Measurement of $CP$ violation in $B^0 \!\rightarrow D^+ D^-$ decays

The $C\!P$ violation observables $S$ and $C$ in the decay channel $B^0 \!\rightarrow D^+ D^-$ are determined from a sample of proton-proton collisions at centre-of-mass energies of $7$ and $8$ TeV, collected by the LHCb experiment and corresponding to an integrated luminosity of $3~ {\text {fb}}^{-1}$. The observable $S$ describes $C\!P$ violation in the interference between mixing and the decay amplitude, and $C$ parametrizes direct $C\!P$ violation in the decay. The following values are obtained from a flavour-tagged, decay-time-dependent analysis: \begin{align*} S &= -0.54 \, ^{+0.17}_{-0.16} \, \text{(stat)} \pm 0.05 \, \text{(syst)}\,, \\ C &= \phantom{-}0.26 \, ^{+0.18}_{-0.17} \, \text{(stat)} \pm 0.02 \, \text{(syst)}\,. \end{align*} These values constrain higher-order Standard Model corrections to be small.