The time evolution of an arbitrary neutral kaon state after solving eq. 2 is given by:
with
where and
are the eigenvalues of the matrix
.
The eigenvectors which follow an exponential decay law are given by:
with arbitrary phases ,
and
In the special case of initial pure or
at time
we obtain:
In the limit of small violation, i.e.
and small
violation, i.e.
, we obtain:
with and
describing
and
violation
in the mass and decay matrix:
The phase of the parameter is identical to the superweak phase
.
The masses and decay widths of the two eigenstates are given
by
:
In the limit of conservation and by fixing the arbitrary phase
,
and
become
eigenstates with
eigenvalues +1 and -1: