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 $ππ$ phase shifts and, in the scalar sector, a coupled-channel treatment with the kaon-antikaon system. In this work an analysis of the decays $\bar B_d^0 \to J/ψπ^+π^-$ and $\bar B_s^0 \to J/ψπ^+π^-$ 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.

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