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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