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

A measurement of the $CP$ asymmetries $S_f$ and $S_{\bar{f}}$ 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 $3.0{\mathrm{f}\mathrm{b}}^{-1}$. The $CP$ asymmetries are measured to be $S_f=0.058\pm 0.020(\mathrm{s}\mathrm{t}\mathrm{a}\mathrm{t})\pm 0.011(\mathrm{s}\mathrm{y}\mathrm{s}\mathrm{t})$ and $S_{\bar{f}} = 0.038\pm 0.020 ($\text{stat}$)\pm 0.007 ($\text{syst}$)$. These results are in agreement with, and more precise than, previous determinations. They are used to constrain $\mathrm{\mid }\sin (2\beta +\gamma )\mathrm{\mid }$ and $\gamma$ to intervals that are consistent with the current world-average values.