Measurement of $CP$ violation in $B^0\to D^{+}{D}^{-}$ and $B_s^0\to D_s^{+}{D}_s^{-}$ decays

A time-dependent, flavour-tagged measurement of $CP$ violation is performed with $B^0\to D^{+}{D}^{-}$ and $B_s^0\to D_s^{+}{D}_s^{-}$ decays, using data collected by the LHCb detector in proton-proton collisions at a centre-of-mass energy of 13 TeV corresponding to an integrated luminosity of 6 fb${}^{-1}$. In $B^0\to D^{+}{D}^{-}$ decays the $CP$-violation parameters are measured to be \begin{align} S_{D^{+}D^{-}} & = -0.552 \pm 0.100,$\text{(stat)}$ \pm 0.010,$\text{(syst)}$, \nonumber \newline C_{D^{+}D^{-}} & = \phantom{-}0.128 \pm0.103,$\text{(stat)}$ \pm 0.010,$\text{(syst)}$. \nonumber \end{align} In $B_s^0\to D_s^{+}{D}_s^{-}$ decays the $CP$-violating parameter formulation in terms of ${\phi }_s$ and $\mathrm{\mid }\lambda \mathrm{\mid }$ results in \begin{align} φ_{s} & = -0.086 \pm 0.106 ,$\text{(stat)}$ \pm 0.028,$\text{(syst)}$ ,$\text{rad}$, \nonumber \newline |λ_{D^{+}{s}D^{-}{s}}| & = \phantom{-}1.145 \pm 0.126,$\text{(stat)}$ \pm 0.031,$\text{(syst)}$. \nonumber \end{align} These results represent the most precise single measurement of the $CP$-violation parameters in their respective channels. For the first time in a single measurement, $CP$ symmetry is observed to be violated in $B^0\to D^{+}{D}^{-}$ decays with a significance exceeding six standard deviations.