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We introduce parametrizations of hadronic three-body $B$ and $D$ weak decayamplitudes that can be readily implemented in experimental analyses and are asound alternative to the simplistic and widely used sum of Breit-Wigner typeamplitudes, also known as the isobar model. These parametrizations can beparticularly useful in the interpretation of CP asymmetries in the Dalitzplots. They are derived from previous calculations based on a quasi-two-bodyfactorization approach in which two-body hadronic final state interactions arefully taken into account in terms of unitary $S$- and $P$-wave $\pi\pi$, $\piK$ and $K \bar K$ form factors. These form factors can be determinedrigorously, fulfilling fundamental properties of quantum field-theoryamplitudes such as analyticity and unitarity, and are in agreement with thelow-energy behaviour predicted by effective theories of QCD. They are derivedfrom sets of coupled-channel equations using $T$-matrix elements constrained byexperimental meson-meson phase shifts and inelasticities, chiral symmetry andasymptotic QCD. We provide explicit amplitude expressions for the decays $B^\pm\to \pi^+ \pi^- \pi^\pm$, $B \to K \ \pi^+ \pi^-$, $B^\pm \to K^+ K^-K^\pm$,$D^+ \to \pi^- \pi^+ \pi^+ $, $D^+ \to K^- \pi^+ \ \pi^+ $, $D^0 \to K^0_S \\pi^+\ \pi^- $, for which we have shown in previous studies that this approachis phenomenologically successful, in addition, we provide expressions for the$D^0 \to K^0_S \ K^+ K^-$ decay. Other three-body hadronic channels can beparametrized likewise.

Parametrizations of three-body hadronic $B$- and $D$-decay amplitudes in terms of analytic and unitary meson-meson form factors