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

The $CP$ violation observables $S$ and $C$ in the decay channel $B^0 \!\rightarrow D^+ D^-$ are determined from a sample of proton-proton collisions at center-of-mass energies of 7 and 8 TeV, collected by the LHCb experiment and corresponding to an integrated luminosity of 3 fb$^{-1}$. The observable $S$ describes $CP$ violation in the interference between mixing and the decay amplitude, and $C$ parametrizes direct $CP$ violation in the decay. The following values are obtained from a flavor-tagged, decay-time-dependent analysis: \begin{align*} S &= -0.54 \, ^{+0.17}_{-0.16} \, \text{(stat)} \pm 0.05 \, \text{(syst)}\,,\newline C &= \phantom{-}0.26 \, ^{+0.18}_{-0.17} \, \text{(stat)} \pm 0.02 \, \text{(syst)}\,. \end{align*} These values provide evidence for $CP$ violation at a significance level of 4.0 standard deviations. The phase shift due to higher-order Standard Model corrections is constrained to a small value of \begin{align*} \Delta\phi = -0.16\,^{+0.19}_{-0.21}\,\text{rad}\,. \end{align*}