In this section we will discuss the possibility to detect CP
violation through the study of the time difference distribution 
,
defined in eq. (8), choosing 
and
[32]. To this purpose we recall some useful
decomposition of the 
decay amplitude, referring to
[9] for a more detailed discussion of these decays.
The amplitude for 
decays can be generally decomposed as
the sum of two terms: the inner bremsstrahlung 
and
the direct emission 
[9].
The first term, which has a pole at zero photon energy,
is completely predicted by QED in terms of the 
amplitude
[34]:
The second term, which is obtained by
subtracting 
from the total amplitude,
depends on the structure of the
effective vertex
and provides a test for mesonic interaction models.
The 
amplitude
is usually decomposed also in a different way, separating the
electric and the magnetic terms. Defining
the dimensionless amplitudes E and M as in [35],
we can write:
where
As can be seen from eq. (55),
the inner bremsstrahlung amplitude can contribute only to the
term, while the direct emission amplitude can
contribute to both the 
and the 
terms.
Summing over photon helicities there is no interference between electric and
magnetic terms:
(
). Thus the two contributions 
and
can interfere in the 
amplitude,
contrary to the case of the amplitude 
where only a direct emission contribution appears:
Finally the magnetic and the electric direct emission amplitudes can be
decomposed in a multipole expansion (see Refs. [9,36]). Since higher
multipoles are suppressed by angular momentum barrier, in the following
we will consider only the lowest multipole component (the dipole one).
In this approximation the electric amplitude
is CP-conserving in the 
decay and CP-violating in the 
one,
while the magnetic amplitude is CP-conserving in the 
decay and
CP-violating in the 
one. For this reason, since 
is enhanced by
the pole at zero photon energy, the 
decay is completely
dominated by the electric transition, while
electric and magnetic contributions are of the same
order in the 
decay.
Similar to 
and 
cases it is convenient to
introduce the CP-violating parameter:
where the subscript 
indicates that only the
lowest multipole component of the electric direct emission
amplitude has been considered. Using eq. (55) we can write:
where 
is the usual 
CP-violating parameter.
The term proportional to 
in eq. (61) is a direct CP-violating
contribution, not related to the 
amplitude and consequently
not suppressed by the 1/22 factor of the 
rule.
However, although 
could be much larger than
, the second term in eq. (61)
is suppressed by the factor 
.
The 
parameter has already been measured at
Fermilab obtaining for the IB contribution [37]
DA
NE should improve these limits by studying
the time evolution of the decay.
Referring to [32] for an extensive analysis,
here we show how to take advantage of the 
-factories possibilities
to measure 
. Choosing as final states
, 
and following the
notation of Section 2, the time difference distribution,
integrated over final phase space, is given by
:
where
and
Neglecting the phase space dependence of 
one should have
, and therefore
the interference term of eq. (64) measures the CP-violating
amplitude.
The expression for t>0 is obtained by interchanging 
and changing
the sign of the 
term.
By fitting the experimental data with the theoretical expression of
eq. (64), one should be able to measure
the interference term and then improve
the measurement of 
. Very useful to this purpose will be
the difference among the fluxes defined in eq. (64)
with positive and negative lepton charges, as discussed for 
decays.
To conclude, we remark that not only the semileptonic tagging but
also the 
one can be used to measure
[32].
