Measurement of $CP$ violation in $B^0\to D^{\mp }{\pi }^{\pm }$ decays

A measurement of the $CP$ asymmetries $S_f$ and $S_{\overline{f}}$ in $B^0\to D^{\mp }{\pi }^{\pm }$ decays is reported. The decays are reconstructed in a dataset collected with the LHCb experiment in proton-proton collisions at centre-of-mass energies of 7 and 8 TeV and corresponding to an integrated luminosity of 3.0 fb${}^{-1}$. The $CP$ asymmetries are measured to be $S_f=0.058\pm 0.020\left(stat\right)\pm 0.011\left(syst\right)$ and $S_{\overline{f}}=0.038\pm 0.020\left(stat\right)\pm 0.007\left(syst\right)$. These results are in agreement with, and more precise than, previous determinations. They are used to constrain angles of the unitarity triangle, $|\sin (2\beta +\gamma )|$ and $\gamma$, to intervals that are consistent with the current world-average values.