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: