Anatomy of $B\to D\bar{D}$ Decays

Abstract

The decays $B_d^0\to D_d^{-}{D}_d^{+}$ and $B_s^0\to D_s^{-}{D}_s^{+}$ probe the CP-violating mixing phases ${\varphi }_d$ and ${\varphi }_s$, 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 $B_{d,s}^0\to D_{d,s}^{-}{D}_{d,s}^{+}$ decays and those with similar dynamics to constrain the involved non-perturbative parameters. Using further information from semileptonic $B_d^0\to D_d^{-}{\ell }^{+}{\nu }_{\ell }$ decays, we perform a test of the factorisation approximation and take non-factorisable $SU(3)$-breaking corrections into account. The branching ratios of the $B_d^0\to D_d^{-}{D}_d^{+}$, $B_s^0\to D_s^{-}{D}_d^{+}$ and $B_s^0\to D_s^{-}{D}_s^{+}$, $B_d^0\to D_d^{-}{D}_s^{+}$ 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 $B_s^0\to D_d^{-}{D}_d^{+}$ channel. Moreover, there are indications of potentially enhanced penguin contributions in the $B_d^0\to D_d^{-}{D}_d^{+}$ and $B_s^0\to D_s^{-}{D}_s^{+}$ decays, which would make it mandatory to control these effects in the future measurements of ${\varphi }_d$ and ${\varphi }_s$. We discuss scenarios for high-precision measurements in the era of Belle II and the LHCb upgrade.

47 pages, 17 figures, matching published version

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Cited by in corpus (13)

• 50 Years of Quantum Chromodynamics
• Towards New Frontiers in the Exploration of Charmless Non-Leptonic $B$ Decays
• In Pursuit of New Physics with $B_d^0\to J/\psi K^0$ and $B_s^0\to J/\psi \varphi$ Decays at the High-Precision Frontier
• New Strategy to Explore CP Violation with $B_s^0\to K^{-}{K}^{+}$
• Measurement of $CP$ violation in $B^0\to D^{+}{D}^{-}$ decays
• Estimating $r_B^{D\pi }$ as an input to the determination of the CKM angle $\gamma$
• Observation of the $B_s^0\to D^{\ast \pm }{D}^{\mp }$ decay
• How to tame penguins: Advancing to high-precision measurements of ${\varphi }_d$ and ${\varphi }_s$
• Measurement of $CP$ violation in $B^0\to D^{\ast \pm }{D}^{\mp }$ decays
• Measurement of the $CP$ asymmetry in $B^{-}\to D_s^{-}{D}^0$ and $B^{-}\to D^{-}{D}^0$ decays
• Measurement of $CP$ violation in $B^0\to D^{+}{D}^{-}$ and $B_s^0\to D_s^{+}{D}_s^{-}$ decays
• Observation of the $B_s^0\to D^{\ast +}{D}^{\ast -}$ decay
• Prediction of the $CP$ asymmetry $C_{00}$ in $B^0\to D^0\overline{D^0}$ decay