Some years ago it was pointed out that the radiative 
decay
(
)
could have a non-negligible branching ratio and therefore
could spoil the power of a 
factory in measuring 
and to single out the suppressed 
decays [12].
More recent determinations of the resonant contribution consider also the
, 
interference effect and
give a much lower value: the ratio
is estimated to be in the range
--
[13].
These predictions are strongly
model-dependent and larger values could perhaps be obtained; however we can
trust that r is certainly smaller than 
.
The non-resonant contribution to 
has been evaluated in the current algebra framework [38] to be
of the order of 
, comparable to the lower
predictions of [13].
As we will show, the effects of the
C-even background on the DA
NE measurements
are negligible also for unrealistically large values of r.
The C-even 
state can be written as:
where terms of order 
have been neglected but the
effect of possible CPT violation has been included.
The 
component has a CP-conserving decay into the 
final states and could be a dangerous background in the 
measurement.
However, the time difference distribution of
these events,
is symmetric and cannot simulate the effect of 
.
Furthermore, it vanishes very rapidly for large values of |t|, and
therefore
it does not affect
the determination of 
. In effect,
as shown in [39], by means of a suitable cut the background
contribution can be eliminated in the
event sample used to determine 
, also for very large values of r.
The background contribution overlaps the signal just in the
interference zone,
, worsening the resolution on 
.
However the signal (
)
and the background
(
) have different
spatial behaviour, which is of help
in disentangling the signal contribution from the
background.
The C-even background has been added to the signal in the
fitting procedure of [20] and the accuracy achievable on
has been estimated again.
The result is that for a realistic vertex
resolution the worsening is around 5%, even if r would be as large
as 
.
The 
component can affect the determination of the suppressed
branching ratios and the corresponding CP-violating asymmetries, as
we will discuss in the following.
If the 
semileptonic decays are
tagged as in eq. (25), the number of events generated by
a single C-even 
pair is:
then eq. (27) is modified in:
and the measured charge asymmetry becomes:
As can be seen the correction is absolutely negligible and cannot
simulate CPT violation, in fact 
.
The number of equal-sign dilepton events generated by
is:
and that of opposite sign is:
Therefore the experimentally measured T- and CPT-violating asymmetries are:
and
Also in this case the effect of the C-even background is negligible
and the CPT prediction 
is still valid.
Figure 6: The effect of the C-even background on 
. The full
line corresponds to r = 0 and the dashed one to 
.
Finally we discuss the effect of C-even background in 
decays, where the largest influence is expected.
The inclusion of the background contribution in eq. (49) gives:
Therefore, for 
the background is comparable to the signal,
enforcing the conclusion that the direct tag of the 
is
not useful to determine Br(
).
On the contrary, if the 
branching ratio is 
, in agreement with ChPT predictions
and preliminary CPLEAR results,
the background contribution to this decay
can be neglected and the corresponding branching ratio can be measured.
The modifications induced in interference measurements require a more
detailed study.
The analogue of the time difference distribution defined in eq. (8)
for an initial 
state is
where the last factor accounts for having both 
decays inside the detector.
Thus the C-even background, which is symmetric in 
momenta, modifies eqs. (51, 52) in the following way:
and
The contribution of the C-even background becomes important (especially in the
numerator) for large and negative values of the time difference,
where the number of events is absolutely negligible,
but, as can be seen from Fig. 6,
does not affect the results for
.
In the CP-conserving ratio 
the C-even background
contributes in the denominator only and can be safely neglected.
