Table 5.1: Rates of 
decays [3]. The data
for 
is from ref.
[60].
We display in table 5.1 the number of events collected
so far.
The data are obviously dominated by the work of Rosselet et al.
[53], which measures the 
final state with
good statistics. The authors parametrize the form factors as
with 
and h assumed to be real
.
Furthermore, they put 
, such that
the form factors R and 
drop out in the decay distribution.
Despite the good statistics, the experiment has not been able to
separate out the full kinematic behaviour of the matrix
elements. Therefore certain approximations/assumptions had to
be made. For example, no dependence on 
was seen within the
limits of the data, so that the results were quoted assuming
that such a dependence is absent. Similarly, 
was found to
be compatible with zero, and hence put equal to zero when the
final result for g was derived. A dependence on 
was
seen, and found to be compatible with
with
These approximations to the form factors do not agree completely
with what is found in the theoretical predictions. Dependence on
and non-zero values for higher partial waves all occur in
the theoretical results.
The experimental results for the threshold values and the slopes of the form factors are [53]
We have used [3] 
in
transcribing these results. (We note that from Eqs. (5.34 - 5.37)
and 
we
obtain 
sec
. This value
must
be compared with 
sec
obtained in the same experiment.) In addition to the threshold
values (5.37) of the form factors, the phase shift difference
was determined [53] in
five energy bins. The S-wave scattering length 
was then
extracted by using a model of Basdevant, Froggatt and Petersen
[58]. This model is based on solutions to Roy
equations. The result for the scattering length is
A study by [59], based on a more recent solution to Roy equations, gives
Turning now to the 
channel, we
consider the following recent data (based on 
events) [60]:
The group also measured the G form factor. Defining
they find
The slope agrees within the errors with the value (5.37) found by Rosselet et al. [53]. To compare the value of the form factor at threshold, we use the isospin prediction
which is not incompatible with 
in eq. (5.37).
(Here
we have used
to transcribe the data. Furthermore, we assume that the form
factor 
measured in Ref. [60] indeed has to be divided by
for the comparison with [53]. This is not quite clear to
us reading [60].)
Finally for the channel 
, we consider the
rate [3]
The kinematic dependence of the form factors on
the variables 
and 
has not yet been resolved
experimentally in this decay. In order to proceed, we assume that the
form factors in this channel are independent of 
, e.g.,
etc.
As a result of this assumption, 
and 
vanish
by Bose statistics. The contribution from 
is completely
negligible in the electron mode, and the contribution from the anomaly form
factor to the decay (5.44) is tiny. We neglect it altogether,
as a result of which the above decay is fully determined by 
. We write
and obtain for the rate
This finally gives with
which compares very well with the isospin prediction
