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

Exploiting $B$-meson decays for Standard Model tests and beyond requires a precise understanding of the strong final-state interactions that can be provided model-independently by means of dispersion theory. This formalism allows one to deduce the universal pion-pion final-state interactions from the accurately known $\pi \pi$ phase shifts and, in the scalar sector, a coupled-channel treatment with the kaon-antikaon system. In this work an analysis of the decays ${\bar{B}}_d^0\to J\mathrm{/}\psi {\pi }^{+}{\pi }^{-}$ and $\bar B_s^0 \to J/\psi \pi^+\pi^-$ is presented. We find very good agreement with the data up to 1.05 GeV with a number of parameters reduced significantly compared to a phenomenological analysis. In addition, the phases of the amplitudes are correct by construction, a crucial feature when it comes to studies of $CP$ violation in heavy-meson decays.