### Speaker

### Description

We discuss some applications of isospin symmetry in the

Cabibbo favoured $D\to\bar{K}\pi\pi$ decays. These processes are important for

precision testing of the Standard Model and for hadronic physics. Combining

isospin symmetry with a dispersive reconstruction theorem we derive a

representation in terms of one-variable functions which allows one to predict

all the $D\to\bar{K}\pi\pi$ amplitudes given inputs from one $D^+$ mode

and one $D^0$ mode. From this, using dispersion relations and unitarity, we

derive a set of Khuri-Treiman type integral equations which enable to take

three-body rescattering effects into account. These could be more significant

in D than in K or B decays. A first test of this approach is

presented using experimental results on the $D^+\to K_S\pi^0\pi^+$ and the

$D^0\to K_S\pi^-\pi^+$ modes.

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