Since both kaons and pions are spinless, all observables (and therefore
the information on the decay dynamics) are embodied in the Dalitz plot
distributions (10), i.e., in the decay rates and in the linear and
quadratic slopes for the different channels. From these, one has to separately
determine the coefficients of the amplitude expansions in
Eq. (15), in order to compare them with theoretical predictions.
In principle, in the CP conserving case, there are fifteen experimentally
measurable numbers from Dalitz plots (four for each of the modes
, 
and 
,
two for the mode 
and one for 
), from
which to determine the isospin amplitudes. In particular, once measured,
the branching ratio 
directly determines
the absolute value of the 
amplitude 
(up to
).
In Tabs. 4 and 5 (located for convenience in Sec. 5.1)
we report the results of the joint fit of 
and
isospin amplitudes to the available experimental data, performed
in Ref. [5],
updating the analysis of
Ref. [10].
Table 4: Determinations of 
isospin amplitudes, in units
.
Tab. 4 indicates the present level of accuracy on the amplitudes in
Eq. (15): in general, 
amplitudes are not so
well-determined, compared to the dominant 
ones. Specifically,
for stringent tests of the chiral Lagrangian description of 
, the
linear coefficient 
is not determined as accurately as one
would wish, and the knowledge of quadratic coefficients, representing
genuine predictions from the next-to-leading order in the chiral expansion,
is generally poor.