To predict how good the tests could be at Da
ne , we consider an experiment
lasting one year with 30% efficiency, (i.e. effective duration 10
s.)
at the luminosity 
cm
s
. The integrated
luminosity is 10 000 pb
. In that time, 
neutral-kaon pairs are expected to be produced.
For both kaons decaying into 
,
using the kaon data of Ref. [7], we compute
We assume the background due to misidentified events in the 
sample
to be no more than what can be tolerated in a measurement
of 
, i.e. let us say 10
of the 
rate
into 
. To that we add the 
-background and yet another
contribution, equivalent to background, due to
the measurement error on the vertex positions of the two kaon decays.
The latter effect generates uncertainties 
and 
in the determinations of the proper times 
and 
, thus 
in z, and populates the region around z = 0. We will assume that
the sample of events can be limited to events where the vertex
uncertainty is 1 mm in average. Then the uncertainty in z
is 
.
Assuming that the contribution of these backgrounds is known within 10% and can be subtracted off with that 10% uncertainty, we find, in the case of no violation, that the systematic error is about equal to the statistical error, given by Eqs. (18) and (20).
It follows that this test would explore possible
values of 
as small as one or two 10
.
This value is better than the one
given in Ref. [6] in the context of neutron interferometry.
Even smaller values of 
can be detected if the vertex
accuracy can be improved.
A similar calculation can be made for the case where both kaons
decay into 
or both into 
. Predictions of the performance
at Da
ne are less reliable than for the 
--decays
because the background due to misidentified events
is more difficult to estimate
at this point in time. The 
background
contributes to 
for much less than
because of the
limited acceptance of the detector for 
-decays.
That background is totally negligible.
Assuming that, as for the 
--mode, the background is dominated by
the effect of the vertex position uncertainty, we get
for each of the two modes 
and 
.
This value of 
would permit exploring values
of 
and of 
comparable to the value
estimated for the 
--mode, i.e. a few 10
.
Of course, if a violation is found, questions will be raised
about the 
rule that was assumed to justify
the test with leptons in the final state.
However studies of correlations between regions of the
--Dalitz plot will permit us
to distinguish a violation of quantum mechanics
from a violation of the 
rule.
