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Exploiting $B$-meson decays for Standard Model tests and beyond requires aprecise understanding of the strong final-state interactions that can beprovided model-independently by means of dispersion theory. This formalismallows one to deduce the universal pion-pion final-state interactions from theaccurately known $\pi\pi$ phase shifts and, in the scalar sector, acoupled-channel treatment with the kaon-antikaon system. In this work ananalysis of the decays $\bar B_d^0 \to J/\psi \pi^+\pi^-$ and $\bar B_s^0 \toJ/\psi \pi^+\pi^-$ is presented. We find very good agreement with the data upto 1.05 GeV with a number of parameters reduced significantly compared to aphenomenological analysis. In addition, the phases of the amplitudes arecorrect by construction, a crucial feature when it comes to studies of $CP$violation in heavy-meson decays.

A model-independent analysis of final-state interactions in \bar B_{d/s}^0 --> J/psi pi pi