The numerical results given above
demonstrate very clearly that the non-trivial
CHPT effects of 
can be detected at DA
NE in all four channels
without any problem of statistics. Of course, the rates are bigger for
the electronic modes. On the other hand, the relative size of the
structure dependent terms is somewhat bigger in the muonic channels
(around 8% for the chosen cuts). We observe that there is negative
interference between the loop and counterterm amplitudes.
The sensitivity
to the counterterm coupling constants 
and to the
chiral anomaly can be expressed as the difference in the number of events
between the tree level and the 
amplitudes (without loops).
In the optimal case of 
, this amounts to more than
events/yr at DA
NE. Almost all of this difference is
due to 
. It will be very difficult to extract the coupling constant
from the total rates. A more detailed study is needed to
determine whether 
can be extracted from differential
distributions.
The chiral anomaly is more important for 
, but even there
it influences the total rates rather little. Once again, a dedicated
study of differential rates is necessary to locate the chiral anomaly,
if possible at all.
On the other hand, taking
into account that 
is already known to good accuracy (see
table 1 in Ref. [2]), 
decays will certainly allow for precise and unambiguous tests
of the one-loop effects in CHPT [11].