Such decays are crucial to the observation of CP violation in these experiments. What the experimenters are looking for is any difference in the rates at which the B 0 and decay to a common CP eigenstate. Any such difference would violate CP symmetry. But then the tagging decay starts a new clock by measuring the flavor of one B and thus projecting the other B into the opposite flavor state. It can be positive or negative, depending on whether the tagging decay comes before or after the CP decay.
L is the longer-lived mass eigenstate of the neutral kaon system.
The amplitude of this CP -violating oscillation, sin 2 b , is the key parameter these experiments set out to measure. If it's zero, there is no CP violation. The first order of business was to see whether the B system exhibits any CP violation at all. That's obviously still up in the air, given that both experiments have measured a sin 2 b that, so far, is only about 1.7 standard deviations from zero. If the measured sin 2 b does not vanish, the next thing is to see how well it agrees with the standard model.