Anatomy of B→DD¯\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ B\to D\overline{D} $$\end{document} decays

The decays Bd0 → Dd−Dd+ and Bs0 → Ds−Ds+ probe the CP-violating mixing phases ϕd and ϕs, respectively. The theoretical uncertainty of the corresponding determinations is limited by contributions from penguin topologies, which can be included with the help of the U-spin symmetry of the strong interaction. We analyse the currently available data for Bd,s0 → Dd,s−Dd,s+ decays and those with similar dynamics to constrain the involved non-perturbative parameters. Using further information from semileptonic Bd0 → Dd−ℓ + νℓ decays, we perform a test of the factorisation approximation and take non-factorisable SU(3)-breaking corrections into account. The branching ratios of the Bd0 → Dd−Dd+, Bs0 → Ds−Dd+ and Bs0 → Ds−Ds+, Bd0 → Dd−Ds+ decays show an interesting pattern which can be accommodated through significantly enhanced exchange and penguin annihilation topologies. This feature is also supported by data for the Bs0 → Dd−Dd+ channel. Moreover, there are indications of potentially enhanced penguin contributions in the Bd0 → Dd−Dd+ and Bs0 → Ds−Ds+ decays, which would make it mandatory to control these effects in the future measurements of ϕd and ϕs. We discuss scenarios for high-precision measurements in the era of Belle II and the LHCb upgrade.