Theory overview on amplitude analyses with charm decays

International audienceThis contribution about amplitude analyses in multibody hadronic charm decays deals with some attempts to introduce theoretical constraints. Different effective hadronic formalism approaches are mentioned. A recent work, based on a basic weak interaction process and a Chiral unitary model to account for the final state interaction, is described in details for the $f_0(980)$ production in $D_s^+ \to \pi^+ \pi^+ \pi^-$ and $D_s^+ \to \pi^+ K^+ K^- $ decays. Within the framework of the diagrammatic approach and flavor symmetry, a global analysis of two-body $D$ decays into a vector meson and a pseudoscalar meson is presented. A quasi-two-body QCD factorization model for $D$ decays into three mesons and its recent application to $D^0 \to K_S^0 \pi^+ \pi^-$ is outlined. For processes with final-state pions and kaons and as an alternative to the sum of Breit-Wigner amplitudes, often used in experimental Dalitz-plot analyses, amplitude parametrizations, in term of unitary $\pi \pi$, $\pi K$ and $K \bar K$ form factors, are proposed. These parametrizations are derived from quasi-two-body factorization models