As extensively discussed, for example in Refs. [3,19,20],
the study of the time difference distribution, for
, 
final states,
leads to the determination of both
and 
.
Introducing as usual the amplitudes
eq. (8), integrated over the pion phase space, gives:
If 
there is an asymmetry between the events
with positive and negative values of t:
neglecting in eq. (11) terms proportional to
,
the 
and 
coefficients, shown in Fig.1, are given by:
It can be seen that 
becomes nearly
independent of t, and equal to 3, for 
; on
the other hand 
is strongly dependent on t and
vanishes for 
.
Figure 1: Coefficients of 
(full line)
and 
(dashed line) defined in eq.(11).
Therefore a measurement of the asymptotic value
of 
or of the value of the integrated asymmetry
allows a clean determination of
. The statistical error on A
is
given by:
where N is the number of 
events.
At the reference DA
NE luminosity the statistical error on
is then:
The integrated asymmetry A allows a precise determination of
but gives no information on the imaginary part of
.
To overcome this problem a further method can be exploited to measure both
and 
from the
decay time difference:
the experimental distribution 
can be fitted by the theoretical distribution of
eq. (10), and 
and
can be used as free parameters of the fit.
It must be stressed that this procedure is very sensitive to the
experimental resolution on the measurement of d.
The information
contained in the shape of the
distribution can be easily washed out, in particular
in the region of interest for the determination of 
,
where 
. In fact only in this range of d
values 
is different from zero and the strongly varying
behaviour of 
can be smeared out by a bad vertex
reconstruction.
This effect is shown in Fig. 2, where the theoretical distribution is compared
with a simulated experimental distribution with a Gaussian error on the d
measurement equal to 5 mm.
Figure 2: Comparison between the theoretical F(d) distribution
for 
and that
obtained with an experimental vertex resolution 
.
The effects of the finite experimental resolution have been
discussed, for example in [20], to which we refer.
The results of the quoted analysis are that the determination of
is practically unaffected by the experimental resolution,
while the statistical error on 
increases by more
than a factor 2.
This analysis estimates that the accuracy achievable
for a realistic detector is:
These numbers have to be compared with the present experimental situation shown in the introduction.
