Measurement of $CP$ violation in B⁰→D⁺D⁻ and B⁰ₛ→D⁺ₛD⁻ₛ decays

A time-dependent, flavour-tagged measurement of $CP$ violation is performed with B⁰→D⁺D⁻ and B⁰ₛ→D⁺ₛD⁻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 B⁰→D⁺D⁻ decays the $CP$-violation parameters are measured to be {align} S_{D⁺D⁻} & = -0.552 ± 0.100\,(stat) ± 0.010\,(syst), C_{D⁺D⁻} & = {-}0.128 ±0.103\,(stat) ± 0.010\,(syst). {align} In B⁰ₛ → D⁺ₛD⁻ₛ decays the $CP$-violating parameter formulation in terms of φₛ and |λ| results in {align} φₛ & = -0.086 ± 0.106 \,(stat) ± 0.028\,(syst) \,rad, |λ_{D⁺ₛD⁻ₛ}| & = {-}1.145 ± 0.126\,(stat) ± 0.031\,(syst). {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 B⁰→D⁺D⁻ decays with a significance exceeding six standard deviations.