Observation of $CP$ violation in $B^{0}\!\to{J\mskip-3mu/\mskip-2muψ}ρ(770)^0$ decays

The time-dependent $CP$ asymmetry in $B^{0}\!\to{J\mskip-3mu/\mskip-2muψ}ρ(770)^0$ decays is measured using proton-proton collision data corresponding to an integrated luminosity of $6\,\text{fb}^{-1}$, collected with the LHCb detector at a center-of-mass energy of $13\,\text{TeV}$ during the years 2015-2018. The $CP$-violation parameters for this process are determined to be $2β^{\rm eff}_{c\bar{c}d} = 0.710 \pm 0.084 \pm 0.028\,\text{rad}$ and $|λ| = 1.019 \pm 0.034 \pm 0.009$, where the first uncertainty is statistical and the second systematic. This constitutes the first observation of time-dependent $CP$ violation in $B$ meson decays to charmonium final states mediated by a $b\!\to{c\bar{c}d}$ transition. These results are consistent with, and two times more precise than, the previous LHCb measurement based on a data sample collected at 7 and $8\,\text{TeV}$ corresponding to an integrated luminosity of $3\,\text{fb}^{-1}$. Assuming approximate SU(3) flavor symmetry, these two measurements are combined to set the most stringent constraint on the enguin contribution, $Δφ_{s}$, to the $CP$-violating phase $φ_{s}$ in $B^{0}_{s}\!\to{J\mskip-3mu/\mskip-2muψ}φ(1020)$ decays, yielding $Δφ_{s} = 5.0 \pm 4.2\,\text{mrad}$.