The {\em isobar model}, widely used for describing
heavy-meson decays into three pseudoscalars,
assumes that these processes are dominated by
spectator-resonance intermediate states, but also includes
non-resonant contributions.
% as a background.
It yields guess functions which include free phases, to be obtained by fitting data displayed in Dalitz plots.
% It yields guess functions including phases, masses and widths which
% are treated as free parameters, to be obtained by fitting data displayed in Dalitz plots.
However,
the question arises as to whether the parameters obtained in the case of a successful fit
have meanings which go beyond the reproduction of a particular set of experimental data.
In particular, can they be used to shed light into yet unknown two-body processes,
especially those concerning kaons?
% In particular, can they be used to shed light into yet unknown sectors of two-body processes?
Can they yield reliable information about scattering amplitudes?
As we argue in the sequence, the answers to these questions do not favour the isobar model.
This happens because, on general grounds,
{\em there is no simple connection between a heavy-meson decay amplitude $T$ and
two-body scattering amplitudes $A$, involving the same particles}.
Reasons read:
\\
{\bf a. dynamics - } The dynamical contents of $T$ and $A$ are rather different,
since the former includes weak vertices, which cannot be present in the latter.
Therefore, although scattering amplitudes $A$ can be substructures of $T$, there
is no reason whatsoever for assuming that these $A$'s are either identical or proportional to $T$.
This is supported by case studies, such as that regarding the process
$D^+ \rightarrow K^- \pi^+ \pi^+$,
which explained the difference between observed $S$-wave decay and scattering phases
by describing the weak sector of the problem in terms of meson loops\cite{BR}.
\\
%
{\bf b. isospin: - } Scattering amplitudes $A$ depend both on the {\em angular momentum} $J$ and on the
{\em isospin} $I$ of the channel considered, whereas just a $J$ dependence
can be extracted from an experimental decay amplitude $T$.
Thus, the latter is always, at best, a linear combination of different isospin states, of the form
$ T^{[J]} = H_1\, A_1^{[J,I_{1}]} + H_2\, A_2^{[J,I_{2}]} + \cdots $,
where the weights $H_k$ are energy dependent functions determined by the weak vertex.
It is impossible to derive directly $A^{[J,I]}$ from $T^{[J]}$
simply because the former contains more structure than the latter.
\\
%
{\bf c. non-resonant term - } The non-resonant term may involve proper
three-body interactions and also tends to blur scattering
information contained in the sub amplitudes $T^{[J]}$.
\\
%
{\bf d. unitarity - } Good fits to Dalitz plots data usually require several
resonances with the {\em same quantum numbers}.
The isobar model describes each of them by means of a line shape (Breit-Wigner),
but sums of line shapes violate unitarity, even in the case of scattering
amplitudes\cite{unit}.
\\
%
{\bf e. coupled channels - } The simple guess functions provided by the isobar model
do not incorporate properly the couplings of intermediate states.
For instance, $K \bar{K}$ intermediate states do contribute to elastic $\pi\pi$
scattering, as discussed by Hyams et al.\cite{Hyams} and
guess functions better suited for accommodating data should have structures similar
to eq.(11) of that paper.