistency test for our treatment of the "collapse of the wavefunction", which can be carried out by a certain measurement of partial decay rates.