next up previous
Next: Semileptonic decay rates Up: Decay Rates Previous: Decay rate into two

Decay rate into three pions

Neutral Kaons can decay into and final states. For the decay mode, the pair can have total isospin I'=0,1 and 2. The total wave function has to be symmetric under exchange of and . If the orbital angular momentum of the state is odd then the isospin must be I'=1 and I'=0,2 for even angular momentum. The total isospin must be I=3,2,1 or 0.


The decay rates of the and state into the final state can be expressed as:

with the usual Dalitz parameters:

The energies are defined in the rest frame of the neutral kaon. The violating contribution to the decay is suppressed due to the centrifugal barrier and neglected in . The conserving contributions to the decay proportional to X vanish in the case of the final state because X is antisymmetric with respect to the exchange of and . The total decay rates of and are given by integrating over the whole phase space:

In this case becomes zero if there is no violation in decays whereas in addition to the violating amplitude contains also the conserving amplitude for the final state. In the limit of small and violation we get and . The interference term can be extracted using the following time dependent decay rate asymmetry:

where . Even with the contribution of the conserving amplitude in the decay we can write the asymmetry to a good approximation as:



Thomas Ruf
Fri Aug 9 14:24:14 MET DST 1996