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A
bstract
We perform a detailed study of the consequences of isospin symmetry in the Cabibbo favoured
D
→
K
¯
ππ
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
→
K
¯
ππ
amplitudes given inputs from one
D
+
mode and one
D
0
mode. From this, using dispersion relations and unitarity, we derive a set of 6+6 Khuri-Treiman type integral equations which enable to take three-body rescattering effects into account. A first test of this approach is presented using experimental results on the
D
+
→ K
S
π
0
π
+
and the
D
0
→ K
S
π
−
π
+
modes.